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@STRING{ajsr = {Australian Journal of Soil Research}}
@STRING{ejss = {European Journal of Soil Science}}
@STRING{espl = {Earth Surface Processes and Landforms}}
@STRING{jgr = {Journal of Geophysical Research}}
@STRING{sssaj = {Soil Science Society of America Journal}}
@STRING{sssap = {Soil Science Society of America Proceedings}}
@STRING{tasae = {Transactions of the ASAE}}
@STRING{wrr = {Water Resources Research}}
@ARTICLE{Abbasi04,
author = {Abbasi, Fariborz and Feyen, Jan and van Genuchten, M.~Th.},
title = {Two-dimensional simulation of water flow and solute transport below
furrows: model calibration and validation},
journal = {Journal of Hydrology},
year = {2004},
volume = {290},
pages = {63 - 79},
number = {1-2},
doi = {DOI: 10.1016/j.jhydrol.2003.11.028},
file = {Abbasi04.pdf:Abbasi04.pdf:PDF},
issn = {0022-1694},
keywords = {Water flow},
owner = {olivier},
timestamp = {2009.07.21},
url = {http://www.sciencedirect.com/science/article/B6V6C-4BRSG4R-2/2/f88ad4f0d8d55db1a32362ff31a9a6e0}
}
@ARTICLE{Abbasi03,
author = {Abbasi, Fariborz and Simunek, Jirka and van Genuchten, M.~Th. and
Feyen, Jan and Adamsen, Floyd~J. and Hunsaker, Douglas~J. and Strelkoff,
Theodore~S. and Shouse, Peter},
title = {Overland {W}ater {F}low and {S}olute {T}ransport {M}odel {D}evelopment
and {F}ield-{D}ata {A}nalysis},
journal = {Journal of Irrigation and Drainage Engineering},
year = {2003},
volume = {129},
pages = {71-81},
number = {2},
month = apr,
abstract = {The application of plant nutrients with irrigation water is an efﬁcient
and cost-effective method for fertilizer application to enhance crop
production and reduce or eliminate potential environmental problems
related to conventional application methods. In this study, a combined
overland water ﬂow and solute transport model for analysis and management
of surface fertigation/chemigation is presented. Water ﬂow is predicted
with the well-known Saint-Venant’s equations using a control volume
of moving cells, while solute transport is modeled with the advection-dispersion
equation. The 1D transport equation was solved using a Crank-Nicholson
ﬁnite-difference scheme. Four, large-scale, ﬁeld experiments were
conducted on blocked-end and free draining furrows to calibrate and
verify the proposed model. The results showed that application of
solute during the entire irrigation event, or during the second half
of the irrigation for blocked end conditions with appropriate inﬂow
rates, produced higher solute uniformity than application of solute
during the ﬁrst half of the irrigation event. Measured fertilizer
distribution uniformity of the low quarter ranged from 21 to 76%
while fertilizer
distribution uniformity of the low half values varied between 62 to
87%. The model was subsequently applied to the experimental data;
results showed good agreement with all ﬁeld data. Water balance errors
for the different experiments varied from 0.004 to 1.8%, whereas
fertilizer mass balance errors ranged from 1.2 to 3.6%. A sensitivity
analysis was also performed to assess the effects of longitudinal
dispersivity parameter on overland solute concentrations. A value
of 10 cm for dispersivity provided a reasonable ﬁt to the experimental
data.},
doi = {10.1061/͑ASCE͒0733-9437͑2003͒129:2͑71͒},
file = {Abbasi03.pdf:Abbasi03.pdf:PDF},
keywords = {Overland ﬂow; Furrow irrigation; Dispersion; Fertilization; Data analysis},
owner = {olivier},
timestamp = {2010.01.29}
}
@PHDTHESIS{Abdallah05,
author = {Abdallah, Maher},
title = {Sur les m\'ethodes de discr\'etisation num\'erique de probl\`emes
hyperboliques non lin\'eaires appliqu\'ees aux \'equations de Barr\'e
de Saint-Venant pour la mod\'elisation de l'hydraulique en r\'eseau
d'assainissement},
school = {Universit\'e Louis Pasteur - Strasbourg I},
year = {2005},
abstract = {The dysfunctions of the sanitation networks and of the natural environments
such as river, particularly in rainy weather, are frequent in certain
agglomerations and can lead to serious problems for local communities.
Pollution of the receiving environment can sustain major damage for
the population, thus the improvement of the quality of the receiving
natural environments of urban pollution is a paramount need and passes
by a control of the flow of pollution discharged from overflows and
to control their hydraulic behavior. In this context, the research
unit of "urban hydraulic system" of the national school of waters
and environment of Strasbourg is interested in management the shallow
water and the solid transport in real time for the sanitation networks.
In order to be able to determine the hydraulic behavior of this type
of structure, it is necessary to take into account the hydraulic
discontinuities and the transitory flow regime when formulating equations
and creating the associated model. The objective of this thesis is
the knowledge and the control of the hydraulic parameters in shallow
water. Initially, we were interested in the one-dimensional numerical
simulation of the hydraulic parameters in channels not presenting
a junction. To this end, we considered the one dimensional shallow
water waves equations known by the Saint Venant equations for modeling
free surface flows. This system is a nonlinear and hyperbolic of
partial differential system, and consequently it does not admit an
analytical solution in the general case. There exist in the literature,
various schemes able to find numerical solutions to the Saint Venant
system in order to calculate the water height and the water discharge
of the flow. These schemes belong to different categories: three
types of space discretisation: finite differences, finite volumes,
finite elements; two types of temporal discretisation: explicit and
implicit; three types of numerical flux discretisation: classical,
Riemann and TVD. Our contribution in this part is summarized by the
following points:
Apply the Runge Kutta Discontinuous Galerkine Finite Elements which
are initially developed for the numerical simulation of the Euler
system and which models the flow of a non viscous compressible fluid.
Develop a numerical test bench with an aim of comparing the various
numerical schemes able to find a numerical solution of the Saint
Venant equations.
Choose the most robust schemes able to capture the shocks and discontinuities
in stationary and transitory flows.
Compare the different strategies of numerical discretisation of the
source term in order to quote the best. A new method is considered
in the case of a non prismatic channel.
We can note that all comparisons were made on various hydraulic problems
that have analytical solutions or experimental results with various
types: steady and transient flow, prismatic and non prismatic channels,
rectangular and trapezoidal section, dry and wet
channel bed, constant and variable bed slope.
In a second time, we were interested in the numerical simulation of
flow in networks containing junctions. To this end, we considered
the Saint Venant equations for modeling free surface flows in channels,
and various models of junction which have developed in the literature
and which simulate the flow through the junctions. Our contribution
in this part is summarized by the following points:
• Couple the numerical schemes developed in the first part with the
junction models in order to simulate the hydraulic parameters in
a network containing several channels and connected by junctions.
We point out that all these models were never be coupled and simulated
with the Saint Venant system.
Compare the various results obtained by the different junction models
and the experimental results found in the literature in the case
of steady and transient flow for two kinds of junction: combining
and dividing junction and for three types of flows: subcritical,
supercritical and transitional. We also point out that no comparison
was made previously in the transitory case.
•We show that the use of the simplest model of the junction “equality
of water stages” largely used in the classical hydraulic engineering
codes is worrying and should be replaced by a model based on momentum
conservation.},
file = {Abdallah05.pdf:Abdallah05.pdf:PDF},
owner = {olivier},
timestamp = {2009.07.22}
}
@INPROCEEDINGS{Abdolmaleki04,
author = {Abdolmaleki, K. and Thiagarajan, K.~P. and {Morris-Thomas}, M.~T.},
title = {Simulation of The Dam Break Problem and Impact Flows Using a {N}avier-{S}tokes
Solver},
booktitle = {Proceedings of the Fifteenth Australasian Fluid Mechanics Conference},
year = {2004},
editor = {M. Behnia and W. Lin and G. D. Mc{B}ain},
address = {The University of Sydney, Sydney, Australia},
month = dec # { 13-17},
publisher = {The University of Sydney},
abstract = {The impact flow on a vertical wall resulting from a dam break problem
is simulated using a Navier-Stokes (NS) solver. The NS solver uses
an Eulerian finite volume method (FVM) along with a volume of fluid
(VOF) scheme for phase interface capturing. The purpose of this study
is to assess the accuracy of the solver for problems in the category
of wave impacts. Previous experiments and other numerical solution
techniques are compared with the solver's results. Different aspects
of the flow such as free-surface elevation before and after the initial
impact have been studied in depth. The pressure peak due to water
impact on the vertical wall has also been analyzed. Water viscosity
and air compressibility effects have been assessed. The significance
of the time step and grid resolution are also discussed. Results
show favorable agreement with experiments before water impact on
the wall. However, both impact pressure and freesurface elevations
after the impact depart from the experiments significantly. Hence
the code is assessed to be good only for qualitative studies.},
file = {Abdolmaleki04.pdf:Abdolmaleki04.pdf:PDF},
keywords = {dam-break; model},
owner = {Fred. DARBOUX},
timestamp = {2008.07.24}
}
@ARTICLE{Aberle03,
author = {Aberle, J. and Smart, G.~M.},
title = {The influence of roughness structure on flow resistance on steep
slopes},
journal = {Journal of {H}ydraulic {R}esearch},
year = {2003},
volume = {41},
pages = {259-269},
abstract = {There is no standard ﬂow resistance equation for the determination
of mean ﬂow velocity in mountain streams. The reason lies in the
morphology of mountain streams, i.e. steep slopes, large roughness
elements, bed forms and water depths of the same order of magnitude
as the bed material size. Logarithmic, Froude and power-law approaches
to determine ﬂow resistance are discussed with respect to the roughness
parameter which is usually a characteristic grain size. As a result
of the irregular nature of gravel-bed proﬁles it is shown that the
structure of these stream beds cannot be described sufﬁciently by
a characteristic percentile of the grain size distribution. Statistical
properties of a series of bed proﬁles are investigated in order to
quantify the effect of roughness on ﬂow resistance. The standard
deviation of the bed elevations is introduced as characteristic roughness
length and its applicability is veriﬁed by the analysis of experimental
data. Based on this roughness parameter, an approach for the determination
of ﬂow resistance is derived which allows for spatial averaging of
the ﬂow ﬁeld. Conclusions concerning the inﬂuence of bed forms on
ﬂow resistance are drawn with the use of the concept of the “at-a-site”
hydraulic geometry.},
file = {Aberle03.pdf:Aberle03.pdf:PDF},
keywords = {Friction factor; steep slopes; hydraulic geometry; roughness},
owner = {olivier},
timestamp = {2010.01.29}
}
@ARTICLE{Abrahams94,
author = {Abrahams, A.D. and Parsons, A.J.},
title = {Hydraulics of interrill overland flow on stone-covered desert surfaces},
journal = {Catena},
year = {1994},
volume = {23},
pages = {111--140},
abstract = {The hydraulics of interrill overland flow on stone-covered desert
surfaces depend on the resistance to flow, which may be partitioned
into grain resistance, wave resistance, and rain resistance. Efforts
to model large-scale roughness in open channels suggest that resistance
to overland flow on such surfaces is a function of grain Reynolds
number, Froude number, flow depth, and the size, shape, spacing,
and pattern of the roughness elements. The effect of flow depth on
flow resistance f is often hidden in the flow Reynolds number Re.
In laboratory and field studies alike, f-Re relations have been found
to be convex-upward and negatively sloping, and these shapes have
been explained in terms of the progressive inundation of the roughness
elements. Where laboratory- or field-based models have been developed
for predicting f, they invariably contain percent stone cover. The
prominence of this variable reflects the strong influence of stone
size and spacing on flow resistance. A laboratory study shows that
where the Froude number F>0.5, wave resistance increases with stone
cover and dominates resistance to flow on all surfaces with stone
covers greater than 10%. A field study indicates that where F<0.5
and wave resistance is inconsequential, grain and form resistance
typically account for about 5% and 95% of f, respectively.
These findings have important implications for sediment transport
modeling because percent grain resistance is equal to percent grain
shear stress, and it has recently been suggested that in overland
flow, as in river flow, sediment transport capacity is determined
by grain shear stress rather than total shear stress. A laboratory
study, however, demonstrates that this is not the case. Sediment
transport capacity is in fact greater than predicted by grain shear
stress because energy dissipated in wakes of roughness elements in
overland flow is transformed into turbulence sufficiently close to
the bed to affect sediment transport.},
file = {Abrahams94.pdf:Abrahams94.pdf:PDF},
keywords = {Darcy-Weisbach; Reynolds; Froude; friction},
owner = {olivier},
timestamp = {2010.06.05}
}
@ARTICLE{Abrahams86,
author = {Abrahams, A.D. and Parsons, A.J. and Luk, S.-H.},
title = {Resistance to overland flow on desert hillslopes},
journal = {Journal of Hydrology},
year = {1986},
volume = {88},
pages = {343--363},
abstract = {This study examines the relation between the Darcy-Weisbach frictio
factor, f, and the Reynolds number, Re, for overland flow on six
runoff plots in semiarid southern Arizona. The surfaces of these
plots are irregular and covered withstones. As overland flow increases,
the stones and microtopographic protuberances, which constitue the
major roughness elements, are progressively inundated, thereby altering
the flow resistance. Analyses of 14 cross-sections reveal that the
resulting f-Re relations have two basic shapes: convex-upward and
negatively sloping. These shapes bear little resemblance to the conventional
f-Re relation for shallow flow over a plane bed, whose shape is a
function of the state flow. Rather, they are explained in terms of
the simultaneous operation of two processes. The first is the progressive
inundation of roughness elements and increase in their wetted upstream-projected
area as discharge increases. This process causes f to increase. The
second is the progressive increase in the depth of flow over already
inundated parts of the bed as discharge increases. This process causes
f to decline. Whether the f-Re relation has a positive or a negative
slope depends on whether the first or second process dominates, and
this depends on configuration of the bed and level discharge.
These findings have profound implications for the mathematical modeling
of overland flow on desert hillslopes. Whether a model is based on
the Saint-Venant equations or makes use of the kinematic-wave approximation,
it requires the specification of a relation between f and Re (or
suttogates thereof), and the computed hydrograph is very sensitive
to the form of this relation. Hitherto, the most widely used relation
has been the conventional one for shallow flow over a plane bed.
However, the present study suggests that this relation does not apply
to desert hillslopes. Additional field and laboratory studies are
needed to learn more of the behavior and controls of f-Re relations
on such hillslopes so that models of overland flow can employ more
realistic relations and better simulate runoff hydrographs.},
file = {Abrahams86.pdf:Abrahams86.pdf:PDF},
keywords = {friction; Darcy-Weisbach; Reynolds},
owner = {olivier},
timestamp = {2010.06.05}
}
@ARTICLE{Afzalimehr01,
author = {Afzalimehr, H. and Anctil, F.},
title = {Friction velocity associated to a non-uniform flow and an intermediate
scale roughness},
journal = {Journal of Hydraulic Research},
year = {2001},
volume = {39},
pages = {181--186},
number = {2},
abstract = {This work consists of an experimental study of the resistance associated
with non-uniform flows over cobble-bed channels, leading to an intermediate
scale roughness. Friction velocity is estimated for twelve cases
of accelerating and decelerating flows. Four estimation methods are
compared: Reynolds stress, logarithmic law, parabolic law and a global
approach. They are all in close agreement. The observed mean longitudinal
velocity profiles are consistent with observations reported in the
literature for non-uniform flows over gravel-bed channels with small
relative roughness. Accelerating flows produce smaller friction velocities
than decelerating flows, which is contrary to observations reported
in the literature.},
file = {Afzalimehr01.pdf:Afzalimehr01.pdf:PDF},
owner = {olivier},
timestamp = {2008.05.04}
}
@ARTICLE{Aizinger02,
author = {Aizinger, Vadym and Dawson, Clint},
title = {A discontinuous Galerkin method for two-dimensional flow and transport
in shallow water},
journal = {Advances in Water Resources},
year = {2002},
volume = {25},
pages = {67--84},
abstract = {A discontinuous Galerkin (DG) finite element method is described for
the two-dimensional, depth-integrated shallow water equations (SWEs).
This method is based on formulating the SWEs as a system of conservation
laws, or advection–diffusion equations. A weak formulation is obtained
by integrating the equations over a single element, and approximating
the unknowns by piecewise, possibly discontinuous, polynomials. Because
of its local nature, the DG method easily allows for varying the
polynomial order of approximation. It is also ‘‘locally conservative’’,
and incorporates upwinded numerical fluxes for modeling problems
with high flow gradients. Numerical results are presented for several
test cases, including supercritical flow, river inflow and standard
tidal flow in complex domains, and a contaminant transport scenario
where we have coupled the shallow water flow equations with a transport
equation for a chemical species.},
file = {Aizinger02.pdf:Aizinger02.pdf:PDF},
keywords = {shallow water equations; discontinuous Galerkin method; pollutant
transport},
owner = {olivier},
timestamp = {2010.11.24}
}
@ARTICLE{Akan02,
author = {Akan, A. Osman},
title = {Sizing {S}tormwater {I}nfiltration {S}tructures},
journal = {Journal of Hydraulic Engineering},
year = {2002},
volume = {128},
pages = {534--537},
number = {5},
month = May,
abstract = {A design aid is presented for sizing stormwater inﬁltration structures.
The proposed procedure is based on the hydrological storage equation
for an inﬁltration structure coupled with the Green and Ampt inﬁltration
equation. For the ﬁlling process, the two equations are solved simultaneously
using a numerical method, and the results are presented in chart
form. These charts are useful to determine the maximum water depth
in an inﬁltration structure. For the emptying process, the governing
equations are integrated analytically resulting in an algebraic equation
that can be solved for the emptying time explicitly. A practical
application is included to demonstrate the ease of the suggested
procedure.},
file = {Akan02.pdf:Akan02.pdf:PDF},
keywords = {Stormwater management; water infiltration; storm runoff},
owner = {olivier},
timestamp = {2010.04.26}
}
@ARTICLE{Akers08,
author = {Akers, Benjamin and Bokhove, Onno},
title = {Hydraulic flow through a channel contraction: Multiple steady states},
journal = {Physics of Fluids},
year = {2008},
volume = {20},
abstract = {We have investigated shallow water ﬂows through a channel with a contraction
by experimental and theoretical means. The horizontal channel consists
of a sluice gate and an upstream channel of constant width b0 ending
in a linear contraction of minimum width bc. Experimentally, we observe
upstream steady and moving bores/shocks, and oblique waves in the
contraction, as single and multiple ͑steady͒ states, as well as a
steady reservoir with a complex hydraulic jump in the contraction
occurring in a small section of the bc / b0 and Froude number parameter
plane. One-dimensional hydraulic theory provides a comprehensive
leading-order approximation, in which a turbulent frictional parametrization
is used to achieve quantitative agreement. An analytical and numerical
analysis is given for two-dimensional supercritical shallow water
ﬂows. It shows that the one-dimensional hydraulic analysis for inviscid
ﬂows away from hydraulic jumps holds surprisingly well, even though
the two-dimensional oblique hydraulic jump patterns can show large
variations across the contraction channel.},
doi = {10.1063/1.2909659},
file = {Akers08.pdf:Akers08.pdf:PDF},
keywords = {steady states; shock; contraction; shallow water},
owner = {olivier},
timestamp = {2010.06.18}
}
@ARTICLE{AlAzawi85,
author = {Al-Azawi, Saadi A.},
title = {Experimental evaluation of infiltration models},
journal = {Journal of Hydrology (NZ)},
year = {1985},
volume = {24},
pages = {77--88},
number = {2},
file = {AlAzawi85.pdf:AlAzawi85.pdf:PDF},
owner = {olivier},
timestamp = {2010.05.15}
}
@ARTICLE{Alastruey08,
author = {Alastruey, J. and Parker, K. H. and Peir\'o, J. and Sherwin, S. J.},
title = {Lumped Parameter Outflow Models for 1-D Blood Flow Simulations: Effect
on Pulse Waves and Parameter Estimation},
journal = {Commun. Comp. Phys.},
year = {2008},
volume = {4},
pages = {317--336},
abstract = {Abstract. Several lumped parameter, or zero-dimensional (0-D), models
of the micro-circulation are coupled in the time domain to the nonlinear,
one-dimensional (1-D) equations of blood ﬂow in large arteries. A
linear analysis of the coupled system, together with in vivo observations,
shows that: (i) an inﬂow resistance that matches the characteristic
impedance of the terminal arteries is required to avoid non-physiological
wave reﬂections; (ii) periodic mean pressures and ﬂow distributions
in large arteries depend on arterial and peripheral resistances,
but not on the compliances and inertias of the system, which only
affect instantaneous pressure and ﬂow waveforms; (iii) peripheral
inertias have a minor effect on pulse waveforms under normal conditions;
and (iv) the time constant of the diastolic pressure decay is the
same in any 1-D model artery, if viscous dissipation can be neglected
in these arteries, and it depends on all the peripheral compliances
and resistances of the system. Following this analysis, we propose
an algorithm to accurately estimate peripheral resistances and compliances
from in vivo data. This algorithm is veriﬁed against numerical data
simulated using a 1-D model network of the 55 largest human arteries,
in which the parameters of the peripheral windkessel outﬂow models
are known a priori. Pressure and ﬂow wave-forms in the aorta and
the ﬁrst generation of bifurcations are reproduced with relative
root-mean-square errors smaller than 3%.},
file = {Alastruey08.pdf:Alastruey08.pdf:PDF},
keywords = {blood flow; 1d; 0d},
owner = {olivier},
timestamp = {2011.03.10}
}
@ARTICLE{Alcrudo01,
author = {Alcrudo, Francisco and Benkhaldoun, Fayssal},
title = {Exact solutions to the Riemann problem of the shallow water equations
with a bottom step},
journal = {Computers \& Fluids},
year = {2001},
volume = {30},
pages = {643 - 671},
number = {6},
doi = {DOI: 10.1016/S0045-7930(01)00013-5},
file = {Alcrudo01.pdf:Alcrudo01.pdf:PDF},
issn = {0045-7930},
keywords = {Shallow water equations},
owner = {olivier},
timestamp = {2009.11.14},
url = {http://www.sciencedirect.com/science/article/B6V26-433PBY2-1/2/5d183c31b53859067d48126173ed929f}
}
@INPROCEEDINGS{Alcrudo99,
author = {Alcrudo, Francisco and Gil, Elena},
title = {The {M}alpasset dam break case study},
booktitle = {the $4^{th}$ {CADAM} {W}orkshop, Zaragoza},
year = {1999},
pages = {95-109},
month = Nov,
abstract = {According to the main aims and objectives of CADAM concerted action
and in continuation of the test program, the Malpasset dam break
study has been performed with the aid of SW2D program. Output generated
by the simulation software has been checked with the aid of field
data provided by EDF (France). This paper describes the simulation
process and analyses the quality of computed results with regards
to measured data in view of the usefulness of mathematical flood
simulation. It is found that the overall picture of the catastrophe
provided by the model is realistic and useful for risk assesment,
but a close up analysis reveals also errors in some areas. These
are not heavily dependent on grid resolution or commonly tunable
parameters such as the friction level, what rises the question of
the validity of the mathematical model itself. Further research is
needed in order to clarify the situations in which shallow water
flow models fail, how their predictions can be improved and at what
costs.},
file = {Alcrudo99.pdf:Alcrudo99.pdf:PDF},
owner = {olivier},
timestamp = {2010.02.17}
}
@PHDTHESIS{Aldrighetti07,
author = {Aldrighetti, Elisa},
title = {Computational hydraulic techniques for the Saint Venant equations
in arbitrarily shaped geometry},
school = {Universit\`a degli studi di Trento},
year = {2007},
abstract = {A numerical model for the one-dimensional simulation of non-stationary
free surface and pressurized ﬂows in open and closed channels with
arbitrary cross-section will be derived, discussed and applied. This
technique is an extension of the numerical model proposed by Casulli
and Zanolli for open channel ﬂows that uses a semi-implicit discretization
in time and a ﬁnite volume scheme for the discretization of the Continuity
Equation: these choices make the method computationally simple and
conservative of the ﬂuid volume both locally and globally. The present
work will ﬁrstly deal with the elaboration of a semi-implicit numerical
scheme for ﬂows in open channels with arbitrary cross-sections that
conserves both the volume and the momentum or the energy head of
the ﬂuid, in such a way that its numerical solutions present the
same characteristics as the physical solutions of the problem considered.
The semi-implicit discretization in time leads to a relatively simple
and computationally eﬃcient scheme whose stability can be shown to
be independent from the wave celerity √gH. The conservation properties
allow dealing properly with problems presenting discontinuities in
the solution, resulting for example from sharp bottom gradients and
hydraulic jumps. The conservation of mass is particularly important
when the channel has a non rectangular cross-section. The numerical
method will be therefore extended to the simulation of closed channel
ﬂows in case of free-surface, pressurized and transition ﬂows. The
accuracy of the proposed method will be controlled by the use of
appropriate ﬂux limiting functions in the discretization of the advective
terms, especially in the case of large gradients of the physical
quantities involved in the problem. In the particular case of closed
channel ﬂows, a new ﬂux limiter will be deﬁned in order to better
represent the transitions between free-surface and pressurized ﬂows.
The numerical solution, at every time step, will be determined by
solving a mildly non-linear system of equations that becomes linear
in the particular case that the channel has a rectangular cross-section.
Careful physical and mathematical considerations about the stability
of the method and the solvability of the system with respect to the
implemented boundary conditions will be also provided. The study
of the existence and uniqueness of the solution requires the solution
of a constrained problem, where the constraint expresses that the
feasible solutions are physically meaningful and present a non-negative
water depth. From this analysis, it will follow an explicit (dependent
only on known quantities) and suﬃcient condition for the time step
to ensure the non-negativity of the water volume. This condition
is valid in almost all the physical situations without more restrictive
assumptions than those necessary for a correct description of the
physical problem. Two suitable solution procedures, the Newton Method
and the conjugate gradient method, will be introduced, adapted and
studied for the mildly non linear system arising in the solution
of the numerical model. Several applications will be presented in
order to compare the numerical results with those available from
the literature or with analytical and experimental solutions. They
will illustrate the properties of the present method in terms of
stability, accuracy and eﬃciency.},
file = {Aldrighetti07.pdf:Aldrighetti07.pdf:PDF},
owner = {olivier},
timestamp = {2009.07.21}
}
@ARTICLE{Alhumaizi07,
author = {Alhumaizi, Khalid},
title = {Flux-limiting solution techniques for simulation of reaction-diffusion-convection
system},
journal = {Communications in Nonlinear Science and Numerical Simulation},
year = {2007},
volume = {12},
pages = {953-965},
abstract = {The aim of this work is to analyze the use of a number of ﬂux-limiters
to simulate numerically the behavior of a homogeneous tubular reactor
which exhibits steep moving fronts. The strength and limitations
of ﬁve diﬀerent ﬂux-limiters are examined for diﬀerent test cases.
All ﬂux-limiters are found successful in capturing the steep concentration
proﬁles. The simulations show that the minmod and MUSCL ﬂux-limiter
are more appropriate for the convection–diﬀusion case. On the other
hand, the superbee limiter shows the best performance in capturing
discontinuities in the convection–diﬀusion–reaction case.},
file = {Alhumaizi07.pdf:Alhumaizi07.pdf:PDF},
keywords = {Reaction–diﬀusion–convection; Moving fronts; Flux-limiter; Superbee;
Minmod; MUSCL},
owner = {olivier},
timestamp = {2009.07.27}
}
@ARTICLE{Aoda88,
author = {Aoda, M.I. and Nedawi, D.R. and Abdul-Rassul, I.A.},
title = {A comparison of the goodness of fit for three theoretically-derived
infiltration equations},
journal = {Journal of Agricultural Engineering Research},
year = {1988},
volume = {41},
pages = {173 - 180},
number = {3},
abstract = {Experimental measurements of the cumulative infiltration over time
were obtained using uniformly packed columns of porous materials
of different particle size ranges and distribution. The relationship
between cumulative infiltrated water and time was fitted by a non-linear
regression program to three infiltration equations, namely, that
of Green and Ampt, the three-term Philip equation and that of Knight,
all of which are theoretically derived. The fit was generally good
for all of the equations, with the Philip three-term equation being
the best, the Green and Ampt equation second and the Knight equation
third. The suction head at the wetting front was evaluated from the
Green and Ampt equation and seems to be related to the size and distribution
of the particles of the porous medium.},
doi = {DOI: 10.1016/0021-8634(88)90176-X},
file = {Aoda88.pdf:Aoda88.pdf:PDF},
issn = {0021-8634},
keywords = {Philip; Green-Ampt; Knight; infiltration},
owner = {olivier},
timestamp = {2010.06.06},
url = {http://www.sciencedirect.com/science/article/B6WH1-494T72Y-RK/2/6c6040a00ad54a074e087e7ac71cb51d}
}
@ARTICLE{Arico09,
author = {Aric\`o, Costanza and Nasello, Carmello and Tucciarelli, Tullio},
title = {Using unsteady-state water level data to estimate channel roughness
and discharge hydrograph},
journal = {Advances in water resources},
year = {2009},
volume = {32},
pages = {1223-1240},
abstract = {A novel methodology for simultaneous discharge and channel roughness
estimation is developed and applied to data sets available at three
experimental sites. The methodology is based on the synchronous measurement
of water level data in two river sections far some kilometers from
each other, as well as on the use of a diffusive ﬂow routing solver
and does not require any direct velocity measurement. The methodology
is ﬁrst analyzed for the simplest case of a channel with a large
slope, where the kinematic assumption holds. A sensitivity and a
model error analysis are carried out in this hypothesis in order
to show the stability of the results with respect to the error in
the input parameters in the case of homogeneous roughness and to
analyze the effect of unknown roughness heterogeneity on the estimated
discharges. The methodology is then extended to the more general
case of channels with mild slope and validated using ﬁeld data previously
collected in three Italian rivers: the Arno (in Tuscany), the Tiber
(in Latium) and the Vallo di Diana, a small tributary of the Tanagro
river (in Southern Italy). The performance of the proposed algorithm
has been investigated according to three performance criteria estimating
the quality of the match between the measured and the computed stage
and discharge hydrographs. Results of the ﬁeld tests can be considered
good, despite the uncertainties of the ﬁeld data and of the measured
values.},
file = {Arico09.pdf:Arico09.pdf:PDF},
keywords = {Flow meter; discharge estimation; flow routing; calibration; shallow
waters; diffusive model},
owner = {olivier},
timestamp = {2010.01.25}
}
@ARTICLE{Arioli06,
author = {Arioli, Mario and Manzini, Gianmarco},
title = {A network programming approach in solving Darcy's equations by mixed
finite-element methods},
journal = {Electronic Transactions on Numerical Analysis},
year = {2006},
volume = {22},
pages = {41--70},
abstract = {Abstract. We use the null space algorithm approach to solve the augmented
systems produced by the mixed ﬁnite-element approximation of Darcy’s
laws. Taking into account the properties of the graph representing
the triangulation, we adapt the null space technique proposed in
[5], where an iterative-direct hybrid method is described. In particular,
we use network programming techniques to identify the renumbering
of the triangles and the edges, which enables us to compute the null
space without ﬂoating-point operations. Moreover, we extensively
take advantage of the graph properties to build efﬁcient preconditioners
for the iterative algorithm. Finally, we present the results of several
numerical tests.},
file = {Arioli06.pdf:Arioli06.pdf:PDF},
keywords = {augmented systems; sparse matrices; mixed finite-element; graph theory;
Darcy},
owner = {olivier},
timestamp = {2010.06.13}
}
@ARTICLE{Arioli03,
author = {Arioli, Mario and Manzini, Gianmarco},
title = {Null space algorithm and spanning trees in solving Darcy's equation},
journal = {BIT Numerical MAthematics},
year = {2003},
volume = {43},
pages = {839--848},
abstract = {A Null Space algorithm is considered to solve the augmented system
produced by the mixed ﬁnite element approximation of Darcy’s Law.
The method is based on the combination of a LU factorization technique
for sparse matrices with an iterative Krylov solver. The computational
eﬃciency of the method relies on the use of spanning trees to compute
the LU factorization without ﬁll-in and on a suitable stopping criterion
for the iterative solver. We experimentally investigate its performance
on a realistic set of selected application problems.},
file = {Arioli03.pdf:Arioli03.pdf:PDF},
keywords = {augmented systems; sparse matrices; mixed finite elements; Darcy},
owner = {olivier},
timestamp = {2010.06.13}
}
@ARTICLE{Arioli02,
author = {Arioli, Mario and Manzini, Gianmarco},
title = {A null space algorithm for mixed finite-element approximations of
Darcy's equation},
journal = {Communications in Numerical Methods in Engineering},
year = {2002},
volume = {18},
pages = {645--657},
abstract = {A null space algorithm is considered to solve the augmented system
produced by the mixed finite element approximation of Darcy’s Law.
The method is based on the combination of an orthogonal factorization
technique for sparse matrices with an iterative Krylov solver. The
computational efficiency of the method relies on a suitable stopping
criterion for the iterative solver. We experimentally investigate
its performance on a realistic set of selected application problems.},
file = {Arioli02.pdf:Arioli02.pdf:PDF},
keywords = {augmented systems; sparse matrices; mixed finite elements; Darcy},
owner = {olivier},
timestamp = {2010.06.13}
}
@ARTICLE{Assouline07,
author = {Assouline, S. and Selker, J.~S. and Parlange, J.-Y.},
title = {A simple accurate method to predict time of ponding under variable
intensity rainfall},
journal = {Water Resources Research},
year = {2007},
volume = {43, W03426},
pages = {1--10},
abstract = {[1] The prediction of the time to ponding following commencement of
rainfall is fundamental to hydrologic prediction of flood, erosion,
and infiltration. Most of the studies to date have focused on prediction
of ponding resulting from simple rainfall patterns. This approach
was suitable to rainfall reported as average values over intervals
of up to a day but does not take advantage of knowledge of the complex
patterns of actual rainfall now commonly recorded electronically.
A straightforward approach to include the instantaneous rainfall
record in the prediction of ponding time and excess rainfall using
only the infiltration capacity curve is presented. This method is
tested against a numerical solution of the Richards equation on the
basis of an actual rainfall record. The predicted time to ponding
showed mean error 7% for a broad range of soils, with and without
surface sealing. In contrast, the standard predictions had average
errors of 87%, and worst-case errors exceeding a factor of 10. In
addition to errors intrinsic in the modeling framework itself, errors
that arise from averaging actual rainfall records over reporting
intervals were evaluated. Averaging actual rainfall records observed
in Israel over periods of as little as 5 min significantly reduced
predicted runoff (75% for the sealed sandy loam and 46% for the silty
clay loam), while hourly averaging gave complete lack of prediction
of ponding in some of the cases.},
file = {Assouline07.pdf:Assouline07.pdf:PDF},
owner = {olivier},
timestamp = {2010.04.23}
}
@TECHREPORT{Audusse04a,
author = {Audusse, E.},
title = {A multilayer {S}aint-{V}enant model},
institution = {INRIA},
year = {2004},
number = {5249},
month = jul,
abstract = {We introduce a new variant of the multilayer Saint-Venant system.
The classical Saint-Venant system is a well-known approximation of
the incompressible Navier-Stokes equations for shallow water flows
with free moving boundary. Its efficiency, robustness and low computational
cost make it very commonly used. Nevertheless its range of application
is limited and it does not allow to access to the vertical profile
of the horizontal velocity. Hence and thanks to a precise analysis
of the shallow water assumption we propose here a new approximation
of the Navier-Stokes equations which consists in a set of coupled
Saint-Venant systems, extends the range of validity and gives a precise
description of the vertical profile of the horizontal velocity while
preserving the computational efficiency of the classical Saint-Venant
system. We validate the model through some numerical examples.},
file = {Audusse04a.pdf:Audusse04a.pdf:PDF},
keywords = {Free surface Navier-Stokes equations; shallow water assumption; hydrostatic
approximation; Saint-Venant system; multilayer model; viscosity},
owner = {olivier},
timestamp = {2008.04.27}
}
@PHDTHESIS{Audusse04b,
author = {Audusse, E.},
title = {Mod{\'e}lisation hyperbolique et analyse num{\'e}rique pour les {\'e}coulements
en eaux peu profondes},
school = {Universit{\'e} Paris VI -- Pierre et Marie Curie},
year = {2004},
month = {14} # sep,
note = {196~pages},
abstract = {In this work we study some hyperbolic conservation laws related to
shallow water flows. First we consider the Saint-Venant system with
source terms and we develop a second order bidimensional well-balanced
finite volumes scheme that is based on a kinetic interpretation of
the system and on a hydrostatic reconstruction of the interfaces
values. The scheme is consistent and conservative and it preserves
the non-negativity of the water height. Then we extend the kinetic
interpretation to the coupling with a transport equation. We construct
a two time steps scheme that takes into account all the eigenvalues
of the problem. This approach preserves the stability properties
of the system and reduces the numerical diffusion and the computational
cost. We also present a new multilayer Saint-Venant system that allows
us to obtain non constant vertical velocity profiles while preserving
an invariant two dimensional domain of calculation. We present the
derivation of the system and we study its stability-energy, hyperbolicity.
We also investigate its relation with other fluid models and we perform
its numerical implementation. Finally we prove a uniqueness theorem
for scalar conservation laws with discontinuous flux. Our proof uses
a new family of entropies that are a natural way to adapt classical
Kruzkov's entropies to the discontinuous case. This new method avoids
the making of some classical hypothesis on the flux such as convexity,
BV bounds or finite number of discontinuities and does not need the
definition of some interface condition.},
file = {Audusse04b.pdf:Audusse04b.pdf:PDF},
keywords = {shallow water equations; source terms; multilayer model; transport
equation; scalar conservation law; discontinuous flux; finite volumes;
well-balanced scheme; kinetic interpretation; hydrostatic reconstruction;
Kruzkov's entropies},
owner = {olivier},
timestamp = {2008.04.27}
}
@MASTERSTHESIS{Audusse99,
author = {Audusse, E.},
title = {Sch\'emas cin\'etiques pour le syst\`eme de {S}aint-{V}enant},
school = {Universit{\'e} Paris 6},
year = {1999},
file = {Audusse99.pdf:Audusse99.pdf:PDF},
keywords = {Saint-Venant;volumes finis;sch{\'e}mas cin{\'e}tiques;termes sources;bathym{\'e}trie},
owner = {olivier},
timestamp = {2009.01.11}
}
@ARTICLE{Audusse04c,
author = {Audusse, E. and Bouchut, F. and Bristeau, M.-O. and Klein, R. and
Perthame, B.},
title = {A fast and stable well-balanced scheme with hydrostatic reconstruction
for shallow water flows},
journal = {SIAM J. Sci. Comput.},
year = {2004},
volume = {25},
pages = {2050--2065},
number = {6},
abstract = {We consider the Saint-Venant system for shallow water flows, with
nonflat bottom. It is a hyperbolic system of conservation laws that
approximately describes various geophysical flows, such as rivers,
coastal areas, and oceans when completed with a Coriolis term, or
granular flows when completed with friction. Numerical approximate
solutions to this system may be generated using conservative finite
volume methods, which are known to properly handle shocks and contact
discontinuities. However, in general these schemes are known to be
quite inaccurate for near steady states, as the structure of their
numerical truncation errors is generally not compatible with exact
physical steady state conditions. This difficulty can be overcome
by using the so-called well-balanced schemes. We describe a general
strategy, based on a local hydrostatic reconstruction, that allows
us to derive a well-balanced scheme from any given numerical flux
for the homogeneous problem. Whenever the initial solver satisfies
some classical stability properties, it yields a simple and fast
well-balanced scheme that preserves the nonnegativity of the water
height and satisfies a semidiscrete entropy inequality.},
doi = {10.1137/S1064827503431090},
file = {Audusse04c.pdf:Audusse04c.pdf:PDF},
keywords = {shallow water equations; finite volume schemes; well-balanced schemes},
owner = {olivier},
timestamp = {2008.05.03}
}
@ARTICLE{Audusse05,
author = {Audusse, Emmanuel and Bristeau, M.-O.},
title = {A well-balanced positivity preserving {"}second-order{"} scheme for
shallow water flows on unstructured meshes},
journal = {Journal of Computational Physics},
year = {2005},
volume = {206},
pages = {311--333},
abstract = {We consider the solution of the Saint-Venant equations with topographic
source terms on 2D unstructured meshes by a finite volume approach.
We first present a stable and positivity preserving homogeneous solver
issued from a kinetic representation of the hyperbolic conservation
laws system. This water depth positivity property is important when
dealing with wet-dry interfaces. Then, we introduce a local hydrostatic
reconstruction that preserves the positivity properties of the homogeneous
solver and leads to a well-balanced scheme satisfaying the steady-state
condition of still water. Finally, a formally second-order extension
based on limited reconstructed values on both sides of each interface
and on an enriched interpretation of the source terms satisfies the
same properties and gives a noticeable accuracy improvement. Numerical
examples on academic and real problems are presented.},
doi = {10.1016/j.jcp.2004.12.016},
file = {Audusse05.pdf:Audusse05.pdf:PDF},
keywords = {Saint-Venant system; shallow water flow; finite volume; Kinetic solver;
hydrostatic reconstruction; well-balanced scheme; positivity preserving
scheme; second-order extension},
owner = {olivier},
timestamp = {2008.04.27}
}
@ARTICLE{Audusse03,
author = {Audusse, Emmanuel and Bristeau, M.-O.},
title = {Transport of Pollutant in Shallow Water A Two Time Steps Kinetic
Method},
journal = {M2AN},
year = {2003},
volume = {37},
pages = {389-416},
number = {2},
month = mar,
abstract = {The aim of this paper is to present a ﬁnite volume kinetic method
to compute the transport of a passive pollutant by a ﬂow modeled
by the shallow water equations using a new time discretization that
allows large time steps for the pollutant computation. For the hydrodynamic
part the kinetic solver ensures – even in the case of a non ﬂat bottom
– the preservation of the steady state of a lake at rest, the non-negativity
of the water height and the existence of an entropy inequality. On
an other hand the transport computation ensures the conservation
of pollutant mass, a non-negativity property and a maximum principle
for the concentration of pollutant and the preservation of discrete
steady states associated with the lake at rest equilibrium. The interest
of the developed method is to preserve these theoretical properties
with a scheme that allows to disconnect the hydrodynamic time step
– related to a classical CFL condition – and the transport one –
related to a new CFL condition – and further the hydrodynamic calculation
and the transport one. The CPU time is very reduced and we can easily
solve diﬀerent transport problems with the same hydrodynamic solution
without large storage. Moreover the numerical results exhibit a better
accuracy than with a classical method especially when using 1D or
2D regular grids.},
doi = {10.1051/m2an:2003034},
file = {Audusse03.pdf:Audusse03.pdf:PDF},
owner = {olivier},
timestamp = {2009.07.27},
url = {\url{http://dx.doi.org/10.1051/m2an:2003034}}
}
@TECHREPORT{Audusse00,
author = {Audusse, E. and Bristeau, M.-O. and Perthame, B.},
title = {Kinetic schemes for {S}aint-{V}enant equations with source terms
on unstructured grids},
institution = {INRIA},
year = {2000},
number = {3989},
month = jul,
abstract = {We consider the Saint-Venant (or Shallow Water) system which is an
usual model to describe the flows in rivers or coastal areas. This
hyperbolic system of conservation laws is solved on unstructured
meshes by a kinetic scheme based on a finite volume approach. An
important property of this scheme is the preservation of the water
height positivity when applications with dry areas are considered.
Following some hypothesis an entropy inequality is proved. The standard
kinetic scheme is modified to deal with varying bed slope and particularly
to preserve aquilibrium states such as still water. Moreover the
source terms due to arbitrary bottom topography have to be discretized
in such a way to balance the flux gradients for these equilibriums.
We illustrate the properties of the scheme on different test cases
for which exact solutions are available and on more realistic applications.},
file = {Audusse00.pdf:Audusse00.pdf:PDF},
keywords = {Saint-Venant system; shallow water system; unstructured grid; finite
volume method; kinetic schemes; source terms; equilibrium scheme},
owner = {olivier},
timestamp = {2008.04.27}
}
@PHDTHESIS{Augeard06,
author = {Augeard, B.},
title = {M{\'e}canisme de gen{\`e}se du ruissellement sur sol agricole drain{\'e}
sensible {\`a} la battance. Etudes exp{\'e}rimentales et mod{\'e}lisation},
school = {ENGREF},
year = {2006},
abstract = {This study aims at describing and organizing into a hierarchy the
processes leading to surface runoff on artificially subsurface drained
area, by considering not only the perched water table fluctuations,
but also the possible soil surface sealing. Three complementary research
issues have been developed. First, the evolution of the tilled layer
structure during rainfall in the presence of a shallow water table
was observed using laboratory rainfall simulation. Bulk density profiles
measured by X-ray radiography show that the increase of bulk density
due to sealing and slumping are more significant in the wettest conditions.
The proposed bulk density evolution model correctly reproduces this
effect. Second, seal hydraulic properties were determined from a
model based on bulk density profiles using other simulated rainfall
experiments. The estimation of model parameters by inverse method
led to an accurate simulation of the measured flows and water pressures,
and conformed to the measured bulk density profiles. Hydraulic conductivity
greatly decreases at the soil surface due to sealing process. The
third issue was based on a drained field investigation in M�larchez
watershed (Seine et Marne) associated to flow modelling (Hydrus 2D).
Data recorded in winter 2003-2004 show that drainage limits surface
runoff amount. Saturation excess runoff is the most frequent observed
process, even if soil sealing, especially due to saturation excess
surface runoff, increases runoff amount. Other rainfall conditions
were tested using Hydrus 2D. The condition of water table reaching
soil surface was particularly analysed in terms of infiltration-runoff
flows and return time of the corresponding rainfalls.},
file = {Augeard06.pdf:Augeard06.pdf:PDF},
owner = {olivier},
timestamp = {2008.05.04}
}
@TECHREPORT{Augeard08b,
author = {Augeard, B{\'e}n{\'e}dicte and Chaumont, C{\'e}dric and N{\'e}delec,
Yves},
title = {Mesure de ruissellement sur deux directions {\`a} petite {\'e}chelle
sur une parcelle agricole de {G}oins (bassin de l'{O}rgeval)},
institution = {UR HBAN, Cemagref Antony},
year = {2008},
type = {Projet ANR M{\'e}thode - Exp{\'e}rimentations terrain 2007-2008},
note = {11 pages},
file = {Augeard08b.pdf:Augeard08b.pdf:PDF},
keywords = {ANR METHODE, overland flow, field experiment, furrow, tillage, plot},
owner = {olivier},
timestamp = {2008.10.07}
}
@ARTICLE{Bai09,
author = {Bai, Lu-hai and Jin, Sheng},
title = {A Conservative Coupled Flow/Transport Model with Zero Mass Error},
journal = {Journal of Hydrodynamics, Ser. B},
year = {2009},
volume = {21},
pages = {166 - 175},
number = {2},
doi = {DOI: 10.1016/S1001-6058(08)60134-1},
file = {Bai09.pdf:Bai09.pdf:PDF},
issn = {1001-6058},
keywords = {transport model},
owner = {olivier},
timestamp = {2009.07.21},
url = {http://www.sciencedirect.com/science/article/B8CX5-4W7KD3R-4/2/bba20d0ac071517b317e962edcd35446}
}
@TECHREPORT{Bajaj06,
author = {Bajaj, Rajit L. and Xu, Guoliang and Zhang, Qin},
title = {Smooth {S}urface {C}onstructions via a {H}igher-{O}rder {L}evel-{S}et
{M}ethod},
institution = {ICES Report 06-18, Institute for Computational and Engineering Sciences,
The University of Texas at Austin},
year = {2006},
file = {Bajaj06.pdf:Bajaj06.pdf:PDF},
owner = {olivier},
timestamp = {2010.03.15}
}
@ARTICLE{Bakhtyar10,
author = {Bakhtyar, R. and Barry, D.A. and Yeganeh-Bakhtiary, A. and Li, L.
and Parlange, J.-Y. and Sander, G.C.},
title = {Numerical simulation of two-phase flow for sediment transport in
the inner-surf and swash zones},
journal = {Advances in Water Resources},
year = {2010},
volume = {33},
pages = {277 - 290},
number = {3},
abstract = {A two-dimensional two-phase flow framework for fluid-sediment flow
simulation in the surf and swash zones was described. Propagation,
breaking, uprush and backwash of waves on sloping beaches were studied
numerically with an emphasis on fluid hydrodynamics and sediment
transport characteristics. The model includes interactive fluid-solid
forces and intergranular stresses in the moving sediment layer. In
the Euler-Euler approach adopted, two phases were defined using the
Navier-Stokes equations with interphase coupling for momentum conservation.
The k-[epsilon] closure model and volume of fluid approach were used
to describe the turbulence and tracking of the free surface, respectively.
Numerical simulations explored incident wave conditions, specifically
spilling and plunging breakers, on both dissipative and intermediate
beaches. It was found that the spatial variation of sediment concentration
in the swash zone is asymmetric, while the temporal behavior is characterized
by maximum sediment concentrations at the start and end of the swash
cycle. The numerical results also indicated that the maximum turbulent
kinetic energy and sediment flux occurs near the wave-breaking point.
These predictions are in general agreement with previous observations,
while the model describes the fluid and sediment phase characteristics
in much more detail than existing measurements. With direct quantifications
of velocity, turbulent kinetic energy, sediment concentration and
flux, the model provides a useful approach to improve mechanistic
understanding of hydrodynamic and sediment transport in the nearshore
zone.},
doi = {DOI: 10.1016/j.advwatres.2009.12.004},
file = {Bakhtyar10.pdf:Bakhtyar10.pdf:PDF},
issn = {0309-1708},
keywords = {Continuous phase; Euler-Euler coupling; Fluid-solid interaction; Momentum
exchange; Nearshore zone; Particle-particle interaction; Wave breaking},
owner = {olivier},
timestamp = {2010.06.04},
url = {http://www.sciencedirect.com/science/article/B6VCF-4Y051JJ-1/2/ecd218c37027bc1cd4362d4da7d8b862}
}
@PHDTHESIS{Balayn01,
author = {Balayn, P.},
title = {Contribution {\`a} la mod{\'e}lisation num{\'e}rique de l'{\'e}volution
morphologique des cours d'eau am{\'e}nag{\'e}s lors de crues},
school = {Universit{\'e} Claude Bernard--Lyon 1},
year = {2001},
month = jul,
file = {Balayn01.pdf:Balayn01.pdf:PDF},
owner = {olivier},
timestamp = {2008.05.07}
}
@ARTICLE{Balzano98,
author = {Balzano, Andrea},
title = {Evaluation of methods for numerical simulation of wetting and drying
in shallow water flow models},
journal = {Coastal Engineering},
year = {1998},
volume = {34},
pages = {83-107},
file = {Balzano98.pdf:Balzano98.pdf:PDF},
keywords = {Shallow water equations; Tidal currents; Tidal flats; Wetting and
drying; Eulerian–Lagrangean models},
owner = {olivier},
timestamp = {2009.07.22}
}
@ARTICLE{Barrenechea02,
author = {Barrenechea, G.~R. and Le Tallec, P. and Valentin, F.},
title = {New wall laws for the unsteady incompressible Navier-Stokes equations
on rough domains},
journal = {Mathematical Modelling and Numerical Analysis},
year = {2002},
volume = {36},
pages = {177--203},
number = {2},
abstract = {Different effective boundary conditions or wall laws for unsteady
incompressible Navier-Stokes equations over rough domains are derived
in the laminar setting. First and second order unsteady wall laws
are proposed using two scale asymptotic expansion techniques. The
roughness elements are supposed to be periodic and the influence
of rough boundary is incorporated through constitutive constants.
These constants are obtained by solving steady Stokes problems and
so they are calculated only once. Numerical tests are presented to
validate and compare the proposed boundary conditions.},
file = {Barrenechea02.pdf:Barrenechea02.pdf:PDF},
owner = {olivier},
timestamp = {2008.04.30}
}
@ARTICLE{Barry00,
author = {Barry, D. A. and Parlange, J. -Y. and Hogarth, W. L. and Govindaraju,
R. S. and Parlange, M. B. and Lockington, D. and Li, L.},
title = {Comment on } # Modeling # transient # stream/aquifer # interaction
# with # the # non-linear # Boussinesq # equation # and # its # analytical
# solution # { by Serrano, S.E., Workman, S.R., 1998. Journal of
Hydrology 206, 245-255},
journal = {Journal of Hydrology},
year = {2000},
volume = {235},
pages = {289 - 292},
number = {3-4},
doi = {DOI: 10.1016/S0022-1694(00)00246-8},
file = {Barry00.pdf:Barry00.pdf:PDF},
issn = {0022-1694},
owner = {olivier},
timestamp = {2010.06.04},
url = {http://www.sciencedirect.com/science/article/B6V6C-4123C64-9/2/e63a415e57eda68c0a93acf51bccd998}
}
@ARTICLE{Barry07,
author = {Barry, D.A. and Lockington, D.A. and Jeng, D.-S. and Parlange, J.-Y.
and Li, L. and Stagnitti, F.},
title = {Analytical approximations for flow in compressible, saturated, one-dimensional
porous media},
journal = {Advances in Water Resources},
year = {2007},
volume = {30},
pages = {927 - 936},
number = {4},
abstract = {A nonlinear model for single-phase fluid flow in slightly compressible
porous media is presented and solved approximately. The model assumes
state equations for density, porosity, viscosity and permeability
that are exponential functions of the fluid (either gas or liquid)
pressure. The governing equation is transformed into a nonlinear
diffusion equation. It is solved for a semi-infinite domain for either
constant pressure or constant flux boundary conditions at the surface.
The solutions obtained, although approximate, are extremely accurate
as demonstrated by comparisons with numerical results. Predictions
for the surface pressure resulting from a constant flux into a porous
medium are compared with published experimental data.},
doi = {DOI: 10.1016/j.advwatres.2006.08.003},
file = {Barry07.pdf:Barry07.pdf:PDF},
issn = {0309-1708},
keywords = {Nonlinear diffusion; constant flow rate hydraulic conductivity test;
permeability measurement; effect of pressure on permeability; effect
of pressure on porosity},
owner = {olivier},
timestamp = {2010.06.04},
url = {http://www.sciencedirect.com/science/article/B6VCF-4M3BGV6-2/2/a751186be7feab14d51b2aca66732f91}
}
@ARTICLE{Barry05,
author = {D.A. Barry and J.-Y. Parlange and L. Li and D.-S. Jeng and M. Crapper},
title = {Green-Ampt approximations},
journal = {Advances in Water Resources},
year = {2005},
volume = {28},
pages = {1003 - 1009},
number = {10},
note = {Flow Processes in Hydrology: Contributions of J.-Y. Parlange},
abstract = {The solution to the Green and Ampt infiltration equation is expressible
in terms of the Lambert W-1 function. Approximations for Green and
Ampt infiltration are thus derivable from approximations for the
W-1 function and vice versa. An infinite family of asymptotic expansions
to W-1 is presented. Although these expansions do not converge near
the branch point of the W function (corresponds to Green-Ampt infiltration
with immediate ponding), a method is presented for approximating
W-1 that is exact at the branch point and asymptotically, with interpolation
between these limits. Some existing and several new simple and compact
yet robust approximations applicable to Green-Ampt infiltration and
flux are presented, the most accurate of which has a maximum relative
error of 5 × 10-5%. This error is orders of magnitude lower than
any existing analytical approximations.},
doi = {DOI: 10.1016/j.advwatres.2005.03.010},
file = {Barry05.pdf:Barry05.pdf:PDF},
issn = {0309-1708},
keywords = {Lambert W-1 function approximations; asymptotic expansions; branch
point; iteration scheme; Green-Ampt},
owner = {olivier},
timestamp = {2010.06.04},
url = {http://www.sciencedirect.com/science/article/B6VCF-4G4N0GR-2/2/03d464d73ad9d57a6587ab3b80a94e5f}
}
@ARTICLE{Barry93,
author = {Barry, D.A. and Parlange, J.-Y. and Sander, G.C. and Sivaplan, M.},
title = {A class of exact solutions for Richards' equation},
journal = {Journal of Hydrology},
year = {1993},
volume = {142},
pages = {29 - 46},
number = {1-4},
abstract = {A new solution satisfying Richards' equation is derived. The solution,
which may be applied for infiltration or capillary rise, is valid
for the condition of an arbitrary moisture tension imposed at the
soil surface. When written in terms of the moisture tension, the
new result is very simple, being derived in terms of a similarity
variable. The solution applies when the form of the soil moisture
characteristic curve is a particular weighted integral of the gradient
of the unsaturated hydraulic conductivity. Thus, if the soil moisture
characteristic curve is selected a priori, then this condition determines
the hydraulic conductivity. The converse of this statement also applies.
The cumulative infiltration derived from the solution is of the form
of the Green-Ampt infiltration equation; however, there is no need
to assume a steep wetting front as Green and Ampt did. Finally, using
the correspondence between Richards' equation and the convection-dispersion
equation with a non-linear solute adsorption isotherm, a new exact
solution for adsorptive solute transport is derived.},
doi = {DOI: 10.1016/0022-1694(93)90003-R},
file = {Barry93.pdf:Barry93.pdf:PDF},
issn = {0022-1694},
keywords = {Richards; exact solution},
owner = {olivier},
timestamp = {2010.06.04},
url = {http://www.sciencedirect.com/science/article/B6V6C-48C7CVP-1G/2/521a257296766c5d012f85cb39eac8a8}
}
@ARTICLE{Barry09,
author = {Barry, D.A. and Wissmeier, L. and Parlange, J.-Y. and Sander, G.C.
and Lockington, D.A.},
title = {Comment on } # An # analytic # solution # of # capillary # rise #
restrained # by # gravity # { by N. Fries and M. Dreyer},
journal = {Journal of Colloid and Interface Science},
year = {2009},
volume = {338},
pages = {293 - 295},
number = {1},
abstract = {The porous medium model of Green and Ampt, describing flow in porous
media, appeared earlier than the capillary model of Washburn, although
both lead to mathematically identical models. Here, the model of
Green and Ampt was related to the Washburn model by an examination
of the parameters involved in each. Fries et al. [N. Fries, M. Dreyer,
J. Colloid Interface Sci. 320 (2008) 259-263] presented an explicit
solution to this model. This solution is identical to the explicit
solution of the Green and Ampt model presented earlier by Barry et
al. [D.A. Barry, J.-Y. Parlange, G.C. Sander, M. Sivaplan, J. Hydrol.
142 (1993) 29-46].},
doi = {DOI: 10.1016/j.jcis.2009.06.015},
file = {Barry09.pdf:Barry09.pdf:PDF},
issn = {0021-9797},
keywords = {Green and Ampt; capillary rise; porous media; Lambert W fiunction;
analytical solution},
owner = {olivier},
timestamp = {2010.06.04},
url = {http://www.sciencedirect.com/science/article/B6WHR-4WGVPT7-2/2/a2ff9be82c90706da13ab022d392f63c}
}
@ARTICLE{Bathurst02,
author = {Bathurst, J.~C.},
title = {At-a-site variation and minimum flow resistance for mountain rivers},
journal = {Journal of Hydrology},
year = {2002},
volume = {269},
pages = {11-26},
number = {1-2},
month = dec,
abstract = {Existing flow resistance relationships for mountain rivers maybe in
error by typically 30%. In part this is because flow resistance is
a complex phenomenon, not easy to quantify with the available data.
However, a further reason is the reliance of past analyses on fitting
relationships to data from multiple sites, hence emphasizing an averaging
between-site variation. A more scientific approach is to derive separate
at-a-site relationships and investigate how they can be collapsed
into a single formula. Twenty-seven carefully selected field datasets
from seven literature sources are therefore analysed empirically
to show at-a-site variations in resistance, with the aim of improving
the accuracy and applicability of mountain river flow resistance
relationships. Considering only the bed grain roughness, the principal
factors likely to determine flow resistance are identified as relative
submergence d/D-84 (where d is depth and D-84 is the bed material
84-percentile size), bed material size, distribution and channel
slope. The dependency of the resistance function (8/f)(1/2) (where
f is the Darcy-Weisbach resistance coefficient) on d/D84 is more
accurately described by a power law than by a semi-logarithmic law,
especially at high flows. From observations of coincident at-a-site
datasets, two equations are derived, distinguished largely according
to channel slope S. For S < 0.8%, (8/f)(1/2) = 3.84(d/D-84)(0.547)
(r(2) = 0.986). For S > 0.8% (8/f)(1/2) = 3.10(d/D-84)(0.93) (r(2)
= 0.959). These equations appear to define minimum values for flow
resistance, probably for ideal conditions of bed grain roughness
and uniform flow. Deviations from this ideal (because of form roughness,
nonuniform flow or bank effects) will increase resistance in a manner
which is not yet quantified. The equations therefore have a very
specific applicability and are not generally applicable to all flows.
The cause of the slope dependency remains unclear, nor is any dependency
on bed material size distribution identified. Nevertheless the high
correlation coefficients suggest an improved accuracy compared with
other field-based relationships. The equations are derived for in-bank
flows with d/D-84 < 11 and slopes in the range 0.2-4%.},
doi = {10.1016/S0022-1694(02)00191-9},
file = {Bathurst02.pdf:Bathurst02.pdf:PDF},
keywords = {bed material size distribution; boulder-bed channels; channel slope;
field data; flow resistance; mountain rivers; GRAVEL-BED RIVERS;
HIGH-GRADIENT STREAMS; VELOCITY; CHANNELS; HYDRAULICS; ROUGHNESS;
DISCHARGE},
owner = {olivier},
timestamp = {2008.10.07}
}
@INPROCEEDINGS{Baumbach06,
author = {Baumbach, K. and Luk\'acov\'a-Medvid'ov\'a, M.},
title = {On the {C}omparison of {E}volution {G}alerkin and {D}iscontinuous
{G}alerkin {S}chemes},
booktitle = {Proceedings of {I}nternational {W}orkshop on {C}omputational {S}cience
and its {E}ducation, Beijing 2005},
year = {2006},
month = Jun,
file = {Baumbach06.pdf:Baumbach06.pdf:PDF},
owner = {olivier},
timestamp = {2010.02.07}
}
@ARTICLE{Bause04,
author = {Bause, M. and Knabner, P.},
title = {Computation of variably saturated subsurface flow by adaptive mixed
hybrid finite element methods},
journal = {Advances in Water Resources},
year = {2004},
volume = {27},
pages = {565--581},
number = {6},
abstract = {We present adaptive mixed hybrid finite element discretizations of
the Richards equation, a nonlinear parabolic partial differential
equation modeling the flow of water into a variably saturated porous
medium. The approach simultaneously constructs approximations of
the flux and the pressure head in Raviart-Thomas spaces. The resulting
nonlinear systems of equations are solved by a Newton method. For
the linear problems of the Newton iteration a multigrid algorithm
is used. We consider two different kinds of error indicators for
space adaptive grid refinement: superconvergence and residual based
indicators. They can be calculated easily by means of the available
finite element approximations. This seems attractive for computations
since no additional (sub-)problems have to be solved. Computational
experiments conducted for realistic water table recharge problems
illustrate the effectiveness and robustness of the approach.},
doi = {DOI: 10.1016/j.advwatres.2004.03.005},
file = {Bause04.pdf:Bause04.pdf:PDF},
issn = {0309-1708},
keywords = {Saturated-unsaturated flow; Nonlinear elliptic-parabolic problem;
Mixed finite element method; Raviart-Thomas spaces; A posteriori
error indicator; Richards},
owner = {olivier},
timestamp = {2010.06.15},
url = {http://www.sciencedirect.com/science/article/B6VCF-4CB665F-2/2/5480a0ec36b4921a39c3abd2c0cd07c5}
}
@ARTICLE{Beaugendre06,
author = {Beaugendre, H. and Ern, A. and Esclaffer, T. and Gaume, E. and Ginzburg,
I. and Kao, C.},
title = {A seepage face model for the interaction of shallow water tables
with the ground surface: Application of the obstacle-type method},
journal = {Journal of Hydrology},
year = {2006},
volume = {329},
pages = {258--273},
abstract = {Summary This paper presents a model to simulate overland ﬂow genesis
induced by shallow water table movements in hillslopes. Variably
saturated subsurface ﬂows are governed by the Richards equation discretized
by continuous ﬁnite elements on unstructured meshes. An obstacle-type
formulation is used to determine where saturation conditions, and
thus seepage face conditions, are met at the ground surface. The
impact of hillslope geometry, boundary conditions, and soil hydraulic
parameters on model predictions is investigated on two-dimensional
test cases at the metric and hectometric scales. The obstacle-type
formulation is also compared with a more detailed model coupling
subsurface and overland ﬂow, the latter being described by the shallow
water equations in the diffusive wave regime.},
file = {Beaugendre06.pdf:Beaugendre06.pdf:PDF},
keywords = {finite elements; Richards equation; seepage face; obstacle-type model;
water table ground; interaction; numerical solutions; diffusive wave;
Manning-Strickler},
owner = {olivier},
timestamp = {2010.06.09}
}
@MASTERSTHESIS{Becque08,
author = {Becque, S.},
title = {Etude exp\'erimentale et num\'erique de l'influence d'une rugosit\'e
orient\'ee sur le ruissellement},
school = {Ecole Polytechnique Universitaire Pierre et Marie Curie},
year = {2008},
address = {Cemagref d'Antony},
month = aug,
note = {Encadrants~: Yves N\'ed\'elec, B\'en\'edicte Augeard, Fr\'ed\'eric
Darboux},
abstract = {The objective of my six months training course at the Cemagref of
Antony was to carry out a
laboratory experimentation of dripping flow on drill, and then to
construct a mathematical model
to describe this kind of flow. Results of this experimentation will
be used by the model makers of
the project METHODE.
Because of very small flow depth, the traditional measuring methods
of flow velocity and flow
depth can not be used. We carried out experimental protocols to measure
these variables with
good precision. We used an instantaneous-profile laser to measure
flow depth. The instantaneous
profile laser usually measured soil surface elevation. In this work;
it was used to measure the
depth of a mix flow of water and paint. Flow velocity was measured
with two conductimetry
sensors set along the flow and salt solution drops dribbling upstream.
A one dimensional flow experiment was carried out in a rectangular
gutter and a polystyrene
drilled surface was used for the two dimensional flow one.
The mathematical one dimensional model developed in this work is based
on the Manning-
Strickler and the Darcy-Weisbach laws. It was applied to simulate
flow in the gutter and in one
drill of the drilled surface. The model simulations were compared
with data of the experiments.},
file = {Becque08.pdf:Becque08.pdf:PDF},
owner = {olivier},
timestamp = {2008.10.01}
}
@ARTICLE{Beecham05,
author = {Beecham, S. and Khiadani, M.~H. and Kandasamy, J.},
title = {Friction factors for spatially varied flow with increasing discharge},
journal = {Journal of Hydraulic Engineering},
year = {2005},
volume = {131},
pages = {792--799},
abstract = {This paper describes an experimental investigation of how friction
factors change for spatially varied flow in sloping channels receiving
lateral inflow. The results are compared with those of Beij in 1934,
and it is concluded that uniform flow resistance coefficients are
not always appropriate for spatially varied flow. Moreover, the common
technique of assuming a constant friction factor over the entire
length of the channel has been found to have little theoretical justification.
The method of Keulegan in 1952 for calculating friction factors in
spatially varied flow gives a better estimate, but does not explicitly
take account of the lateral inflow rate or velocity. Beij's 1934
experimental data, which was used by Keulegan does not show a systematic
variation of friction factor with lateral inflow rate for a constant
Reynolds number although this may be due to the low flowrates used.
The results of the present study indicate that the friction factor
increases with lateral inflow rate for a constant Reynolds number
in the experiments that included subcritical and supercritical flow
conditions. A method for calculating friction factors which allows
for lateral inflow is presented as a precursor to the development
of a general method of evaluating friction factors for spatially
varied flow with increasing discharge.},
doi = {10.1061/(ASCE)0733-9429(2005)131:9(792)},
file = {Beecham05.pdf:Beecham05.pdf:PDF},
keywords = {friction factor; water discharge; channel flow; slopes; flow resistance},
owner = {olivier},
timestamp = {2008.05.04}
}
@ARTICLE{Begnudelli07,
author = {Begnudelli, L. and Sanders, Brett~F.},
title = {Conservative Wetting and Drying Methodology for Quadrilateral Grid
Finite-Volume Models},
journal = {Journal of hydraulic engineering},
year = {2007},
pages = {312-322},
abstract = {Algebraic equations relating ﬂuid volume and the free surface elevation
in partially wetted quadrilateral computational cells are derived
and incorporated into a Godunov-type, ﬁnite-volume, shallow-water
model. These equations make it straightforward to reconstruct the
free surface elevation based on the volume of ﬂuid in a computational
cell, the dependent variable tracked by ﬁnite volume models for conservation
purposes, regardless of whether the cell is fully or partially wetted.
Improvements to the variable reconstruction process streamline the
computation of mass and momentum ﬂuxes with approximate Riemann solvers,
yielding a model that simulates sub-, super-, and transcritical ﬂows
over irregular topography with wetting and drying fronts. Furthermore,
the model is free from ﬂuid and scalar mass conservation errors and
it eliminates nonphysical distributions of scalars by avoiding artiﬁcial
concentration and/or dilution at wet/dry interfaces. Use of this
wetting and drying methodology adds roughly 10% to the execution
time of ﬂow simulations.},
doi = {10.1061/},
file = {Begnudelli07.pdf:Begnudelli07.pdf:PDF},
keywords = {Dewatering; Grid systems; Simulation; Methodology},
owner = {olivier},
timestamp = {2009.07.27}
}
@ARTICLE{Belardinelli92,
author = {Belardinelli, E. and Cavalcanti, S.},
title = {Theoretical analysis of pressure pulse propagation in arterial vessels},
journal = {J. Biomechanics},
year = {1992},
volume = {25},
pages = {1337--1349},
number = {11},
abstract = {An original mathematical model of viscous fluid motion in a tapered
and distensible tube is presented. The model equations are deduced
by assuming a two-dimensional flow and taking into account the nonlinear
terms in the fluid motion equations, as well as the nonlinear deformation
of the tube wall. One distinctive feature of the model is the formal
integration with respect to the radial coordinate of the Navier-Stokes
equations by power series expansion. The consequent computational
frame allows an easy accurate evaluation of the effects produced
by changing the values of all physical and geometrical tube parameters.
The model is employed to study the propagation along an arterial
vessel of a pressure pulse produced by a single flow pulse applied
at the proximal vessel extremity. In particular, the effects of the
effects of the natural taper angle of the arterial wall on pulse
propagation are investigated. The simulation results show that tapering
considerably influences wave attenuation but not wave velocity. The
substantially different behavior of pulse propagation depending upon
whether it travels towards the distal extremity or in the opposite
direction is observed: natural tapering causes a continuous increase
in the pulse amplitude as it moves towards the distal extremity:
on the contrary the reflected pulse running in the opposite direction
is greatly damped. For a vessel with physical and geometrical properties
similar to those of a canine femoral artery and 0.1 taper angle the
forward amplification is about 0.9m-1 and the backward attenuation
is 1.4m-1 so that the overall tapering effect gives a remarkably
damped pressure response. For a natural taper angle of 0.14 the perturbation
is almost extinct when the pulse wave returns to the proximal extremity.},
file = {Belardinelli92.pdf:Belardinelli92.pdf:PDF},
keywords = {blood flow; artery; vessel},
owner = {olivier},
timestamp = {2010.11.26}
}
@ARTICLE{Bell89,
author = {Bell, N.~C. and Wheater, H.~S. and Johnston, P.~M.},
title = {Evaluation of overland flow models using laboratory catchment data.
II: Parameter identification of physically based (kinematic wave)
models},
journal = {Hydrological sciences journal},
year = {1989},
volume = {34},
pages = {289-317},
number = {3},
abstract = {Using the Imperial College laboratory catchment facility data from
96 experiments on a slightly-roughened varnished strip catchment
(1 m x 9.925 m) are used to investigate the performance of numerical
models of overland flow based on the kinematic wave approximation.
A simple four-parameter model incorporates the Darcy-Weisbach laminar
flow and Manning turbulent flow friction relationships, with different
values of the friction parameter permitted under "rain" and "no-rain"
flow states. The optimization strategy combines grid-search and gradient-search
algorithms. Model fits are good by conventional standards and the
effect of raindrop impact on effective roughness is clearly identified.
However, the Manning relationship is not valid in the zone of transition
to rough turbulent flow and some
physical inconsistencies in optimal parameter values are apparent.
Incorporation of a Colebrook-White friction relationship gives similar
goodness of fit, but identified parameters conform more closely to
expectation from hydraulic theory.},
file = {Bell89.pdf:Bell89.pdf:PDF},
keywords = {Drainage basins ; Runoff ; Numerical models},
owner = {olivier},
timestamp = {2009.07.19}
}
@ARTICLE{Benkhaldoun07,
author = {Benkhaldoun, Fayssal and Elmahi, Imad and Sea\¨id, Mohammed},
title = {Well-balanced finite volume schemes for pollutant transport by shallow
water equations on unstructured meshes},
journal = {Journal of Computational Physics},
year = {2007},
volume = {226},
pages = {180-203},
abstract = {Pollutant transport by shallow water ﬂows on non-ﬂat topography is
presented and numerically solved using a ﬁnite volume scheme. The
method uses unstructured meshes, incorporates upwinded numerical
ﬂuxes and slope limiters to provide sharp resolution of steep bathymetric
gradients that may form in the approximate solution. The scheme is
non-oscillatory and possesses conservation property that conserves
the pollutant mass during the transport process. Numerical results
are presented for three test examples which demonstrate the accuracy
and robustness of the scheme and its applicability in predicting
pollutant transport by shallow water ﬂows. In this paper, we also
apply the developed scheme for a pollutant transport event in the
Strait of Gibraltar. The scheme is eﬃcient, robust and may be used
for practical pollutant transport phenomena.},
file = {Benkhaldoun07.pdf:Benkhaldoun07.pdf:PDF},
keywords = {Shallow water equations; Pollutant transport; Finite volume method;
Unstructured grids; Strait of Gibraltar},
owner = {olivier},
timestamp = {2010.01.25}
}
@ARTICLE{Benkhaldoun09,
author = {Benkhaldoun, Fayssal and Sahmim, Slah and Sea\¨id, Mohammed},
title = {A two-dimensional finite volume morphodynamic model on unstructured
triangular grids},
journal = {International Journal for Numerical Methods in Fluids},
year = {2009},
abstract = {We discuss the application of a ﬁnite volume method to morphodynamic
models on unstructured triangular meshes. The model is based on coupling
the shallow water equations for the hydrodynamics with a sediment
transport equation for the morphodynamics. The ﬁnite volume method
is formulated for the quasi-steady approach and the coupled approach.
In the ﬁrst approach, the steady hydrodynamic state is calculated
ﬁrst and the corresponding water velocity is used in the sediment
transport equation to be solved subsequently. The second approach
solves the coupled hydrodynamics and sediment transport system within
the same time step. The gradient ﬂuxes are discretized using a modiﬁed
Roe’s scheme incorporating the sign of the Jacobian matrix in the
morphodynamic system. A well-balanced discretization is used for
the treatment of source terms. We also describe an adaptive procedure
in the ﬁnite volume method by monitoring the bed–load in the computational
domain during its transport process. The method uses unstructured
meshes, incorporates upwinded numerical ﬂuxes and slope limiters
to provide sharp resolution of steep bed gradients that may form
in the approximate solution. Numerical results are shown for a test
problem in the evolution of an initially hump-shaped bed in a squared
channel. For the considered morphodynamical regimes, the obtained
results point out that the coupled approach performs better than
the quasi-steady approach only when the bed–load rapidly interacts
with the hydrodynamics.},
doi = {10.1002/fld.2129},
file = {Benkhaldoun09.pdf:Benkhaldoun09.pdf:PDF},
keywords = {morphodynamic model; shallow water flow; finite volume scheme; well-balanced
discretization; unstructured mesh; adaptive method; erosion},
owner = {olivier},
timestamp = {2010.11.12}
}
@ARTICLE{Benkhaldoun10a,
author = {Benkhaldoun, Fayssal and Sea\¨id, Mohammed},
title = {A simple finite volume method for the shallow water equations},
journal = {Journal of Computational and Applied Mathematics},
year = {2010},
volume = {234},
pages = {58--72},
abstract = {We present a new finite volume method for the numerical solution of
shallow water equations for either flat or non-flat topography. The
method is simple, accurate and avoids the solution of Riemann problems
during the time integration process. The proposed approach consists
of a predictor stage and a corrector stage. The predictor stage uses
the method of characteristics to reconstruct the numerical fluxes,
whereas the corrector stage recovers the conservation equations.
The proposed finite volume method is well balanced, conservative,
non-oscillatory and suitable for shallow water equations for which
Riemann problems are difficult to solve. The proposed finite volume
method is verified against several benchmark tests and shows good
agreement with analytical solutions.},
doi = {10.1016/j.cam.2009.12.005},
file = {Benkhaldoun10a.pdf:Benkhaldoun10a.pdf:PDF},
keywords = {Shallow water equations; Finite volume scheme; Method of characteristics;
Dam-break problems},
owner = {olivier},
timestamp = {2010.10.29}
}
@ARTICLE{Bennethum97,
author = {Bennethum, L. Schreyer and Murad, M. A. and Cushman, J. H.},
title = {Modified Darcy's Law, Terzaghi's Effective Stress Principle and Fick's
Law for Swelling Clay Soils},
journal = {Computers and Geotechnics},
year = {1997},
volume = {20},
pages = {245--266},
number = {3/4},
abstract = {Governing equations often used in soil mechanics and hydrology include
the classical Darcy’s law, Terzaghi’s effective stress principle,
and the classical Fick’s first law. It is known that the classical
forms of these relations apply only to non-swelling, granular materials.
In this paper, we summarize recent generalizations of these results
for swelling porous media obtained using hybrid mixture theory (HMT)
by the authors. HMT is a methodical procedure for obtaining macroscopic
constitutive restrictions which are thermodynamically admissible
by exploiting the entropy inequality for spatially-averaged properties.
HMT applied to the modeling of swlelling clay particles, viewed as
clusters of adsorbed water and clay minerals, produces additional
terms necessary to account for the physico-chemical forces between
the adsorbed water and clay minerals or, more generally, for swelling
colloids. New directions for modeling consolidation of swelling clays
are proposed based on our view of clay particles as a two-phase system.},
file = {Bennethum97.pdf:Bennethum97.pdf:PDF},
keywords = {Darcy; Terzaghi; Fick},
owner = {olivier},
timestamp = {2010.06.13}
}
@ARTICLE{Bermudez98,
author = {Berm\'udez, Alfredo and Dervieux, Alain and Desideri, Jean-Antoine
and V\'azquez, M. Elena},
title = {Upwind schemes for the two-dimensional shallow water equations with
variable depth using unstructured meshes},
journal = {Computer Methods in Applied Mechanics and Engineering},
year = {1998},
volume = {155},
pages = {49 - 72},
number = {1-2},
abstract = {In this paper, certain well-known upwind schemes for hyperbolic equations
are extended to solve the two-dimensional Saint-Venant (or shallow
water) equations. We consider unstructured meshes and a new type
of finite volume to obtain a suitable treatment of the boundary conditions.
The source term involving the gradient of the depth is upwinded in
a similar way as the flux terms. The resulting schemes are compared
in terms of a conservation property. For the time discretization
we consider both explicit and implicit schemes. Finally, we present
the numerical results for tidal flows in the Pontevedra ria, Galicia,
Spain.},
doi = {DOI: 10.1016/S0045-7825(97)85625-3},
file = {Bermudez98.pdf:Bermudez98.pdf:PDF},
issn = {0045-7825},
keywords = {C-property; shallow water; upwind; conservation property},
owner = {olivier},
timestamp = {2010.06.06},
url = {http://www.sciencedirect.com/science/article/B6V29-3WN739F-4/2/3120ee07ea5c43b3318fbfb6c05d2dde}
}
@ARTICLE{Bermudez94,
author = {Bermudez, Alfredo and Vazquez, M. Elena},
title = {Upwind methods for hyperbolic conservation laws with source terms},
journal = {Computers \& Fluids},
year = {1994},
volume = {23},
pages = {1049 - 1071},
number = {8},
abstract = {This paper deals with the extension of some upwind schemes to hyperbolic
systems of conservation laws with source term. More precisely we
give methods to get natural upwind discretizations of the source
term when the flux is approximated by using flux-difference or flux-splitting
techniques. In particular, the Q-schemes of Roe and van Leer and
the flux-splitting techniques of Steger-Warming and Vijayasundaram
are considered. Numerical results for a scalar advection equation
with nonlinear source and for the one-dimensional shallow water equations
are presented. In the last case we compare the different schemes
proposed in terms of a conservation property. When this property
does not hold, spurious numerical waves can appear which is the case
for the centred discretization of the source term.},
doi = {DOI: 10.1016/0045-7930(94)90004-3},
file = {Bermudez94.pdf:Bermudez94.pdf:PDF},
issn = {0045-7930},
keywords = {conservation property; shallow water; C-property; analytical solution},
owner = {olivier},
timestamp = {2010.06.06},
url = {http://www.sciencedirect.com/science/article/B6V26-47YMXJT-16/2/4485b4adb616198b768daff172258660}
}
@ARTICLE{Bernetti08,
author = {Bernetti, R. and Titarev, V.~A. and Toro, E.~F.},
title = {Exact solution of the Riemann problem for the shallow water equations
with discontinuous bottom geometry},
journal = {Journal of Computational Physics},
year = {2008},
volume = {227},
pages = {3212 - 3243},
number = {6},
abstract = {In this paper we present the exact solution of the Riemann problem
for the non-linear shallow water equations with a step-like bottom.
The solution has been obtained by solving an enlarged system that
includes an additional equation for the bottom geometry and then
using the principles of conservation of mass and momentum across
the step. The resulting solution is unique and satisfies the principle
of dissipation of energy across the shock wave. We provide examples
of possible wave patterns. Numerical solution of a first-order dissipative
scheme as well as an implementation of our Riemann solver in the
second-order upwind method are compared with the proposed exact Riemann
problem solution. A practical implementation of the proposed exact
Riemann solver in the framework of a second-order upwind TVD method
is also illustrated.},
doi = {DOI: 10.1016/j.jcp.2007.11.033},
file = {Bernetti08.pdf:Bernetti08.pdf:PDF},
issn = {0021-9991},
keywords = {Shallow water equations},
owner = {olivier},
timestamp = {2009.11.14},
url = {http://www.sciencedirect.com/science/article/B6WHY-4R9GH15-4/2/54f93d9795106c5b9a1135580d32bf77}
}
@ARTICLE{Berthon05,
author = {Berthon, Christophe},
title = {Stability of the MUSCL schemes for the Euler equations},
journal = {Comm. Math. Sci.},
year = {2005},
volume = {3},
pages = {133-157},
number = {2},
abstract = {The second-order Van-Leer MUSCL schemes are actually one of the most
popular high order schemes for ﬂuid dynamic computations. In the
frame work of the Euler equations, we introduce a new slope limitation
procedure to enforce the scheme to preserve the invariant region:
namely the positiveness of both density and pressure as soon as the
associated ﬁrst order scheme does it. In addition, we obtain a second-order
minimum principle on the speciﬁc entropy and second-order entropy
inequalities. This new limitation is developed in the general framework
of the MUSCL schemes and the choice of the numerical ﬂux functions
remains free. The proposed slope limitation can be applied to any
change of variables and we do not impose the use of conservative
variables in the piecewise linear reconstruction. Several examples
are given in the framework of the primitive variables. Numerical
1D and 2D results are performed using several ﬁnite volume methods.},
file = {Berthon05.pdf:Berthon05.pdf:PDF},
keywords = {Euler equations; MUSCL schemes; invariant regions; minimum principle
on the speciﬁc entropy; entropy inequalities},
owner = {olivier},
timestamp = {2009.07.27}
}
@ARTICLE{Berthon07,
author = {Berthon, Christophe and Coquel, Fr\'ed\'eric},
title = {Nonlinear projection methods for multi-entropies Navier-Stokes systems},
journal = {Mathematics of Computation},
year = {2007},
volume = {76},
pages = {1163--1194},
abstract = {This paper is devoted to the numerical approximation of the compressible
Navier–Stokes equations with several independent entropies. Various
models for complex compressible materials typically enter the proposed
framework. The striking novelty over the usual Navier–Stokes equations
stems from the generic impossibility of recasting equivalently the
present system in full conservation form. Classical ﬁnite volume
methods are shown to grossly fail in the capture of viscous shock
solutions that are of primary interest in the present work. To enforce
for validity a set of generalized jump conditions that we introduce,
we propose a systematic and eﬀective correction procedure, the so-called
nonlinear projection method, and prove that it preserves all the
stability properties satisﬁed by suitable Godunov-type methods. Numerical
experiments assess the relevance of the method when exhibiting approximate
solutions in close agreement with exact solutions.},
file = {Berthon07.pdf:Berthon07.pdf:PDF},
keywords = {Navier-Stokes; finite volume; non-conservative},
owner = {olivier},
timestamp = {2011.03.10}
}
@ARTICLE{Berthon,
author = {Berthon, Christophe and Turpault, Rodolphe},
title = {Asymptotic preserving HLL schemes},
journal = {(A para\^itre dans},
year = {0000},
file = {Berthon.pdf:Berthon.pdf:PDF},
owner = {olivier},
timestamp = {2010.07.04}
}
@ARTICLE{Bertolazzi04,
author = {Bertolazzi, Enrico and Manzini, Gianmarco},
title = {A finite-volume method for transport of contaminants in porous media},
journal = {Applied Numerical Mathematics},
year = {2004},
volume = {49},
pages = {291--305},
abstract = {A cell-centered ﬁnite-volume method is proposed to solve the unsteady
reactive diffusive transport of a contaminant in porous media. Two
theoretical properties of the analitical solution, namely non-negativity
and maximum principle, are mentioned and their implication on the
approximation method are discussed.},
file = {Bertolazzi04.pdf:Bertolazzi04.pdf:PDF},
keywords = {contaminant transport; finite volumes; least square reconstructions;
advective and diffusive transport},
owner = {olivier},
timestamp = {2010.06.13}
}
@ARTICLE{Bertolazzi04b,
author = {Bertolazzi, Enrico and Manzini, Gianmarco},
title = {Least square-based finite volumes for solving the advection-diffusion
of contaminants in porous media},
journal = {Applied Numerical Mathematics},
year = {2004},
volume = {51},
pages = {451--461},
abstract = {A second-order cell-centered ﬁnite-volume method is proposed to solve
the steady advection–diffusion equation for contaminant transport
in porous media. This method is based on a linear least square reconstruction
that maintains the approximate cell-average values. The reconstruction
is combined with an appropriate slope limiter to prevent the formation
of spurious oscillations in the convection-dominated case. The theoretical
convergence rate is investigated on a boundary layer problem, and
the preliminar results show that the method is promising in the numerical
simulation of more complex groundwater ﬂow problems.},
file = {Bertolazzi04b.pdf:Bertolazzi04b.pdf:PDF},
keywords = {finite volume; non-oscillatory reconstructions; limiters; advective
and diffusive transport},
owner = {olivier},
timestamp = {2010.06.13}
}
@ARTICLE{Beven04,
author = {Beven, Keith},
title = {Robert E. Horton's perceptual model of infiltration processes},
journal = {Hydrological Processes},
year = {2004},
volume = {18},
pages = {3447--3460},
abstract = {Robert E. Horton is best known as the originator of the inﬁltration
excess overland ﬂow concept for storm hydrograph analysis and prediction,
which, in conjunction with the unit hydrograph concept, provided
the foundation for engineering hydrology for several decades. Although
these concepts, at least in their simplest form, have been largely
superseded, a study of Horton’s archived scientiﬁc papers reveals
that his perceptual model of inﬁltration processes and appreciation
of scale problems in modelling were far more sophisticated and complete
than normally presented in hydrological texts. His understanding
of surface controls on inﬁltration remain relevant today.},
doi = {10.1002/hyp.5740},
file = {Beven04.pdf:Beven04.pdf:PDF},
keywords = {history of hydrology; macropores; sun-checks; soil air; infiltration
capacity; scale},
owner = {olivier},
timestamp = {2010.04.24}
}
@ARTICLE{Bittelli10,
author = {Bittelli, Marco and Tomei, Fausto and Pistocchi, Alberto and Flury,
Markus and Boll, Jan},
title = {Development and testing of a physically based, three-dimensional
model of surface and subsurface hydrology},
journal = {Advances in water resources},
year = {2010},
volume = {33},
pages = {106--122},
abstract = {We present a numerical, catchment-scale model that solves ﬂow equations
of surface and subsurface ﬂow in a three-dimensional domain. Surface
ﬂow is described by the two-dimensional parabolic approximation of
the St. Venant equation, using Manning’s equation of motion; subsurface
ﬂow is described by the three-dimensional Richards’ equation for
the unsaturated zone and by three-dimensional Darcy’s law for the
saturated zone, using an integrated ﬁnite difference formulation.
The hydrological component is a dynamic link library implemented
within a comprehensive model which simulates surface energy, radiation
budget, snow melt, potential evapotranspiration, plant development
and plant water uptake. We tested the model by comparing distributed
and integrated three-dimensional simulated and observed perched water
depth (PWD), stream ﬂow data, and soil water contents for a small
catchment. Additional tests were performed for the snow melting algorithm
as well as the different hydrological processes involved. The model
successfully described the water balance and its components as evidenced
by good agreement between measured and modelled data.},
file = {Bittelli10.pdf:Bittelli10.pdf:PDF},
keywords = {surface hydrology; subsurface hydrology; models; physically based;
catchment; distributed; Manning; Richards; Darcy's},
owner = {olivier},
timestamp = {2010.06.09}
}
@ARTICLE{Blayo05,
author = {Blayo, E. and Debreu, L.},
title = {Revisiting open boundary conditions from the point of view of characteristic
variables},
journal = {Ocean Modelling},
year = {2005},
volume = {9},
pages = {231-252},
abstract = {This paper emphasizes the peculiar role of characteristic variables
in the design of open boundary conditions (OBCs). It is shown that
local OBCs leading to positive results in previous comparative studies
do fulﬁl two requirements: they make use of incoming characteristic
variables (i.e. privilege the hyperbolic aspect of the equations),
and satisfy a consistency relationship between the model solution
and some external data. The classical OBCs used in atmosphere and
ocean modeling are revisited from this point of view. It is shown
that several usual boundary conditions should be avoided, while conditions
satisfying the two preceding criteria are pointed out. Finally, the
application of these criteria to the design of OBCs for primitive
equations is discussed.},
file = {Blayo05.pdf:Blayo05.pdf:PDF},
owner = {olivier},
timestamp = {2010.01.25}
}
@PHDTHESIS{Bohorquez08b,
author = {Boh\'orquez Rodr\'iguez de Medina, Patricio},
title = {Study and {N}umerical {S}imulation of {S}ediment {T}ransport in {F}ree-{S}urface
{F}low},
school = {University of M\'alaga in the subject of Fluid Mechanics},
year = {2008},
month = Jul,
abstract = {The ﬂow after the rupture of a dam on an inclined plane of arbitrary
slope, and the induced transport of non-cohesive sediment, is analysed
using the shallow-water approximation. An asymptotic (analytical)
solution is presented for the ﬂow hydrodynamics, and compared with
the numerical simulation of the dam-break ﬂood. Differences arise
due to the appearance of hydrodynamic instabilities (hereafter called
roll-waves) in the numerical solution. These roll-waves point out
the unstable behaviour of the dam-break wave. It is found that roll-waves
enhance the transport of suspended sediment. The limitations of this
simple model to predict the transport of sediment in dam-break ﬂoods
on steep inclines are discussed. Then, a numerical experiment is
designed to analyse the unstable character of the dam-break wave,
that constitutes a non-parallel and unsteady base ﬂow. By analysing
the linear and non-linear numerical evolution of small perturbations,
it is possible to reveal how the nature of the ensuing ﬂow depends
not only on the Froude number (as it happens in the classical problem
of roll-waves over a uniform and steady ﬂow) but also on the non-parallel
and time-varying characteristics of the background ﬂow. Consequently,
it is also shown that these eﬀects stabilise turbulent roll-waves
and raise the critical Froude number required to achieve an unstable
ﬂow. This stability result diﬀers with that obtained with a non-parallel
spatial stability analysis, pointing out the strong inﬂuence of the
base-ﬂow time-dependence in the stability criteria. A novel Continuum
Mechanics model is presented to study the transport of sediment in
a laminar/turbulent free-surface ﬂow. The mixture equations for non-cohesive
sediment transport in turbulent free-surface ﬂow are derived from
the ensemble averaged Navier-Stokes equations of the three-phases
(water, sediment and air). This model avoids the limitations of traditional
shallow-water models, and is suitable to study, for instance, the
transport of sediment in non-hydrostatic shallow-water ﬂows over
bed of arbitrary bottom slopes. The model developed in this work
reveals a mathematical equivalence between the propagation of the
volumetric concentration of the sediment and the phase function used
to capture the free surface. We take advantage of this fact to formulate
an explicit Finite Volume Method (FVM) with the exact conservation
property, that is implemented in the open source software OpenFOAM.
Finally, this model is applied to solve the problem of local scour
around a pipeline and the transport of sediment after the rupture
of a horizontal dam. It is demonstrated that one-dimensional models
based on depth-averaged variables (e.g. generalisations of the one-dimensional
Saint-Venant equations to predict morphological changes) are superseded
by more sophisticated and accurate procedures valid for hyperconcentrated
shallow-water ﬂows over bed of arbitrary bottom slopes (e.g. the
model described herein).},
file = {Bohorquez08b.pdf:Bohorquez08b.pdf:PDF},
keywords = {shallow-water flow; sediment transport; dam-break; roll-waves; kinematic
wave},
owner = {olivier},
timestamp = {2010.04.25}
}
@ARTICLE{Bohorquez07,
author = {Bohorquez, P.},
title = {Roll waves in floods on inclines},
year = {2007},
pages = {361--366},
abstract = {The unstable nature of kinematic waves, resulting from outburst floods
on steep inclines, is investigated theoretically using the shallow
water equations. A numerical experiment is designed in order to efficiently
perform a stability analysis. By analysing the linear and non-linear
numerical evolution of small perturbations, it is possible to reveal
how the nature of the ensuing flow depends not only on the Froude
number but also on non-parallel and time-varying characteristics
of the background flow. It is also demonstrated that these effects
stabilize turbulent roll-waves and raise the critical Froude number
required for instability.},
address = {London},
affiliation = {OTHER},
booktitle = {Numerical {M}odelling of {H}ydrodynamics for {W}ater {R}esources},
details = {http://infoscience.epfl.ch/record/130124},
documenturl = {http://infoscience.epfl.ch/getfile.py?recid=130124&mode=best},
editor = {Garcia-Navarro, P. and Playan, E.},
file = {Bohorquez07.pdf:Bohorquez07.pdf:PDF},
keywords = {Roll waves; Dam-break flood},
location = {Zaragoza, España},
oai-id = {oai:infoscience.epfl.ch:130124},
oai-set = {conf; fulltext-public; fulltext},
owner = {olivier},
publisher = {Taylor and Francis},
review = {REVIEWED},
status = {PUBLISHED},
timestamp = {2010.01.27},
unit = {LHE},
url = {http://www.unizar.es/nmhs}
}
@ARTICLE{Bohorquez10,
author = {Bohorquez, P.},
title = {Competition between kinematic and dynamic waves in floods on steep
slopes},
journal = {Journal of Fluid Mechanics},
year = {2010},
volume = {645},
pages = {375--409},
number = {-1},
abstract = {ABSTRACT We present a theoretical stability analysis of the flow after
the sudden release of a fixed mass of fluid on an inclined plane
formally restricted to relatively long time scales, for which the
kinematic regime is valid. Shallow-water equations for steep slopes
with bed stress are employed to study the threshold for the onset
of roll waves. An asymptotic solution for long-wave perturbations
of small amplitude is found on background flows with a Froude number
value of 2. Small disturbances are stable under this condition, with
a linear decay rate independent of the wavelength and with a wavelength
that increases linearly with time. For larger values of the Froude
number it is shown that the basic flow moves at a different scale
than the perturbations, and hence the wavelength of the unstable
modes is characterized as a function of the plane-parallel Froude
number Frp and a measure of the local slope of the free-surface height
> 0, introduce substantial differences with respect to the plane-parallel
flow with 345), because of the fundamental role that the non-parallel,
time-dependent characteristics of the kinematic-wave play in the
behaviour of small disturbances, which was neglected in their stability
analyses. The present work concludes with supporting numerical simulations
of the evolution of small disturbances, within the framework of the
frictional shallow-water equations, that are superimposed on a base
state which is essentially a kinematic wave, complementing the asymptotic
theory relevant near the onset. The numerical simulations corroborate
the cutoff in wavelength for the spectrum that stabilizes the tail
of the dam-break flood.},
doi = {10.1017/S002211200999276X},
eprint = {http://journals.cambridge.org/article_S002211200999276X},
file = {Bohorquez10.pdf:Bohorquez10.pdf:PDF},
keywords = {roll waves; dam break},
owner = {olivier},
timestamp = {2010.07.01},
url = {http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=7280568&fulltextType=RA&fileId=S002211200999276X}
}
@ARTICLE{Bohorquez08c,
author = {Bohorquez, P. and Darby, S.E.},
title = {The use of one- and two-dimensional hydraulic modelling to reconstruct
a glacial outburst flood in a steep Alpine valley},
journal = {Journal of Hydrology},
year = {2008},
volume = {361},
pages = {240--261},
abstract = {The hydrologic characteristics of the 1943 outburst ﬂood from the
Glacier du Mont Mine, Switzerland, are herein reconstructed using
ﬁeld evidence (palaeostage indicators) in conjunction with shallow
water modelling techniques. These techniques rely on accurately characterising
the hydraulic roughness of the channel, the water height established
as boundary conditions, and the main ﬂow path during the former ﬂood,
but the selection of appropriate parameter values can be problematic
and hence there is uncertainty in the estimated discharge. In this
study, minimal ﬂow discharge estimates derived from one-dimensional
modelling were found to vary between 429 and 557 m3 s-1 as the hydraulic
roughness (ks) and water height at the inlet were varied over a realistic
range of values (0.8–1.4 m and 3.31–6 m, respectively), whereas ﬂow
rates derived via two-dimensional modelling were conﬁned in a narrower,
lower, range of 358–454 m3 s-1. This degree of sensitivity to bed
roughness ks , boundary conditions and the spatial dimensions of
the modelling approach is, for the one-dimensional modelling, higher
than reported in previous studies, but the precision of ﬂow discharge
values reconstructed using the two-dimensional modelling approach
appears to be acceptable, even for ﬂoods in the very steep valley
(0.1 m/m) that is subject of this study.},
doi = {10.1016/j.jhydrol.2008.07.043},
file = {Bohorquez08c.pdf:Bohorquez08c.pdf:PDF},
keywords = {Palaeoflood; outburst; uncertainty; modelling; Saint-Venant; Darcy-Weisbach},
owner = {olivier},
timestamp = {2010.11.12}
}
@INPROCEEDINGS{Bohorquez06,
author = {Bohorquez, P. and Fernandez-Feria, R.},
title = {Nonparallel spatial stability of shallow water flow down an inclined
plane of arbitrary slope},
booktitle = {River {F}low 2006},
year = {2006},
editor = {Ferreira, RML and Alves, ECTL and Leal, JGAB and Cardoso, AH},
volume = {1},
pages = {503--512},
address = {London},
publisher = {Taylor and Francis Group},
abstract = {Roll waves are known to occur in the frictional flow of a thin layer
of water down an inclined solid surface. For a layer of constant
depth, the formation of these waves on a solid plane with small slope
angle have been explained as a hydrodynamic instability occurring
above a critical Froude number by analyzing the temporal stability
of the constant velocity flow. Here we analyze the linear, spatial
stability of the shallow-water flow down an inclined plane of arbitrary
slope including the first order effects of the gradients of both
the velocity and the water depth. For constant water depth (parallel
case) we reproduce previous results of the temporal stability analysis.
Then we apply the nonparallel stability formulation to the kinematic
wave approximation of the shallow-water flow down an inclined plane
of arbitrary slope and characterize, analytically, the frequency
and the wavelength of the most unstable waves as a function of the
Froude number, slope angle, velocity and velocity gradient. We find
important qualitative differences with respect to the parallel (constant
depth) case. These stability results are used to discuss the numerical
solution to the nonlinear shallow-water flow equations for the dam-break
problem on an inclined surface of arbitrary slope. A good agreement
between the waves resulting from the numerical simulations and the
predictions of the stability analysis is found.},
affiliation = {OTHER},
details = {http://infoscience.epfl.ch/record/130126},
documenturl = {http://infoscience.epfl.ch/getfile.py?recid=130126&mode=best},
file = {Bohorquez06.pdf:Bohorquez06.pdf:PDF},
keywords = {Roll waves; Nonparallel spatial stability},
location = {Lisboa, Portugal},
oai-id = {oai:infoscience.epfl.ch:130126},
oai-set = {conf; fulltext-public; fulltext},
owner = {olivier},
review = {REVIEWED},
status = {PUBLISHED},
timestamp = {2010.01.27},
unit = {LHE},
url = {http://www.riverflow2006.org/}
}
@ARTICLE{Bohorquez08,
author = {Bohorquez, P. and Fernandez-Feria, R.},
title = {Transport of suspended sediment under the dam-break flow on an inclined
plane bed of arbitrary slope},
journal = {Hydrological {P}rocesses},
year = {2008},
volume = {22},
pages = {2615--2633},
number = {14},
abstract = {The problem of transport of suspended sediment after the break of
a dam on an inclined bed is considered. To that end we use the shallow-water
approximation for arbitrary, constant slopes of the bottom, taking
into consideration the effect of friction. The numerical technique
and the frictional model are validated by comparison with available
experimental data and asymptotic analytical solutions, with special
attention to the numerical solution near the wetting front. The transport
of suspended sediment down the inclined bed is obtained and discussed
as a function of the slope of the bed for different values of the
parameters characterizing the sediment and its transport properties.
For sufficiently large times we always find the formation of roll
waves near the water front, which affects the transport of sediments
significantly. These strong oscillations are accurately computed
with the numerical method used. The relative importance of the bed
load (to the suspended load) sediment transport is also discussed
as a function of the size of the sediment particles and the slope
of the bed for different models on the initiation of sediment suspension
from bed load. We also check the dilute sediment approach and characterize
the conditions for its failure. Finally, the results of the present
simplified model are intended to be used as tests of more complex
numerical models.},
affiliation = {OTHER},
details = {http://infoscience.epfl.ch/record/130123},
doi = {10.1002/hyp.6858},
file = {Bohorquez08.pdf:Bohorquez08.pdf:PDF},
keywords = {dam-break flow; sediment transport; roll waves},
oai-id = {oai:infoscience.epfl.ch:130123},
oai-set = {article},
owner = {olivier},
review = {REVIEWED},
status = {PUBLISHED},
timestamp = {2010.01.27},
unit = {LHE},
url = { }
}
@ARTICLE{Bokhove05,
author = {Bokhove, Onno},
title = {Flooding and Drying in Discontinuous Galerkin Finite-Element Discretizations
of Shallow-Water Equations. Part 1: One Dimension},
journal = {Journal of Scientific Computing},
year = {2005},
volume = {22--23},
pages = {47--82},
abstract = {Free boundaries in shallow-water equations demarcate the time-dependent
water line between “ﬂooded” and “dry” regions. We present a novel
numerical algorithm to treat ﬂooding and drying in a formally second-order
explicit space discontinuous Galerkin ﬁnite-element discretization
of the one-dimensional or symmetric shallow-water equations. The
algorithm uses ﬁxed Eulerian ﬂooded elements and a mixed Eulerian–Lagrangian
element at each free boundary. When the time step is suitably restricted,
we show that the mean water depth
is positive. This time-step restriction is based on an analysis of
the discretized continuity equation while using the HLLC ﬂux. The
algorithm and its implementation are tested in comparison with a
large and relevant suite of known exact solutions. The essence of
the ﬂooding and drying algorithm pivots around the analysis of a
continuity equation with a ﬂuid velocity and a pseudodensity (in
the shallow water case the depth). It therefore also applies, for
example, to space discontinuous Galerkin ﬁnite-element discretizations
of the compressible Euler equations in which vacuum regions emerge,
in analogy of the above dry regions. We believe that the approach
presented can be extended to ﬁnite-volume discretizations with similar
mean level and slope reconstruction.},
doi = {10.1007/s10915-004-4136-6},
file = {Bokhove05.pdf:Bokhove05.pdf:PDF},
keywords = {shallow-water equations; flooding and drying; free-boundary dynamics;
discontinuous Galerkin finite-element method; positivity of mean
water depth; HLLC; Greenspan and Carrier},
owner = {olivier},
timestamp = {2010.11.12}
}
@UNPUBLISHED{Bonaventura08,
author = {Bonaventura, Luca and Decoene, Astrid and Saleri, Fausto},
title = {Asymptotic derivation of the section-averaged shallow water equations
for natural river hydraulics.},
year = {2008},
abstract = {The section-averaged shallow water model usually applied in river
and open channel hydraulics is derived asymptotically up to second
order in the vertical/longitudinal length ratio, starting from the
three-dimensional Reynolds-averaged Navier-Stokes equations for incompressible
free surface flows. The derivation is carried out under quite general
assumptions on the geometry of the channel, thus allowing for the
application of the resulting equations to natural rivers with arbitrarily
shaped cross sections. As a result of the derivation, a generalized
friction term is obtained, that does not rely on local uniformity
assumptions and that can be computed directly from three-dimensional
turbulence models, without need for local uniformity assumptions.
The modified equations including the novel friction term are compared
to the classical Saint Venant equations in the case of steady state
open channel flows, where analytic solutions are available, showing
that the solutions resulting from the modified equation set are much
closer to the three-dimensional solutions than those of the classical
equation set. Furthermore, it is shown that the proposed formulation
yields results that are very similar to those obtained with empirical
friction closures widely applied in computational hydraulics. The
generalized friction term derived therefore justifies a posteriori
these empirical closures, while allowing to avoid the assumptions
on local flow uniformity on which these closures rely.},
file = {Bonaventura08.pdf:Bonaventura08.pdf:PDF},
institution = {INRIA a CCSD electronic archive server based on P.A.O.L [http://hal.inria.fr/oai/oai.php]
(France)},
keywords = {Mathematics/Analysis of PDEs, Mathematics/Numerical Analysis},
owner = {olivier},
publisher = {HAL - CCSD},
timestamp = {2009.07.19},
url = {http://hal.archives-ouvertes.fr/hal-00275460/en/}
}
@ARTICLE{Bonneton07,
author = {Bonneton, P.},
title = {Modelling of periodic wave transformation in the inner surf zone},
journal = {Ocean Engineering},
year = {2007},
volume = {34},
pages = {1459 - 1471},
number = {10},
doi = {DOI: 10.1016/j.oceaneng.2006.09.002},
file = {Bonneton07.pdf:Bonneton07.pdf:PDF},
issn = {0029-8018},
keywords = {Surf zone},
owner = {olivier},
timestamp = {2009.07.21},
url = {http://www.sciencedirect.com/science/article/B6V4F-4MJJGPR-1/2/b1f2b2826486fa2d1648ab5e2947fe71}
}
@ARTICLE{Borsi04,
author = {Borsi, I. and Farina, A. and Fasano, A.},
title = {On the infiltration of rain water through the soil with runoff of
the excess water},
journal = {Nonlinear Analysis: Real World Applications},
year = {2004},
volume = {5},
pages = {763 - 800},
number = {5},
abstract = {This paper deals with the modelling of the rain water infiltration
through the soil above the aquifer in case of runoff of the excess
water. The main feature of the model lies on the correct definition
of the boundary condition on the ground surface. The latter allows
to estimate, after saturation, the real amount of the water that
penetrates the soil and the one which runs off. The quantity playing
a key role is the so-called rain pressure, defined as the pressure
exerted by the rain on the soil. Although its importance is basically
theoretical and it can be neglected for practical purposes, it helps
understanding the real evolution of the physical problem, providing
a theoretical justification of the empirical procedures.},
doi = {DOI: 10.1016/j.nonrwa.2003.06.002},
file = {Borsi04.pdf:Borsi04.pdf:PDF},
issn = {1468-1218},
keywords = {Rain water percolation; constrained boundary conditions; free boundary
problems; classical solutions; Richards},
owner = {olivier},
timestamp = {2010.06.03},
url = {http://www.sciencedirect.com/science/article/B6W7S-4D04PC5-1/2/a606f8812378784fce3f1034c282b272}
}
@ARTICLE{Borthwick01,
author = {Borthwick, A.~G.~L. and Cruz Le\'on, S. and J\'ozsa, J.},
title = {The shallow flow equations solved on adaptative quadtree grids},
journal = {International Journal for Numerical Methods in Fluids},
year = {2001},
volume = {37},
pages = {691-719},
abstract = {This paper describes an adaptive quadtree grid-based solver of the
depth-averaged shallow water equations. The model is designed to
approximate flows in complicated large-scale shallow domains while
focusing on important smaller-scale localized flow features. Quadtree
grids are created automatically by recursive subdivision of a rectangle
about discretized boundary, bathymetric or flow-related seeding points.
It can be fitted in a fractal-like sense by local grid refinement
to any boundary, however distorted, provided absolute convergence
to the boundary is not required and a low level of stepped boundary
can be tolerated. Grid information is stored as a tree data structure,
with a novel indexing system used to link information on the quadtree
to a finite volume discretization of the governing equations. As
the flow field develops, the grids may be adapted using a parameter
based on vorticity and grid cell size. The numerical model is validated
using standard benchmark tests, including seiches, Coriolis-induced
set-up, jet-forced flow in a circular reservoir, and wetting and
drying. Wind-induced flow in the Nichupte Lagoon, Mexico, provides
an illustrative example of an application to flow in extremely complicated
multi-connected regions.},
file = {Borthwick01.pdf:Borthwick01.pdf:PDF},
keywords = {computational hydraulics; quadtrees; shallow-flow hydrodynamics},
owner = {olivier},
timestamp = {2010.01.26}
}
@ARTICLE{Botta04,
author = {Botta, N. and Klein, R. and Langenberg, S. and Lützenkirchen, S.},
title = {Well balanced finite volume methods for nearly hydrostatic flows},
journal = {Journal of Computational Physics},
year = {2004},
volume = {196},
pages = {539 - 565},
number = {2},
abstract = {In numerical approximations of nearly hydrostatic flows, a proper
representation of the dominant hydrostatic balance is of crucial
importance: unbalanced truncation errors can induce unacceptable
spurious motions, e.g., in dynamical cores of models for numerical
weather prediction (NWP) in particular near steep topography. In
this paper we develop a new strategy for the construction of discretizations
that are #well-balanced# with respect to dominant hydrostatics. The
classical idea of formulating the momentum balance in terms of deviations
of pressure from a balanced background distribution is realized here
through local, time dependent hydrostatic reconstructions. Balanced
discretizations of the pressure gradient and of the gravitation source
term are achieved through a #discrete##Archimedes'##buoyancy##principle#.
This strategy is applied to extend an explicit standard finite volume
Godunov-type scheme for compressible flows with minimal modifications.
The resulting method has the following features: (i) It inherits
its conservation properties from the underlying base scheme. (ii)
It is exactly balanced, even on curvilinear grids, for a large class
of near-hydrostatic flows. (iii) It solves the full compressible
flow equations without reference to a background state that is defined
for an entire vertical column of air. (iv) It is robust with respect
to details of the implementation, such as the choice of slope limiting
functions, or the particularities of boundary condition discretizations.},
doi = {DOI: 10.1016/j.jcp.2003.11.008},
file = {Botta04.pdf:Botta04.pdf:PDF},
issn = {0021-9991},
keywords = {Conservation laws; hydrostatic balance; conservation form},
owner = {olivier},
timestamp = {2010.06.03},
url = {http://www.sciencedirect.com/science/article/B6WHY-4B6KFKV-6/2/e4bcb5c4911970ef655c3258bd87f4c9}
}
@BOOK{Bouchut04,
title = {Nonlinear stability of finite volume methods for hyperbolic conservation
laws, and well-balanced schemes for sources},
publisher = {Birkh{\"a}user Basel},
year = {2004},
editor = {Birkh{\"a}user Basel},
author = {Bouchut, F.},
volume = {2/2004},
abstract = {This book is devoted to finite volume methods for hyperbolic systems
of conservation laws. It differs from previous expositions on the
subject in that the accent is put on the development of tools and
the design of schemes for which one can rigorously prove nonlinear
stability properties. Sufficient conditions for a scheme to preserve
an invariant domain or to satisfy discrete entropy inequalities are
systematically exposed, with analysis of suitable CFL conditions.
The monograph intends to be a useful guide for the engineer or researcher
who needs very practical advice on how to get such desired stability
properties. The notion of approximate Riemann solver and the relaxation
method, which are adapted to this aim, are especially explained.
In particular, practical formulas are provided in a new variant of
the HLLC solver for the gas dynamics system, taking care of contact
discontinuities, entropy conditions, and including vacuum. In the
second half of the book, nonconservative schemes handling source
terms are analyzed in the same spirit. The recent developments on
well-balanced schemes that are able to capture steady states are
explained within a general framework that includes analysis of consistency
and order of accuracy. Several schemes are compared for the Saint
Venant problem concerning positivity and the ability to treat resonant
data. In particular, the powerful and recently developed hydrostatic
reconstruction method is detailed.},
doi = {10.1007/b95203},
file = {Bouchut04.pdf:Bouchut04.pdf:PDF},
keywords = {conservation laws; hyperbolic systems; kinetic solvers; numerical
analysis; partial differential equations;},
owner = {olivier},
timestamp = {2008.04.28}
}
@INCOLLECTION{Bouchut07b,
author = {Bouchut, Fran\c{c}ois},
title = {Chapter 4 Efficient Numerical Finite Volume Schemes for Shallow Water
Models},
booktitle = {Nonlinear Dynamics of Rotating Shallow Water: Methods and Advances},
publisher = {Elsevier Science},
year = {2007},
editor = {V. Zeitlin},
volume = {2},
series = {Edited Series on Advances in Nonlinear Science and Complexity},
pages = {189 - 256},
abstract = {This chapter is devoted to the description of recently developed efficient
tools for the numerical resolution of shallow water models, and in
particular for the case of Coriolis force. We try to give a general
introduction to the finite volume approach, but nevertheless our
presentation is especially focused on the approach that has been
developed by Audusse, Bouchut, Bristeau, Klein and Perthame (A fast
and stable well-balanced scheme with hydrostatic reconstruction for
shallow water flows. SIAM J. Sci. Comput. 25 (2004) 2050-2065), Bouchut
(Nonlinear Stability of Finite Volume Methods for Hyperbolic Conservation
Laws, and Well-Balanced Schemes for Sources. Frontiers in Mathematics
Series, 2004, Birkhäuser, Basel), and intensively tested by Bouchut,
Le Sommer and Zeitlin (Frontal geostrophic adjustment and nonlinear-wave
phenomena in one dimensional rotating shallow water. Part 2: High-resolution
numerical simulations. J. Fluid Mech. 514 (2004) 35-63), Le Sommer,
Reznik and Zeitlin (Nonlinear geostrophic adjustment of long-wave
disturbances in the shallow water model on the equatorial beta-plane.
J. Fluid Mech. 515 (2004) 135-170), Bouchut, Le Sommer and Zeitlin
(Breaking of balanced and unbalanced equatorial waves. Chaos 15 (2005)
13503-13521).},
doi = {DOI: 10.1016/S1574-6909(06)02004-1},
file = {Bouchut07b.pdf:Bouchut07b.pdf:PDF},
issn = {1574-6909},
keywords = {shallow water; well-balanced; friction; boundary condition; HLL; HLLC;
apparent topography; MUSCL; ENO},
owner = {olivier},
timestamp = {2010.06.19},
url = {http://www.sciencedirect.com/science/article/B8JG3-4PS6TNS-6/2/f4c3dbcf476626c1cb6f353e9bc66cc9}
}
@ARTICLE{Bouchut05,
author = {Bouchut, Fran\c{c}ois},
title = {An introduction to finite volume methods for hyperbolic conservation
laws},
journal = {{ESAIM}: {PROCEEDINGS}, {T}. {G}oudon, {E}. {S}onnendrucker \& {D}.
{T}alay, {E}ditors},
year = {2005},
volume = {15},
pages = {1-17},
file = {Bouchut05.pdf:Bouchut05.pdf:PDF},
owner = {olivier},
timestamp = {2010.04.01}
}
@MISC{Bouchut09,
author = {Bouchut, F. and Morales, T.},
title = {A subsonic-well-balanced reconstruction scheme for shallow water
flows},
howpublished = {http://www.math.ntnu.no/conservation/2009/032.html},
year = {2009},
note = {Preprint},
abstract = {We consider the Saint Venant system for shallow water flows with non-flat
bottom. In the past years, efficient well-balanced methods have been
proposed in order to well resolve solutions close to steady states
at rest. Here we describe a strategy based on a local subsonic steady-state
reconstruction that allows to derive a subsonic-well-balanced scheme,
preserving exactly all the subsonic steady states. It generalizes
the now well-known hydrostatic solver, and as the latter it preserves
nonnegativity of water height and satisfies a semi-discrete entropy
inequality. An application to the Euler-Poisson system is proposed.},
file = {Bouchut09.pdf:Bouchut09.pdf:PDF},
keywords = {shallow water; well-balanced; subsonic reconstruction},
owner = {olivier},
timestamp = {2010.06.20}
}
@ARTICLE{Bouchut07,
author = {Bouchut, F. and Ounaissa, H. and Perthame, B.},
title = {Upwinding of the source term at interfaces for Euler equations with
high friction},
journal = {Computers and Mathematics with Applications},
year = {2007},
volume = {53},
pages = {361-–375},
doi = {10.1016/j.camwa.2006.02.055},
file = {Bouchut07.pdf:Bouchut07.pdf:PDF},
keywords = {Finite volume schemes; Source terms; Friction term; Upwind source
at interface; Multi-scale analysis},
owner = {olivier},
timestamp = {2009.01.11}
}
@ARTICLE{Bradford01,
author = {Bradford, S.~F. and Katopodes, N.~D.},
title = {Finite volume model for nonlevel basin irrigation},
journal = {Journal of Irrigation and Drainage Engineering},
year = {2001},
volume = {127},
pages = {216--223},
number = {4},
month = jul # {-} # aug,
abstract = {A finite volume model for unsteady, two-dimensional, shallow water
flow is developed and applied to simulate the advance and infiltration
of an irrigation wave in two-dimensional basins of complex topography.
The fluxes are computed with Roe's approximate Riemann solver and
the monotone upstream scheme for conservation laws is used in conjunction
with predictor-corrector time-stepping to provide a second-order
accurate solution. Flux-limiting is implemented to eliminate spurious
oscillations and the model incorporates an efficient and robust scheme
to capture the wetting and drying of the soil. Model predictions
are compared with experimental data for one- and two-dimensional
problems involving rough, impermeable, and permeable beds, including
a poorly leveled basin.},
file = {Bradford01.pdf:Bradford01.pdf:PDF},
owner = {olivier},
timestamp = {2008.05.04}
}
@INPROCEEDINGS{Braschi94,
author = {Braschi, G. and Dadone, F. and Gallati, M.},
title = {Plain flooding: near field and far field simulations},
booktitle = {Modelling of flood propagation over initially dry areas},
year = {1994},
editor = {Paolo Molinaro and Luigi Natale},
pages = {45--59},
address = {Milan, Italy},
month = jun # { 29-} # jul # { 1},
publisher = {American Society of Civil Engineers, New York, USA},
file = {Braschi94.pdf:Braschi94.pdf:PDF},
keywords = {dam-break; experiment; depth; flood; velocity},
owner = {Fred. DARBOUX},
timestamp = {2008.07.24}
}
@ARTICLE{Braud05,
author = {Braud, I. and De Condappa, D. and Soria, J.~M. and Haverkamp, R.
and Angulo-Jaramillo, R. and Galle, S. and Vauclin, M.},
title = {Use of scaled forms of the infiltration equation for the estismation
of unsatured soil hydraulic properties (the Beerkan method)},
journal = {European Journal of Soil Science},
year = {2005},
volume = {56},
pages = {361--374},
abstract = {Water movement in soil can be described accurately at the local scale,
provided that soil hydraulic properties can be determined with precision.
Traditional methods for characterizing soil are often time consuming,
and large areas cannot be sampled easily. We present a simple method
for overcoming these difficulties. It is easy to implement and cheap.
It is known as the Beerkan method, and it relies on particle-size
analysis, dry bulk density and simple infiltration tests in cylinders.
We describe the experimental protocol and the method of data analysis,
leading to the estimation of parameters describing hydraulic properties.
Shape parameters depend on soil texture and are derived from particle-size
data. Normalization parameters depend on soil structure. They are
derived by inverse modelling and optimization from the infiltration
tests. The theoretical background relies on the sorptivity concept
and scaled forms of the infiltration equation. The formalism for
one- and three-dimensional analysis is described. We assess the accuracy
of the method using published data and simulated values, showing
the soundness of the approach. For the purpose of illustration, we
implemented a simple optimization technique on two bounding cases.},
doi = {10.1111/j.1365-2389.2004.00660.x},
file = {Braud05.pdf:Braud05.pdf:PDF},
owner = {olivier},
timestamp = {2008.05.08}
}
@ARTICLE{Braudrick01,
author = {Braudrick, Christian~A. and Grant, Gordon~E.},
title = {Transport and deposition of large woody debris in streams: a flume
experiment},
journal = {Geomorphology},
year = {2001},
volume = {41},
pages = {263 - 283},
number = {4},
abstract = {Large woody debris (LWD) is an integral component of forested streams
of the Pacific Northwest and elsewhere, yet little is known about
how far wood is transported and where it is deposited in streams.
In this paper, we report the results of flume experiments that examine
interactions among hydraulics, channel geometry, transport distance
and deposition of floating wood. These experiments were carried out
in a 1.22-m-wide×9.14-m-long gravel bed flume using wooden dowels
of various sizes as surrogate logs. Channel planforms were either
self-formed or created by hand, and ranged from meanders to alternate
bars. Floating pieces tended to orient with long axes parallel to
flow in the center of the channel. Pieces were deposited where channel
depth was less than buoyant depth, typically at the head of mid-channel
bars, in shallow zones where flow expanded, and on the outside of
bends. We hypothesize that the distance logs travel may be a function
of the channel's debris roughness, a dimensionless index incorporating
ratios of piece length and diameter to channel width, depth and sinuosity.
Travel distance decreased as the ratio of piece length to both channel
width and radius of curvature increased, but the relative importance
of these variables changed with channel planform. Large pieces can
move further than our debris roughness models predict if greater
than 50% of the active channel area is deeper than the buoyant depth
of the piece, or if momentum is high enough to carry pieces across
shallows. Our debris roughness model allows first-order prediction
of the amount of wood transport under various channel geometries.},
doi = {DOI: 10.1016/S0169-555X(01)00058-7},
file = {Braudrick01.pdf:Braudrick01.pdf:PDF},
issn = {0169-555X},
keywords = {Woody debris},
owner = {olivier},
timestamp = {2009.11.14},
url = {http://www.sciencedirect.com/science/article/B6V93-449V0TD-2/2/267f3b406776cccfc7ef0aa626c77e85}
}
@ARTICLE{Briganti09,
author = {Briganti, Riccardo and Dodd, Nicholas},
title = {Shoreline motion in nonlinear shallow water coastal models},
journal = {Coastal Engineering},
year = {2009},
volume = {56},
pages = {495 - 505},
number = {5-6},
abstract = {Different shoreline boundary conditions for numerical models of the
Non-Linear Shallow Water Equations based on Godunov-type schemes
are compared. The study focuses on the Peregrine and Williams [Peregrine,
D.H., Williams, S.M., 2001. Swash overtopping a truncated plane beach.
Journal of Fluid Mechanics 440, 391-399.] problem of a single bore
collapsing on a slope. This is considered the best test to assess
performances of the shoreline boundary treatments in terms of all
the parameters of interest in swash zone modelling. Emphasis is given
to the shoreline trajectory and flow velocity modelling. A mismatch
of the velocity at the early stage of the motion is highlighted.
Most of the tested techniques perform similarly in terms of maximum
run-up, the backwash phase is critical in all cases. Starting from
the Brocchini et al. [Brocchini, M., Bernetti, R., Mancinelli, A.,
Albertini, G., 2001. An efficient solver for nearshore flows based
on the WAF method. Coastal Engineering 43(2), 105-129.] shoreline
boundary treatment, a simple technique that improves the accuracy
of velocity predictions is also developed. A sensitivity analysis
of the domain resolution and the threshold value of the water depth
that defines a wet cell is also presented.},
doi = {DOI: 10.1016/j.coastaleng.2008.10.008},
file = {Briganti09.pdf:Briganti09.pdf:PDF},
issn = {0378-3839},
keywords = {Bore-driven swash},
owner = {olivier},
timestamp = {2009.07.24},
url = {http://www.sciencedirect.com/science/article/B6VCX-4V5XP2C-1/2/e5f3c7d396ab3987e1c62be682535b3c}
}
@TECHREPORT{Bristeau01,
author = {Bristeau, M.-O. and Coussin, Beno\^it},
title = {Boundary conditions for the shallow water equations solved by kinetic
schemes},
institution = {INRIA},
year = {2001},
number = {4282},
month = oct,
abstract = {We consider the Saint-Venant system for Shallow Water which is an
usual model to describe the flows in rivers, coastal areas or floodings.
The hyperbolic system of conservation laws is solved on unstructured
meshes using a finite volume method together with a kinetic solver.
We add ti this system a friction term, the role of which is important
when small water depths are considered. In this paper we address
the treatment of the boundary conditions, the difficulty is due to
the fact that in some cases (fluvial flows) the given boundary conditions
are not sufficient to apply directly the scheme, we discuss here
how to treat these boundary conditions using a Riemann invariant.
Some numerical results illustrate the ability of the method to treat
complex problems like the filling up or the draining off of a river
bed.},
file = {Bristeau01.pdf:Bristeau01.pdf:PDF},
keywords = {shallow water system; finite volume method; kinetic solver; friction;
boundary conditions},
owner = {olivier},
timestamp = {2008.04.27}
}
@PHDTHESIS{Brivois05,
author = {Brivois, Olivier},
title = {Contribution \`a la mod\'elisation de l'\'erosion de fortes pentes
par un \'ecoulement turbulent diphasique},
school = {Universit\'e de la M\'editerran\'ee Aix-Marseille II},
year = {2005},
file = {Brivois05.pdf:Brivois05.pdf:PDF},
owner = {olivier},
timestamp = {2009.07.21}
}
@ARTICLE{Brook99,
author = {Brook, B.~S. and Falle, S.~A.~E.~G. and Pedley, T.~J.},
title = {Numerical solutions for unsteady gravity-driven flows in collapsible
tubes: evolution and roll-wave instability of a steady state},
journal = {Journal of Fluid Mechanics},
year = {1999},
volume = {396},
pages = {223--256},
file = {Brook99.pdf:Brook99.pdf:PDF},
owner = {olivier},
timestamp = {2009.01.11}
}
@ARTICLE{Brufau02,
author = {Brufau, P. and Garc\'ia-Navarro, P. and Play\'an, E. and Zapata,
N.},
title = {Numerical modeling of basin irrigation with an upwind scheme},
journal = {Journal of Irrigation and Drainage Engineering},
year = {2002},
volume = {128},
pages = {212-223},
number = {4},
month = jul # {-} # aug,
abstract = {In recent years, upwind techniques have been successfully applied
in hydrology to simulate two-dimensional free surface flows. Basin
irrigation is a surface irrigation system characterized by its potential
to use water very efficiently. In basin irrigation, the field is
leveled to zero slope and flooded from a point source. The quality
of land leveling has been shown to influence irrigation performance
drastically. Recently, two-dimensional numerical models have been
developed as tools to design and manage basin irrigation systems.
In this work, a finite volume-based upwind scheme is used to build
a simulation model considering differences in bottom level. The discretization
is made on triangular or quadrilateral unstructured grids and the
source terms of the equations are given a special treatment. The
model is applied to the simulation of two field experiments. Simulation
results resulted in a clear improvement over previous simulation
efforts and in a close agreement with experimental data. The proposed
model has proved its ability to simulate overland flow in the presence
of undulated bottom elevations, inflow hydrographs, and colliding
fronts.},
file = {Brufau02.pdf:Brufau02.pdf:PDF},
keywords = {Surface irrigation ; Southern Europe ; Mathematical model ; Hydrology
; Europe ; Basin irrigation ; Contour line ; Land slope ; Field study
; Spain ; Water infiltration ; Finite volume method ; Discretization
method ; Hydrodynamic model ; Simulation model ; Overland flow ;
Land grading ; Upwind scheme ;
Free surface flow ; Numerical simulation ; Irrigation},
owner = {olivier},
timestamp = {2009.07.19}
}
@ARTICLE{Brufau03,
author = {Brufau, P. and Garc\`ia-Navarro, P.},
title = {Unsteady free surface flow simulation over complex topography with
a multidimensional upwind technique},
journal = {Journal of Computational Physics},
year = {2003},
volume = {186},
pages = {503--526},
abstract = {In the context of numerical techniques for solving unsteady free surface
problems, finite element and finite volume approximations are widely
used. A class of upwind methods which attempts to model the equations
in a genuinely multidimensional manner has been recently introduced
as an alternative. Multidimensional upwind schemes (MUS) were developed
initially for the approximation of steady-state solutions of the
two-dimensional Euler equations on unstructured grids, although they
can be applicable to any system of hyperbolic conservation laws,
such as the shallow water equations. The formal analogy between the
two systems of equations is useful for simple cases. However, in
practical applications of interest in hydraulics, complex geometries
and bottom slope variation can lead to important numerical errors
produced by an inadequate source term discretization. This problem
has been analyzed and, in this work, the necessity of a multidimensional
upwind discretization of the source terms is justified. The basis
of the numerical method is stated and the particular adaptation to
unsteady shallow water flows over irregular geometry is described.
As test cases, laboratory experimental data are used together with
academic tests for validation.},
doi = {10.1016/S0021-9991(03)00072-X},
file = {Brufau03.pdf:Brufau03.pdf:PDF},
keywords = {multidimensional upwind; shallow water; unsteady flow; source terms},
owner = {olivier},
timestamp = {2008.05.04}
}
@ARTICLE{Buffard00,
author = {Buffard, T. and Gallou\"et, T. and H\'erard, J.-M.},
title = {A sequel to a rough Godunov scheme: application to real gases},
journal = {Computers \& Fluids},
year = {2000},
volume = {29},
pages = {813--847},
abstract = {We present here an approximate Riemann solver to compute Euler equations
using real gas state laws. The scheme is based on an earlier proposition,
called VFRoe, introduced by one of the authors. It makes use of non
conservative variables in ordrer to preserve numerically Riemann
invariants through the contact discontinuity. Detailed investigation
of actual rate of convergence of the scheme is reported. The study
also includes a comparison with original VFRoe and Roe schemes.},
owner = {olivier},
timestamp = {2009.02.11}
}
@ARTICLE{Bunya09,
author = {Bunya, Shintaro and Kubatko, Ethan~J. and Westerink, Joannes~J. and
Dawson, Clint},
title = {A wetting and drying treatment for the Runge–Kutta discontinuous
Galerkin solution to the shallow water equations},
journal = {Computer Methods in Applied Mechanics and Engineering},
year = {2009},
volume = {198},
pages = {1548--1562},
number = {17-20},
month = apr,
abstract = {This paper proposes a wetting and drying treatment for the piecewise
linear Runge–Kutta discontinuous Galerkin approximation to the shallow
water equations. The method takes a fixed mesh approach as opposed
to mesh adaptation techniques and applies a post-processing operator
to ensure the positivity of the mean water depth within each finite
element. In addition, special treatments are applied in the numerical
flux computation to prevent an instability due to excessive drying.
The proposed wetting and drying treatment is verified through comparisons
with exact solutions and convergence rates are examined. The obtained
orders of convergence are close to or approximately equal to 1 for
solutions with discontinuities and are improved for smooth solutions.
The combination of the proposed wetting and drying treatment and
a TVB slope limiter is also tested and is found to be applicable
on condition that they are applied exclusively to an element at the
same Runge–Kutta step.},
citeulike-article-id = {4184359},
citeulike-linkout-0 = {http://dx.doi.org/10.1016/j.cma.2009.01.008},
citeulike-linkout-1 = {http://linkinghub.elsevier.com/retrieve/pii/S0045782509000383},
doi = {10.1016/j.cma.2009.01.008},
file = {Bunya09.pdf:Bunya09.pdf:PDF},
issn = {00457825},
keywords = {discontinuous-galerkin, st-venant, wet-dry-fronts},
owner = {olivier},
posted-at = {2009-03-16 19:44:39},
priority = {2},
timestamp = {2009.07.19},
url = {http://dx.doi.org/10.1016/j.cma.2009.01.008}
}
@ARTICLE{Burguete01,
author = {Burguete, J. and Garc\'ia-Navarro, P.},
title = {Efficient construction of high-resolution TVD conservative schemes
for equations with source terms: application to shallow water flows},
journal = {International Journal for Numerical Methods in Fluids},
year = {2001},
volume = {37},
pages = {209--248},
file = {Burguete01.pdf:Burguete01.pdf:PDF},
owner = {olivier},
timestamp = {2010.05.12}
}
@ARTICLE{Burguete09,
author = {Burguete, J. and Garc\'ia-Navarro, P. and Murillo, J.},
title = {One-dimensional conservative coupled discretization of the shallow-water
with scalar transport equations},
journal = {Monograf\'ias de la Real Academia de Ciencias de Zaragoza},
year = {2009},
volume = {31},
pages = {21--33},
abstract = {The quality of the solutions obtained by numerical methods in shallow-water
equations is strongly dependent on the discretization used. This
is the greatest diﬃculty in shallow-water simulations. In this work
we show that only a coupled discretization of the whole system of
equations and a careful deﬁnition of the ﬂux limiter function in
second order TVD schemes are necessary in order to preserve uniform
solute proﬁles in situations of 1D unsteady subcritical ﬂow. An ideal
dam-break with analytical solution and two practical applications
on river ﬂow and furrow irrigation are presented.},
file = {Burguete09.pdf:Burguete09.pdf:PDF},
keywords = {One dimensional ﬂow; advection; dispersion; coupled discretization;
upwind schemes; conservative formulation; shallow water; river ﬂow;
furrow irrigation},
owner = {olivier},
timestamp = {2010.05.02}
}
@ARTICLE{Burguete08,
author = {Burguete, J. and Garc\'ia-Navarro, P. and Murillo, J.},
title = {Friction term discretization and limitation to preserve stability
and conservation in the 1D shallow-water model: Application to unsteady
irrigation and river flow},
journal = {International Journal for Numerical Methods in Fluids},
year = {2008},
volume = {58},
pages = {403-425},
number = {4},
abstract = {Friction is one of the relevant forces included in the momentum equation
of the 1D shallow-water model. This work shows that a pointwise discretization
of the friction term unbalances this term with the rest of the terms
in the equation in steady state. On the other hand, an upwind discretization
of the friction term ensures the correct discrete balance. Furthermore,
a conservative technique based on the limitation of the friction
value is proposed in order to avoid unbounded values of the friction
term in unsteady cases of advancing front over dry and rough surfaces.
This limitation improves the quality of unsteady solutions in wet/dry
fronts and guarantees the numerical stability in cases with dominant
friction terms. The proposed discretization is validated in some
test cases with analytical solution or with measured data and used
in some practical cases.},
doi = {10.1002/fld.1727},
file = {Burguete08.pdf:Burguete08.pdf:PDF},
owner = {olivier},
timestamp = {2009.07.24}
}
@ARTICLE{Burguete04,
author = {Burguete, J. and Garc\`ia-Navarro, P.},
title = {Implicit schemes with large time step for non-linear equations :
application to river flow hydraulics},
journal = {International Journal for Numerical Methods in Fluids},
year = {2004},
volume = {46},
pages = {607--636},
abstract = {In this work, first-order upwind implicit schemes are considered.
The traditional tridiagonal scheme is rewritten as a sum of two bidiagonal
schemes in order to produce a simpler method better suited for unsteady
transcritical flows. On the other hand, the origin of the instabilities
associated to the use of upwind implicit methods for shock propagations
is identified and a new stability condition for non-linear problems
is proposed. This modification produces a robust, simple and accurate
upwind semi-explicit scheme suitable for discontinuous flows with
high Courant-Friedrichs-Lewy (CFL) numbers. The discretization at
the boundaries is based on the condition of global mass conservation
thus enabling a fully conservative solution for all kind of boundary
conditions. The performance of the proposed technique will be shown
in the solution of the inviscid Burgers' equation, in an ideal dambreak
test case, in some steady open channel flow test cases with analytical
solution and in a realistic flood routing problem, where stable and
accurate solutions will be presented using CFL values up to 100.},
doi = {10.1002/fld.772},
file = {Burguete04.pdf:Burguete04.pdf:PDF},
keywords = {implicit schemes; upwind discretization; shallow water; unsteady flow
with shocks; non-linear equations; high CFL number},
owner = {olivier},
timestamp = {2008.05.03}
}
@ARTICLE{Burguete02,
author = {Burguete, J. and Garc\`ia-Navarro, P. and Aliod, R.},
title = {Numerical simulation of runoff from extreme rainfall events in a
mountain water catchment},
journal = {Natural Hazards and Earth System Sciences},
year = {2002},
volume = {2},
pages = {109--117},
abstract = {A numerical model for unsteady shallow water flow over initially dry
areas is applied to a case study in a small drainage area at the
Spanish Ebro River basin. Several flood mitigation measures (reforestation,
construction of a small reservoir and channelization) are simulated
in the model in order to compare different extreme rainfall-runoff
scenarios.},
file = {Burguete02.pdf:Burguete02.pdf:PDF},
owner = {olivier},
timestamp = {2008.05.03}
}
@ARTICLE{vanBuuren97,
author = {van Buuren, R. and Kuerten, J.~G.~M. and Geurts, B.~J.},
title = {Instabilities of stationary inviscid compressible flow around an
airfoil},
journal = {Journal of Computational Physics},
year = {1997},
volume = {138},
pages = {520-539},
file = {vanBuuren97.pdf:vanBuuren97.pdf:PDF},
owner = {olivier},
timestamp = {2009.07.28}
}
@ARTICLE{Cai06,
author = {Cai, Li and Feng, J.-H. and Xie, W.-X. and Zhou, Jun},
title = {Computations of steady and unsteady transport of pollutant in shallow
water},
journal = {Mathematics and Computers in Simulation},
year = {2006},
volume = {71},
pages = {31-43},
abstract = {We present new models for simulating the steady and unsteady transport
of pollutant. Then the simple central-upwind schemes based on central
weighted essentially non-oscillatory reconstructions are proposed
in this paper for computing the one- and two-dimensional steady and
unsteady models. Since the non-uniform width of the different local
Riemann fans is calculated more accurately, the central-upwind schemes
enjoy a much smaller numerical viscosity as well as the staggering
between two neighboring sets of grids is avoided. Synchronously,
due to the central-upwind schemes are combined with the fourth-order
central weighted essentially non-oscillatory reconstructions, the
schemes have the non-oscillatory behavior. The numerical results
show the desired accuracy, high-resolution, and robustness of our
methods.},
file = {Cai06.pdf:Cai06.pdf:PDF},
keywords = {Transport of pollutant; Shallow water equations; Central-upwind schemes;
Central weighted essentially non-oscillatory (CWENO) schemes},
owner = {olivier},
timestamp = {2010.01.25}
}
@ARTICLE{Cai07,
author = {Cai, Li and Xie, W.-X. and Feng, J.-H. and Zhou, Jun},
title = {Computations of transport of pollutant in shallow water},
journal = {Applied Mathematical Modelling},
year = {2007},
volume = {31},
pages = {490-498},
abstract = {The focus of this paper is to simulate the transport of a passive
pollutant by a ﬂow modelled by the two-dimensional shallow water
equations. Considering the friction terms, new model for simulating
the steady and unsteady transport of pollutant is established. Then
the adaptive semi-discrete central-upwind scheme based on central
weighted essentially non-oscillatory reconstruction is utilized for
simulating the two-dimensional steady and unsteady transport of pollutant.
The non-oscillatory behavior and accuracy of the scheme are demonstrated
by the numerical result.},
file = {Cai07.pdf:Cai07.pdf:PDF},
keywords = {Transport of pollutant; 2-D shallow water equations; Adaptive semi-discrete
central-upwind schemes; Central weighted essentially non-oscillatory
(CWENO) scheme},
owner = {olivier},
timestamp = {2010.01.25}
}
@ARTICLE{Caleffi06,
author = {Caleffi, V. and Valiani, A. and Bernini, A.},
title = {Fourth-order balanced source term treatment in central WENO schemes
for shallow water equations},
journal = {Journal of Computational Physics},
year = {2006},
volume = {218},
pages = {228--245},
abstract = {The aim of this work is to develop a well-balanced central weighted
essentially non-oscillatory (CWENO) method, fourth-order accurate
in space and time, for shallow water system of balance laws with
bed slope source term. Time accuracy is obtained applying a Runge–Kutta
scheme (RK), coupled with the natural continuous extension (NCE)
approach. Space accuracy is obtained using WENO reconstructions of
the conservative variables and of the water-surface elevation. Extension
of the applicability of the standard CWENO scheme to very irregular
bottoms, preserving high-order accuracy, is obtained introducing
two original procedures. The former involves the evaluation of the
point-values of the ﬂux derivative, coupled with the bed slope source
term. The latter involves the spatial integration of the source term,
analytically manipulated to take advantage from the regularity of
the free-surface elevation, usually smoother than the bottom elevation.
Both these procedures satisfy the C-property, the property of exactly
preserving the quiescent ﬂow. Several standard one-dimensional test
cases are used to verify high-order accuracy, exact C-property, and
good resolution properties for smooth and discontinuous solutions.},
doi = {10.1016/j.jcp.2006.02.001},
file = {Caleffi06.pdf:Caleffi06.pdf:PDF},
keywords = {High-order methods; CWENO schemes; shallow water equations; source
terms; C-property; bump; pulse; dam-break},
owner = {olivier},
timestamp = {2011.02.23}
}
@ARTICLE{Caleffi03,
author = {Caleffi, V. and Valiani, A. and Zanni, A.},
title = {Finite volume method for simulating extreme flood events in natural
channels},
journal = {Journal of Hydraulic Research},
year = {2003},
volume = {41},
pages = {167--177},
number = {2},
abstract = {The need for mitigating damages produced by extreme hydrologic events
has stimulated the European Community to fund several projects. The
Concerted Action on Dam-break Modelling workgroup (CADAM) performed
a considerable work for the development of new codes and for the
adequate verification of their performance. In the context of the
CADAM project, a new 2D computer code is developed, tested and applied,
as described in the present paper. The algorithm is obtained through
the spatial discretisation of the shallow water equations by a finite
volume method, based on the Godunov approach. The HLL Riemann solver
is used. A second order accuracy in space and time is achieved, respectively
by MUSCL and predictor-corrector techniques. The high resolution
requirement is ensured by satisfaction of TVD property. Particular
attention is posed to the numerical treatment of source terms. Accuracy,
stability and the reliability of the code are tested on a selected
set of study cases. A grid refinement analysis is performed. Numerical
results are compared with experimental data, obtained by the physical
modelling of a submersion wave on a portion of the Toce river valley,
Italy, performed by ENEL-HYDRO and considered as representative of
a real life flood occurrence.},
file = {Caleffi03.pdf:Caleffi03.pdf:PDF},
keywords = {SWE; FVM; HLL approximate Riemann solver; source terms; overland flood
flow; Toce river},
owner = {olivier},
timestamp = {2008.05.04}
}
@ARTICLE{Calver89,
author = {Calver, A. and Wood, W.L.},
title = {On the discretization and cost-effectiveness of a finite element
solution for hillslope subsurface flow},
journal = {Journal of Hydrology},
year = {1989},
volume = {110},
pages = {165--179},
number = {1-2},
abstract = {An investigation is carried out into the effects of the size of time
and space steps on the discharge and hydraulic potential predictions
of a finite element rainfall-runoff model, the Institute of Hydrology
Distributed Model version 4. Accuracy of hydrological predictions
is viewed in the light of computer processing times and recommendations
are given for suitable discretizations for this type of model.},
doi = {DOI: 10.1016/0022-1694(89)90242-4},
file = {Calver89.pdf:Calver89.pdf:PDF},
issn = {0022-1694},
keywords = {Richards},
owner = {olivier},
timestamp = {2010.06.15},
url = {http://www.sciencedirect.com/science/article/B6V6C-4893V74-P/2/1d2c3f629f5c77496f2174828e02dea5}
}
@ARTICLE{Campbell84,
author = {Campbell, S.Y. and Parlange, J.-Y. and Rose, C.W.},
title = {Overland flow on converging and diverging surfaces -- Kinematic model
and similarity solutions},
journal = {Journal of Hydrology},
year = {1984},
volume = {67},
pages = {367--374},
abstract = {The solutions for the equations of kinematic flow on a converging
surface, found by the method of characteristics, suggest an alternative
method of solution in the form of a similarity solution. This method
is illustrated here by considering flow on a cone, for which an exact
analytical solution is found to represent the steady-state flow,
allowing a check for numerical calculations. In general, the similarity
technique reduces the partial differential equation of kinematic
flow to an ordinary differential equation as long as the excess rainfall
can be expressed as a power of time.},
file = {Campbell84.pdf:Campbell84.pdf:PDF},
keywords = {inverted cone; converging surface; similarity solution; conical surface;
exact analytical solution; kinematic},
owner = {olivier},
timestamp = {2010.06.12}
}
@ARTICLE{Caselles09,
author = {Caselles, V. and Donat, R. and Haro, G.},
title = {Flux-gradient and source term balancing for certain high resolution
shock-capturing schemes},
journal = {Computers \& Fluids},
year = {2009},
volume = {38},
pages = {16--36},
number = {1},
file = {Caselles09.pdf:Caselles09.pdf:PDF},
owner = {olivier},
timestamp = {2010.03.15}
}
@ARTICLE{Castillo03,
author = {Castillo, V.~M. and G\'omez-Plaza, A. and Mart\'inez-Mena, M.},
title = {The role of antecedent soil water content in the runoff response
of semiarid catchments: a simulation approach},
journal = {Journal of Hydrology},
year = {2003},
volume = {284},
pages = {114--130},
abstract = {The soil water content is recognized as one of many runoff controlling
factors in semiarid environments. A simple, physically based distributed
model has been developed to study the role of antecedent soil water
content in runoff generation in three small catchments in semiarid
southeast Spain. The catchments were set up in two different zones:
a burnt area with scarce vegetation and unburnt area with a denser
plant cover. The inﬁltration process is determined by the Green –
Ampt equation and the initial soil water content is taken into account
by means of maps obtained by Conditional Gaussian simulation. The
model was run 2700 times with different soil moisture scenarios and
design storms. Stochastic sensitivity analysis was used to examine
the role of antecedent soil water content in the runoff response.
The results showed that the hydrological response after high intensity,
low frequency storms is independent of the initial soil water content.
On the other hand, the antecedent soil water content is an important
factor controlling runoff during medium and low intensity storms,
a type of rainstorm that is relatively frequent in semiarid areas.
The sensitivity of the runoff response to soil moisture depended
on the predominant runoff mechanisms. When inﬁltration excess overland
ﬂow is predominant, as a result of high rain intensities or less
permeable soils, the runoff response is more uniform and does not
depend on initial soil moisture. Runoff from less intense storms
on soils of higher permeability is controlled by the soil water content
of the surface soil layers and is more dependent on initial conditions.
The role of the initial soil water content is more important in catchments
where the presence of plant cover produces a patchwork of runoff
and runon sites, whose spatial pattern is highly dependent on the
soil water status.},
doi = {10.1016/S0022-1694(03)00264-6},
file = {Castillo03.pdf:Castillo03.pdf:PDF},
keywords = {Soil moisture; Sensitivity analysis; Conditional simulation; Monte
Carlo; Overland ﬂow; Runoff modelling; Green-Ampt; kinematic wave},
owner = {olivier},
timestamp = {2010.04.24}
}
@ARTICLE{CastroDiaz09,
author = {Castro D\'iaz, M.J. and Fern\'andez-Nieto, E.D. and Ferreiro, A.M.
and Par\'es, C.},
title = {Two-dimensional sediment transport models in shallow water equations.
A second order finite volume approach on unstructured meshes},
journal = {Computer Methods in Applied Mechanics and Engineering},
year = {2009},
volume = {198},
pages = {2520 - 2538},
number = {33-36},
abstract = {In this paper, we study the numerical approximation of bedload sediment
transport due to shallow layer flows. The hydrodynamical component
is modeled by a 2D shallow water system and the morphodynamical component
by a solid transport discharge formula that depends on the hydrodynamical
variables. The coupled system can be written as a nonconservative
hyperbolic system. To discretize it, first we consider a Roe-type
first order scheme as well as a variant based on the use of flux
limiters. These first order schemes are then extended to second order
accuracy by means of a new MUSCL-type reconstruction operator on
unstructured meshes. Finally, some numerical tests are presented.},
doi = {DOI: 10.1016/j.cma.2009.03.001},
file = {CastroDiaz09.pdf:CastroDiaz09.pdf:PDF},
issn = {0045-7825},
keywords = {Finite volume method},
owner = {olivier},
timestamp = {2010.02.01},
url = {http://www.sciencedirect.com/science/article/B6V29-4VWB151-1/2/b1cf68d800ba7d81d182133a1945bc35}
}
@ARTICLE{Castro08,
author = {Castro, M.~J. and Garc\'ia-Rodr\'iguez, J.~A. and Gonz\'alez-Vida,
J.~M. and Par\'es, C.},
title = {Solving shallow-water systems in 2D domains using Finite Volume methods
and multimedia SSE instructions},
journal = {J. Comput. Appl. Math.},
year = {2008},
volume = {221},
pages = {16--32},
number = {1},
abstract = {The goal of this paper is to construct efficient parallel solvers
for 2D hyperbolic systems of conservation laws with source terms
and nonconservative products. The method of lines is applied: at
every intercell a projected Riemann problem along the normal direction
is considered which is discretized by means of well-balanced Roe
methods. The resulting 2D numerical scheme is explicit and first-order
accurate. In [M.J. Castro, J.A. Garcia, J.M. Gonzalez, C. Pares,
A parallel 2D Finite Volume scheme for solving systems of balance
laws with nonconservative products: Application to shallow flows,
Comput. Methods Appl. Mech. Engrg. 196 (2006) 2788-2815] a domain
decomposition method was used to parallelize the resulting numerical
scheme, which was implemented in a PC cluster by means of MPI techniques.
In this paper, in order to optimize the computations, a new parallelization
of SIMD type is performed at each MPI thread, by means of SSE (''Streaming
SIMD Extensions''), which are present in common processors. More
specifically, as the most costly part of the calculations performed
at each processor consists of a huge number of small matrix and vector
computations, we use the Intel(C) Integrated Performance Primitives
small matrix library. To make easy the use of this library, which
is implemented using assembler and SSE instructions, we have developed
a C++ wrapper of this library in an efficient way. Some numerical
tests were carried out to validate the performance of the C++ small
matrix wrapper. The specific application of the scheme to one-layer
Shallow-Water systems has been implemented on a PC's cluster. The
correct behavior of the one-layer model is assessed using laboratory
data.},
address = {Amsterdam, The Netherlands, The Netherlands},
doi = {http://dx.doi.org/10.1016/j.cam.2007.10.034},
file = {Castro08.pdf:Castro08.pdf:PDF},
issn = {0377-0427},
owner = {olivier},
publisher = {Elsevier Science Publishers B. V.},
timestamp = {2009.07.19}
}
@ARTICLE{Castro08b,
author = {Castro, Manuel J. and LeFloch, Philippe G. and Luz Munoz-Ruiz, Mar\'ia
and Par\'es, Carlos},
title = {Why many theories of shock waves are necessary: Convergence error
in formally path-consistent schemes},
journal = {Journal of Computational Physics},
year = {2008},
volume = {227},
pages = {8107--8129},
number = {17},
abstract = {We are interested in nonlinear hyperbolic systems in nonconservative
form arising in fluid dynamics, and, for solutions containing shock
waves, we investigate the convergence of finite difference schemes
applied to such systems. According to Dal Maso, LeFloch, and Murat's
theory, a shock wave theory for a given nonconservative system requires
prescribing a priori a family of paths in the phase space. In the
present paper, we consider schemes that are formally consistent with
a given family of paths, and we investigate their limiting behavior
as the mesh is refined. we first generalize to systems a property
established earlier by Hou and LeFloch for scalar conservation laws,
and we prove that nonconservative schemes generate, at the level
of the limiting hyperbolic system, an convergence error source-term
which, provided the total variation of the approximations remains
uniformly bounded, is a locally bounded measure. This convergence
error measure is supported on the shock trajectories and, as we demonstrate
here, is usually #small#. In the special case that the scheme converges
in the sense of graphs - a rather strong convergence property often
violated in practice - then this measure source-term vanishes. We
also discuss the role of the equivalent equation associated with
a difference scheme; here, the distinction between scalar equations
and systems appears most clearly since, for systems, the equivalent
equation of a scheme that is formally path-consistent depends upon
the prescribed family of paths. The core of this paper is devoted
to investigate numerically the approximation of several (simplified
or full) hyperbolic models arising in fluid dynamics. This leads
us to the conclusion that for systems having nonconservative products
associated with linearly degenerate characteristic fields, the convergence
error vanishes. For more general models, this measure is evaluated
very accurately, especially by plotting the shock curves associated
with each scheme under consideration; as we demonstrate, plotting
the shock curves provide a convenient approach for evaluating the
range of validity of a given scheme.},
doi = {DOI: 10.1016/j.jcp.2008.05.012},
file = {Castro08b.pdf:Castro08b.pdf:PDF},
issn = {0021-9991},
keywords = {Nonconservative hyperbolic system; Shock wave; Family of paths; Equivalent
equation; Convergence error measure; Formally path-consistent scheme},
owner = {olivier},
timestamp = {2010.07.02},
url = {http://www.sciencedirect.com/science/article/B6WHY-4SMNY18-1/2/a96e0bdf121ac34604742fdc9165bd07}
}
@ARTICLE{Castro07,
author = {Castro, M.~J. and Pardo, A. and Par\`es, C.},
title = {Well-balanced numerical schemes based on a generalized hydrostatic
reconstruction technique},
journal = {Mathematical Models and Methods in Applied Sciences},
year = {2007},
volume = {17},
pages = {2065--2113},
number = {12},
abstract = {The goal of this paper is to generalize the hydrostatic reconstruction
technique introduced in Ref. 2 for the shallow water system to more
general hyperbolic systems with source term. The key idea is to interpret
the numerical scheme obtained with this technique as a path-conservative
method, as defined in Ref. 35. This generalization allows us, on
the one hand, to construct well-balanced numerical schemes for new
problems, as the two-layer shallow water system. On the other hand,
we construct numerical schemes for the shallow water system with
better well-balanced properties. In particular we obtain a Roe method
which solves exactly every stationary solution, and not only those
corresponding to water at rest.},
file = {Castro07.pdf:Castro07.pdf:PDF},
keywords = {nonconservative products; finite volume method; well-balanced schemes;
approximate Riemann solvers; Godunov methods; Roe methods; relaxation
methods; high order methods},
owner = {olivier},
timestamp = {2008.05.03}
}
@ARTICLE{Cavallini08,
author = {Cavallini, N. and Caleffi, V. and Coscia, V.},
title = {Finite volume and WENO scheme in one-dimensional vascular system
modelling},
journal = {Computers and Mathematics with Applications},
year = {2008},
volume = {56},
pages = {2382--2397},
abstract = {A finite volume and WENO model is developed, validated and applied
to a one-dimensional numerical investigation of the vascular system.
Suitable balance laws are spatially integrated using a finite volume
WENO approach. Time integration is performed using a five steps,
fourth order accurate Runge–Kutta strong stability preserving scheme.
A detailed investigation of different sets of reflecting and non-reflecting
boundary conditions is performed to achieve a correct representation
of limited portions of the vascular system. Moreover, special attention
is devoted to the numerical discretisation of the source term. Finally,
as an application of the whole model, the effect of an abdominal
aorta aneurysm on the blood flow is evaluated.},
doi = {10.1016/J.camwa.2008.05.039},
file = {Cavallini08.pdf:Cavallini08.pdf:PDF},
keywords = {finite volume methods; one-dimensional flow models; blood flow models;
non-reflecting boundary conditions; abdominal aorta aneurysms},
owner = {olivier},
timestamp = {2011.02.23}
}
@INCOLLECTION{Cavallini10,
author = {Cavallini, Nicola and Coscia, Vincenzo},
title = {One-dimensional Modelling of Venous Pathologies: Finite Volume and
WENO Schemes},
booktitle = {Advances in Mathematical Fluid Mechanics},
publisher = {Springer Berlin Heidelberg},
year = {2010},
editor = {Rannacher, Rolf and Sequeira, Ad\'elia},
pages = {147-170},
abstract = {An efficient and accurate numerical scheme, based on Finite Volumes
and WENO (Weighted Essentially Non-Oscillatory) techniques, is used
to implement a one-dimensional model of the venous network of the
inferior limb, that includes a suitable modelling of venous valves.
The model is applied to the physiological as well as to the pathological
situation, with data obtained experimentally using an Echo-Color
Doppler device.},
affiliation = {Research Center “Mathematics for Technology”, University of Ferrara,
Scientific-Technological Campus, 44100 Ferrara, Italy},
file = {Cavallini10.pdf:Cavallini10.pdf:PDF},
isbn = {978-3-642-04068-9},
keyword = {Mathematics},
keywords = {blood flow; finite volume},
owner = {olivier},
timestamp = {2011.03.10},
url = {http://dx.doi.org/10.1007/978-3-642-04068-9_9}
}
@PHDTHESIS{Cerdan01,
author = {Cerdan, O.},
title = {Analyse et mod{\'e}lisation du transfert de particules solides {\`a}
l'{\'e}chelle de petits bassins versants cultiv{\'e}s},
school = {Universit{\'e} d'Orl{\'e}ans},
year = {2001},
month = jun,
file = {Cerdan01.pdf:Cerdan01.pdf:PDF},
owner = {olivier},
timestamp = {2008.05.05}
}
@ARTICLE{Cherif04,
author = {Ch\'erif, R. and Robert, J.-L. and Lagac\'e, R.},
title = {Optimisation des parametres Green et Ampt pour un modèle conceptuel
pluie-infiltration-ruissellement},
journal = {Canadian biosystems engineering},
year = {2004},
volume = {46},
pages = {7--14},
file = {Cherif04.pdf:Cherif04.pdf:PDF},
owner = {olivier},
timestamp = {2009.01.11}
}
@PHDTHESIS{Chahinian04,
author = {Chahinian, N.},
title = {Param{\'e}trisation multi-crit{\`e}re et multi-{\'e}chelle d'un mod{\`e}le
hydrologique spatialis{\'e} de crue en milieu agricole},
school = {universit{\'e} de Montpellier II--sciences et techniques de Languedoc},
year = {2004},
month = jan,
file = {Chahinian04.pdf:Chahinian04.pdf:PDF},
owner = {olivier},
timestamp = {2008.05.04}
}
@ARTICLE{Chahinian05,
author = {Chahinian, Nan\'ee and Moussa, Roger and Andrieux, Patrick and Voltz,
Marc},
title = {Comparison of infiltration models to simulate flood events at the
field scale},
journal = {Journal of Hydrology},
year = {2005},
volume = {306},
pages = {191--214},
abstract = {Most runoff simulation and inﬁltration models have been developed
at the global-catchment scale or the local-soil column scale. Few
models have been speciﬁcally developed at the scale of agricultural
ﬁelds and there are no guidelines to help modellers choose an adequate
model to simulate overland ﬂow and hence analyse the impact of different
soil management practices on ﬂood generation. A comparison is undertaken
to select and calibrate models that simulate Hortonian overland ﬂow
at the ﬁeld or small plot scale. The proposed methodology couples
a runoff production model to a unit hydrograph transfer function.
Four different models were tested: Philip, Morel-Seytoux, Horton
and SCS. These models differ by their mathematical structure and
the parameters to be calibrated while input hydrologic data are the
same site data: rainfall/runoff and initial water content. The models
are calibrated on 14 events and validated on 14 others. The results
of both the calibration and validation phases are compared on the
basis of their performance with regards to six objective criteria,
three global criteria and three relative criteria representing volume,
peakﬂow, and the root mean square error. The ﬁrst type of criteria
gives more weight to strong events whereas the second considers all
events to be of equal weight. The results show that the calibrated
parameter values are dependent on the type of objective criteria
used. Furthermore, when analysing the performance of the six objective
criteria used, it can be seen that the global volume, global RMSE
and relative peakﬂow criteria give the best compromise between bias
and precision. Within the selected modelling framework, Morel-Seytoux’s
model performed better than the other three and the SCS gave the
worst results. Horton’s model showed to be more consistent in overall
performance than Philip’s
model. Results also highlight problems related to the simulation of
low ﬂow events and intermittent rainfall events.},
file = {Chahinian05.pdf:Chahinian05.pdf:PDF},
keywords = {Inﬁltration model; Runoff; Field scale; Model calibration},
owner = {olivier},
timestamp = {2010.05.03}
}
@ARTICLE{Chalons,
author = {Chalons, Christophe and Coquel, Fr\'ed\'eric and Godlewski, Edwige
and Raviart, Pierre-Arnaud and Seguin, Nicolas},
title = {Godunov-type schemes for hyperbolic systems with parameter dependent
source. The case of Euler system with friction.},
journal = {A para{\^i}tre dans M3AS},
year = {0000},
volume = {Rapport interne du LJLL R09039},
abstract = {Well balanced or asymptotic preserving schemes are receiving an increasing
amount of interest. This paper gives a precise setting for studying
both properties in the case of Euler system with friction. We derive
a simple solver which, by construction, preserves discrete equilibria
and reproduces at the discrete level the same asymptotic behavior
as that of the solutions of the continuous system. Numerical illustrations
are convincing and show that not all methods share these properties.},
file = {Chalons.pdf:Chalons.pdf:PDF},
keywords = {friction; asymptotic preserving; Riemann solver; well-balanced},
owner = {olivier},
timestamp = {2010.07.04}
}
@ARTICLE{Chanson06,
author = {Chanson, Hubert},
title = {Solutions analytiques de l'onde de rupture de barrage sur plan Horizontal
et Inclin\'e},
journal = {La Houille Blanche},
year = {2006},
pages = {76--86},
number = {3},
abstract = {Dam break waves have been responsible for numerous losses and tragedies.
The present work is focused on simple solutions of the dam break
wave problem using the Saint-Venant equations Theoretical solutions
are developed for instantaneous dam break of semi-infinite reservoir
in initially-dry channels. Both laminar and turbulent flow conditions
are considered. Solutions for horizontal inverts are compared successfully
with previous experimental results, and they are then extended to
sloping channels. The results yield a series of simple analytical
solutions that are well-suited for educational purposes as well as
for emergency services.},
doi = {10.1051/lhb:200603012},
file = {Chanson06.pdf:Chanson06.pdf:PDF},
keywords = {Dam break wave; Analytical solutions; Saint-Venant equations; Turbulent
and laminar flows; horizontal and sloping channels; shallow flow
equations},
owner = {Fred. DARBOUX},
timestamp = {2008.07.24}
}
@ARTICLE{Chanson05a,
author = {Chanson, Hubert},
title = {Applications of the {S}aint-{V}enant {E}quations and {M}ethod of
{C}haracteristics to the {D}am {B}reak {W}ave {P}roblem},
journal = {Report No. CH55/05},
year = {2005},
volume = {Dept. of Civil Engineering, The University of Queensland, Brisbane,
Australia, May},
pages = {135 pages},
month = May,
file = {Chanson05a.pdf:Chanson05a.pdf:PDF},
owner = {olivier},
timestamp = {2010.02.22}
}
@ARTICLE{Charbeneau09,
author = {Charbeneau, Randall J. and Jeong, Jaehak and Barrett, Michael E.},
title = {Physical {M}odeling of {S}heet {F}low on {R}ough {I}mpervious {S}urfaces},
journal = {Journal of Hydraulic Engineering},
year = {2009},
volume = {135},
pages = {487--494},
number = {6},
month = Jun,
abstract = {Abstract: This paper presents results from an extensive experimental
study of sheet ﬂow on rough impervious surfaces that are used to
represent highway pavement. Experiments were performed on three surfaces
under no-rainfall and simulated rainfall conditions, and with slopes
of 1, 2, and 3%. Measurements include ﬂow depth and unit discharge.
Turbulent boundary layer theory for a rough surface is used to describe
the depth-discharge relationship, resulting in a model with a single
parameter directly related to the surface roughness. Comparisons
are made with Manning’s equation, and the variability of the Manning
coefﬁcient is assessed. Hydraulic effects of rainfall are generally
found to be small compared to other factors.},
doi = {10.1061/͑ASCE͒HY.1943-7900.0000043},
file = {Charbeneau09.pdf:Charbeneau09.pdf:PDF},
keywords = {sheet flow; surface roughness; rainfall; hydraulic models; highway
and roads; slopes},
owner = {olivier},
timestamp = {2010.04.22}
}
@ARTICLE{Chen06,
author = {Chen, Li and Young, Michael H.},
title = {Green-Ampt infiltration model for sloping surfaces},
journal = {Water Resources Research},
year = {2006},
volume = {42, W07420},
pages = {1--9},
abstract = {[1] This work quantifies and explains the direct physical effects
of slope angle on infiltration and runoff generation by extending
the Green-Ampt equation onto sloping surfaces. A new extended solution
using identical precipitation hydrographs was compared to the original
formulation and then used to calculate the infiltration and runoff
generation for different slope angles but for identical horizontal
projection lengths. Homogeneous and isotropic soil is assumed, and
two different boundary conditions for vertical rainfall are studied:
ponded infiltration and infiltration under steady rainfall. Infiltration
under unsteady rainfall was found to be similar to cases with steady
rainfall. Both theoretical and numerical results show that infiltration
increases with increasing slope angle. For cases with ponded infiltration
the slope effect was generally not significant for mild to moderate
slopes, but the slope effect became more important for
low-intensity and short-duration rainfall events, especially as it
delayed the time for ponding. It was also found that the cumulative
vertical infiltration depth (Ihp) at ponding (or the initial loss)
increases with increasing slope angle. The model was compared to
Richards’ equation on horizontal and sloping surfaces and found to
perform well. The model’s applicability for nonuniform slopes was
discussed, and it was found that the model is generally applicable
for isotropic and mildly anisotropic soils except for some small-scale
topographic elements. Finally, the occurrence of nonvertical rainfall
could increase runoff with increasing slope angle when rainfall deflects
a large angle to upslope.},
file = {Chen06.pdf:Chen06.pdf:PDF},
keywords = {Green-Ampt; slopîng surfaces;},
owner = {olivier},
timestamp = {2010.04.23}
}
@ARTICLE{Chen09,
author = {Chen, Y.-C. and Kao, S.-P. and Lin, J.-Y. and Yang, H.-C.},
title = {Retardance coefficient of vegetated channels estimated by the Froude
number},
journal = {Ecological Engineering},
year = {2009},
volume = {35},
pages = {1027 - 1035},
number = {7},
doi = {DOI: 10.1016/j.ecoleng.2009.03.002},
file = {Chen09.pdf:Chen09.pdf:PDF},
issn = {0925-8574},
keywords = {Aquatic plants},
owner = {olivier},
timestamp = {2009.07.21},
url = {http://www.sciencedirect.com/science/article/B6VFB-4W6FNFC-1/2/fe8d84a31abce3e557bcd012e73fa7ad}
}
@TECHREPORT{Cheng75,
author = {Cheng, Edmond D.H.},
title = {Numerical analysis of one-dimensional water infiltration},
institution = {Laboratory and finite element method of analyzing one-dimensional
water infiltration into unsatured layered hawaiian soils},
year = {1975},
number = {92},
abstract = {In attempting to numerically solve the nonlinear moisture flow equation,
the Galerkin process, which bears a great similarity to direct methods
of the calculus of variations, and the Continuous System Mode Zing
Peoqram (CSMP) approach have been emp Loued. In the finite element
formulation of the governing equation, systems of nonlinear algebraic
equations were developed on the basis of linear two-dimensional triangular
elements. These nonlinear algebraic equations were solved simultaneous
at each time step, by a programmed logic of i.teoatrione, In the
CSMP approach, Boltzmann's function application and layered soils
formulation were demonstrated in obtaining horizontal and vertical
moisture profiles.
The second and third degrees of polynomial interpretations of moisture
diffusivity, D(\theta), and hydraulic conductivity, K(\theta), of
the media were conducted. However, it was established that the former
representation had only very limited applicability (as far as some
Hawaiian soils are concerned), because a second degree polynomial
can accurately describe the D(\theta) and K(\theta) functions
only of the wetter portion of the D(\theta) and K(\theta) vs. moisture
content, \theta, curves. The finite element, CSMP, and finite difference
solutions were investigated and compared for Wahiawa soils with lateral
moisture movement. Vertical moisture profi Lee for the
Molokai soils and Tantalus silty clay loams were also investigated
by means of the finite element method and the CSMP approach, re-
spectively.},
file = {Cheng75.pdf:Cheng75.pdf:PDF},
owner = {olivier},
timestamp = {2010.04.24}
}
@ARTICLE{Cheng00,
author = {Cheng, H. -P. and Yeh, G. -T. and Cheng, J. -R.},
title = {A numerical model simulating reactive transport in shallow water
domains: model development and demonstrative applications},
journal = {Advances in Environmental Research},
year = {2000},
volume = {4},
pages = {187 - 209},
number = {3},
abstract = {We present a two-dimensional depth-averaged numerical model simulating
reactive transport in shallow water domains subject to given flow
conditions. A new approach is used to account for more conceivable
kinetically-controlled chemical reactions than have been included
in previous models. In this model, a chemical may dissolve in the
water column or in the interstitial water of the bed sediments, react
with other dissolved chemicals to form new chemicals also in the
dissolved phase, or be sorbed onto sediments to become particulate
chemicals. To save computer time, we employ a predictor-corrector
strategy to deal with the reactive transport equations of mobile
substances where transport equations are computed in the predictor
step with reaction rates estimated at the previous time step, and
rate correction is achieved node by node in the corrector step to
obtain the concentration distributions at the present time step.
For immobile substances, we solve the corresponding ordinary differential
equations together with the corrector equations of mobile substances
in the corrector step by using the Newton-Raphson method. Two examples
are demonstrated to show the capability of our model.},
doi = {DOI: 10.1016/S1093-0191(00)00015-0},
file = {Cheng00.pdf:Cheng00.pdf:PDF},
issn = {1093-0191},
keywords = {Reactive transport},
owner = {olivier},
timestamp = {2010.02.01},
url = {http://www.sciencedirect.com/science/article/B6W75-412RWTW-2/2/3e18b73a2485c63d4435e1a37124e8e2}
}
@ARTICLE{Chertock06,
author = {Chertock, Alina and Kurganov, Alexander and Petrova, Guergana},
title = {Finite-{V}olume-{P}article {M}ethods for {M}odels of {T}ransport
of {P}ollutant in {S}hallow {W}ater},
journal = {Journal of Scientific Computing},
year = {2006},
volume = {27},
pages = {189-199},
month = jun,
abstract = {We present a new hybrid numerical method for computing the transport
of a passive pollutant by a ﬂow. The ﬂow is modeled by the Saint-Venant
system of shallow water equations and the pollutant propagation is
described by a transport equation. The idea behind the new ﬁnite-volume-particle
(FVP) method is to use different schemes for the ﬂow and the pollution
computations: the shallow water equations are numerically integrated
using a ﬁnite-volume scheme, while the transport equation is solved
by a particle method. This way the speciﬁc advantages of each scheme
are utilized at the right place. This results in a signiﬁcantly enhanced
resolution of the computed solution.},
doi = {10.1007/s10915-005-9060-x},
file = {Chertock06.pdf:Chertock06.pdf:PDF},
keywords = {Saint-Venant system of shallow water equations; transport of pollutant;
ﬁnite-volume schemes; particle methods; central-upwind schemes; balance
laws},
owner = {olivier},
timestamp = {2010.01.29}
}
@ARTICLE{Chidyagwai10,
author = {Chidyagwai, Prince and Rivi\`ere, Beatrice},
title = {Numerical modelling of coupled surface and subsurface flow systems},
journal = {Advances in water resources},
year = {2010},
volume = {33},
pages = {92--105},
abstract = {This paper presents and compares several numerical solutions of the
coupled system of Navier–Stokes and Darcy equations. The schemes
are based on combinations of the ﬁnite element method and the discontinuous
Galerkin method. Accuracy and robustness of the methods are investigated
for heterogeneous porous media. The importance of local mass conservation
for ﬁltration problems is also discussed.},
file = {Chidyagwai10.pdf:Chidyagwai10.pdf:PDF},
keywords = {Navier-Stokes equations; Darcy's law; discontinuous Galerkin finite
element method; Beavers-Joseph-Saffman; mass conservation; fractured
porous media},
owner = {olivier},
timestamp = {2010.06.13}
}
@MISC{Chinnayya99,
author = {Chinnayya, Ashwin and Le{R}oux, A.-Y.},
title = {A new {G}eneral {R}iemann {S}olver for the {S}hallow {W}ater equations,
with friction and topography},
howpublished = {http://www.math.ntnu.no/conservation/1999/021.html},
year = {1999},
note = {Preprint},
file = {Chinnayya99.pdf:Chinnayya99.pdf:PDF},
owner = {olivier},
timestamp = {2009.08.27}
}
@ARTICLE{Cho09,
author = {Sung Eun Cho},
title = {Infiltration analysis to evaluate the surficial stability of two-layered
slopes considering rainfall characteristics},
journal = {Engineering Geology},
year = {2009},
volume = {105},
pages = {32 - 43},
number = {1-2},
abstract = {Shallow slope failures in residual soil during periods of prolonged
infiltration are common throughout the world. Using a one-dimensional
infiltration model and an infinite slope analysis, this study examines
an approximate method of determining how infiltration influences
the surficial stability of two-layered slopes. The method extends
Moore's infiltration model, which is based on the Green-Ampt model,
to cover more general situations, including those where water moves
upward from a perched water table in decreasingly permeable soil.
The method has also been used to evaluate the likelihood of a shallow
slope failure being induced by a particular rainfall event. In making
this evaluation, the method takes into accounts the rainfall intensity
and duration of various return periods in a two-layered soil profile.
A comparison of the results of the infiltration model with the results
of numerical analyses shows that, with the use of properly estimated
input parameters, the proposed model compares reasonably well with
other model that rely on more rigorous finite element method.},
doi = {DOI: 10.1016/j.enggeo.2008.12.007},
file = {Cho09.pdf:Cho09.pdf:PDF},
issn = {0013-7952},
keywords = {Infiltration},
owner = {olivier},
timestamp = {2010.05.12},
url = {http://www.sciencedirect.com/science/article/B6V63-4V94X17-1/2/0e78d6aa6180b4bb2b1ff82c164bed93}
}
@ARTICLE{Choi05,
author = {Choi, Eunwoo and Ryu, Dongsu},
title = {Numerical relativistic hydrodynamics based on the total variation
diminishing scheme},
journal = {New Astronomy},
year = {2005},
volume = {11},
pages = {116 - 129},
number = {2},
abstract = {This paper describes a multidimensional hydrodynamic code which can
be used for studies of relativistic astrophysical flows. The code
solves the special relativistic hydrodynamic equations as a hyperbolic
system of conservation laws based on the total variation diminishing
(TVD) scheme. It uses a new set of conserved quantities and employs
an analytic formula for transformation from the conserved quantities
in the reference frame to the physical quantities in the local rest
frame. Several standard tests, including relativistic shock tubes,
a relativistic wall shock, and a relativistic blast wave, are presented
to demonstrate that the code captures discontinuities correctly and
sharply in ultrarelativistic regimes. The robustness and flexibility
of the code are demonstrated through test simulations of the relativistic
Hawley-Zabusky shock and a relativistic extragalactic jet.},
doi = {DOI: 10.1016/j.newast.2005.06.010},
file = {Choi05.pdf:Choi05.pdf:PDF},
issn = {1384-1076},
keywords = {Hydrodynamics; numerical methods; relativity},
owner = {olivier},
timestamp = {2010.06.03},
url = {http://www.sciencedirect.com/science/article/B6TJK-4GMJ7RX-1/2/778ef25bfa6a5a4979e5f44a20b6d7ba}
}
@BOOK{Chow59,
title = {Open-Channel Hydraulics},
publisher = {Mc{G}raw-Hill},
year = {1959},
editor = {New York},
author = {Chow, V.~T.},
owner = {olivier},
timestamp = {2009.09.28}
}
@INBOOK{Chow88a,
chapter = {9 - Distributed flow routing},
pages = {272--309},
title = {Applied hydrology},
publisher = {Mc{G}raw-Hill Book Company},
year = {1988},
author = {Ven Te Chow and David R. Maidment and Larry W. Mays},
series = {water resources and environmental engineering},
file = {Chow88a.pdf:Chow88a.pdf:PDF},
keywords = {MacCormack; hydrology; scheme; shallow flow equation},
owner = {Fred. DARBOUX},
timestamp = {2008.07.24}
}
@BOOK{Chow88b,
title = {Applied Hydrology},
publisher = {Mc{G}raw-Hill Book Company},
year = {1988},
author = {Chow, V. T. and Maidment, David R. and Mays, Larry W.},
owner = {olivier},
timestamp = {2010.05.15}
}
@ARTICLE{Chung08,
author = {Chung, W.-H. and Smith, James~A.},
title = {Viscosity-excluded formulations of 2-{D} river flow with a new wetting
and drying algorithm},
journal = {Advances in Water Resources},
year = {2008},
volume = {31},
pages = {298-312},
abstract = {An eﬃcient method for simulating 2-D river ﬂow is developed in which
horizontal turbulent shears are omitted from the 2-D depth-averaged
momentum equations. It is shown that a pseudo-viscosity can be reproduced
to take into account the lost shear action, by incorporating the
vertically integrated continuity equation to the momentum equations
and transforming the latter into a discrete integral form. To simulate
river ﬂows with wet and dry areas, negative water depths are allowed
when solving the continuity equation. The concept of negative water
depth enables us to track ﬂow boundaries with about the same accuracy
but much less eﬀort as compared with traditional numerical methods.
An optimal threshold value deﬁning dry areas is ﬁrst obtained by
one-dimensional theoretical analysis and then sought by trial-and-error
for two-dimensional ﬂow simulation with tolerable node-to-node spurious
oscillations, while mass is best conserved. Numerical solutions using
the new procedure are compared with the one-dimensional benchmark
solution of the Saint Venant equations and the experimental data
from a two-stage channel. Robustness of the present approach is also
tested through the study of water ﬂow in a natural river and a hypothetical
channel with several bumps.},
file = {Chung08.pdf:Chung08.pdf:PDF},
keywords = {Eddy viscosity; Negative water depth; Switching scheme; Mass conservation},
owner = {olivier},
timestamp = {2010.01.27}
}
@ARTICLE{Cockerham92,
author = {Cockerham, C. and Yoganathan, A. P.},
title = {A Computer Method for Simulation of Cardiovascular Flow Fields: Validation
of Approach},
journal = {Journal of Computational Physics},
year = {1992},
volume = {99},
pages = {271--287},
abstract = {An existing pressure correction method to model unsteady flow with
arbitrarily moving boundaries has been adapted to simulate three-dimensional
blood flow in compliant vessels. This noniterative method, which
is first-order time accurate, solves the three-dimensional unsteady
Navier-Stokes equations with arbitrarily moving boundaries or the
no slip boundary condition. It is capable of realistically modeling
blood flow in the heart, since it allows the simulation of both passive
tissue (e.g., heart valves) and active tissue (e.g., heart muscle
fibers). The boundaries, which represent cardiovascular tissue, are
displaced by the fluid motion. When they are moved, the boundaries
have the ability to exert a force which opposes fluid motion. The
force the boundary exerts is assumed to be proportional to strain.
The results of simulating pulsatile flow through a flexible tube
are presented, as well as a comparison to Womersley's analytic approximate
solution for axisymetric pulsatile flow in a flexible tube.},
file = {Cockerham92.pdf:Cockerham92.pdf:PDF},
keywords = {blood flow; vessels; Navier-Stokes; flexible tube},
owner = {olivier},
timestamp = {2011.03.03}
}
@ARTICLE{Colgan87,
author = {Colgan, Tracy and Terrill, Robert M.},
title = {On peristaltic transport of fluids},
journal = {Journal of theoretical and applied mechanics},
year = {1987},
volume = {6},
pages = {3--22},
number = {1},
abstract = {An analytic solution of the Navier-Stokes equations for peristaltic
pipe flow valid for all Reynolds number is found. The solution represents
a new approach to peristaltic flows and its features illuminate much
of the previous numerical and analytical research on this problem.
The solution could also have considerable importance in the peristaltic
pumping of industrial fluids.
Une solution explicite des \'equations de Navier-Stokes, valable pour
tous les nombres de Reynolds est obtenue. Elle permet d'aborder d'une
nouvelle mani\`ere l'\'ecoulement p\'eristaltique et \'eclaire les
\'etudes ant\'erieures analytiques et num\'eriques. Cette solution
est susceptible d'avoir une grande importance pour le pompage p\'eristaltique
des fluides en milieu industriel.},
file = {Colgan87.pdf:Colgan87.pdf:PDF},
owner = {olivier},
timestamp = {2011.03.03}
}
@INPROCEEDINGS{Coquel08,
author = {Coquel, F. and Godlewski, E. and Raviart, P.-A. and Seguin, N.},
title = {An asymptotic preserving scheme for Euler equations with gravity
and friction},
booktitle = {Finite volumes for complex applications V, Aussois, France, 8-13
juin 2008, p. 305--312, ISTE, Londres.},
year = {2008},
abstract = {We are interested in the approximation of the one-dimensional Euler
equations with gravity and friction. When the friction coefficient
becomes large, the solutions of this system formally satisfy a Darcy-like
system. We propose an explicit numerical scheme which enables us
to recover this asymptotic behavior whatever the space step is. Some
numerical tests attest this good behavior.},
file = {Coquel08.pdf:Coquel08.pdf:PDF},
keywords = {asymptotic preserving scheme; source term; approximate Riemann solver},
owner = {olivier},
timestamp = {2010.06.12}
}
@TECHREPORT{Cordier07,
author = {Cordier, St\'ephane and Darboux, Fr\'ed\'eric and Delestre, Olivier
and James, Fran\c{c}ois},
title = {Etude d'un mod{\`e}le de ruissellement {1D}},
institution = {Universit{\'e} d'Orl{\'e}ans},
year = {2007},
address = {France},
month = {10 @dec},
file = {Cordier07.pdf:Cordier07.pdf:PDF},
keywords = {shallow flow equations; ANR METHODE; finite volume; model; hydrostatic
reconstruction; well-balanced scheme},
owner = {Fred. DARBOUX},
timestamp = {2008.08.11}
}
@ARTICLE{Cornish34,
author = {Cornish, Vaughan},
title = {Ocean waves and kindred geophysical phenomena},
journal = {Cambridge University Press},
year = {1934},
file = {Cornish34.pdf:Cornish34.pdf:PDF},
keywords = {roll-waves},
owner = {olivier},
timestamp = {2010.06.27}
}
@BOOK{Cornish10,
title = {Waves of the sea and other water waves},
publisher = {London, T. Fisher Unwin},
year = {1910},
author = {Cornish, Vaughan},
file = {Cornish10.pdf:Cornish10.pdf:PDF},
keywords = {waves; tides; roll-waves},
owner = {olivier},
timestamp = {2010.06.27}
}
@ARTICLE{Cornish07,
author = {Cornish, Vaughan},
title = {Progressive Waves in Rivers},
journal = {The Geographical Journal},
year = {1907},
volume = {29},
pages = {23--31},
number = {1},
copyright = {Copyright © 1907 The Royal Geographical Society (with the Institute
of British Geographers)},
file = {Cornish07.pdf:Cornish07.pdf:PDF},
issn = {00167398},
jstor_articletype = {primary_article},
jstor_formatteddate = {Jan., 1907},
keywords = {roll-waves; photo},
owner = {olivier},
publisher = {Blackwell Publishing on behalf of The Royal Geographical Society
(with the Institute of British Geographers)},
timestamp = {2010.06.29},
url = {http://www.jstor.org/stable/1776113}
}
@ARTICLE{Cotter10,
author = {Cotter, Colin and Bokhove, Onno},
title = {Variational water-wave model with accurate dispersion and vertical
vorticity},
journal = {J. Eng. Math.},
year = {2010},
volume = {67},
pages = {33--54},
abstract = {Abstract A new water-wave model has been derived which is based on
variational techniques and combines a depth-averaged vertical (component
of) vorticity with depth-dependent potential ﬂow. The model facilitates
the further restriction of the vertical proﬁle of the velocity potential
to n-th order polynomials or a ﬁnite-element proﬁle with a small
number of elements (say), leading to a framework for efﬁcient modelling
of the interaction of steepening and breaking waves near the shore
with a large-scale horizontal ﬂow. The equations are derived from
a constrained variational formulation which leads to conservation
laws for energy, mass, momentum and vertical vorticity. It is shown
that the potential-ﬂow water-wave equations and the shallow-water
equations are recovered in the relevant limits. Approximate shock
relations are provided, which can be used in numerical schemes to
model breaking waves.},
doi = {10.1007/s10665-009-9346-3},
file = {Cotter10.pdf:Cotter10.pdf:PDF},
keywords = {bores; coastal engineering; variational principles; wave-current interactions;
wave},
owner = {olivier},
timestamp = {2010.11.12}
}
@ARTICLE{Craya52,
author = {Craya, A.},
title = {The criterion for the possibility of roll-wave formation},
journal = {Proceedings of the Gravity Waves Symposium, U.S. National Bureau
of Standards, Circular 521},
year = {1952},
pages = {141--151},
file = {Craya52.pdf:Craya52.pdf:PDF},
owner = {olivier},
timestamp = {2010.04.21}
}
@ARTICLE{Crnjaric06,
author = {Crnjaric-Zic, N. and Vukovic, S. and Sopta, L.},
title = {On different flux splittings and flux functions in WENO schemes for
balance laws},
journal = {Computers \& Fluids},
year = {2006},
volume = {35},
pages = {1074--1092},
number = {10},
month = {December},
abstract = {In this paper we focus our attention on obtaining well-balanced schemes
for balance laws by using Marquina's flux in combination with the
finite difference and finite volume WENO schemes. We consider also
the Rusanov flux splitting and the HLL approximate Riemann solver.
In particular, for the presented numerical schemes we develop corresponding
discretizations of the source term, based on the idea of balancing
with the flux gradient. When applied to the open-channel flow and
to the shallow water equations, we obtain the finite difference WENO
scheme with Marquina's flux splitting, which satisfies the approximate
conservation property, and also the balanced finite volume WENO scheme
with Marquina's solver satisfying the exact conservation property.
Finally, we also present an improvement of the balanced finite difference
WENO scheme with the Rusanov (locally Lax-Friedrichs) flux splitting,
we previously developed in [Vukovic S, Sopta L. ENO and WENO schemes
with the exact conservation property for one-dimensional shallow
water equations. J Comput Phys 2002;179:593-621].},
citeulike-article-id = {822216},
citeulike-linkout-0 = {http://dx.doi.org/10.1016/j.compfluid.2005.08.005},
citeulike-linkout-1 = {http://www.sciencedirect.com/science/article/B6V26-4HTCTCR-1/2/796abd7ecf3ba59ad90ad8b5f42f3f70},
doi = {10.1016/j.compfluid.2005.08.005},
file = {Crnjaric06.pdf:Crnjaric06.pdf:PDF},
keywords = {flux-splitting, weno},
owner = {olivier},
posted-at = {2006-08-30 16:35:08},
priority = {2},
timestamp = {2010.03.15},
url = {http://dx.doi.org/10.1016/j.compfluid.2005.08.005}
}
@ARTICLE{Crnkovic09,
author = {Crnkovic, Bojan and Crnjaric-Zic, Nelida and Kranjcevic, Lado},
title = {Improvements of semi-implicit schemes for hyperbolic balance laws
applied on open channel flow equations},
journal = {Computers \& Mathematics with Applications},
year = {2009},
volume = {58},
pages = {292 - 309},
number = {2},
doi = {DOI: 10.1016/j.camwa.2009.04.004},
file = {Crnkovic09.pdf:Crnkovic09.pdf:PDF},
issn = {0898-1221},
keywords = {Open channel equations},
owner = {olivier},
timestamp = {2009.07.21},
url = {http://www.sciencedirect.com/science/article/B6TYJ-4W8KHNY-2/2/5dc01ff709a5473e083234532dc139ae}
}
@PHDTHESIS{Crossley99,
author = {Crossley, A.~J.},
title = {Accurate and efficient numerical solutions for the Saint Venant equations
of open channel flow},
school = {university of Nottingham},
year = {1999},
month = oct,
abstract = {Within the field of hydraulics there is a growing trend towards the
use of computer based models, which have proven to be an invaluable
tool in engineering. A range of commercial packages is available
which encompass different mathematical models and a variety of solution
strategies. A number of problems can be identified with the software
currently available, and as aresult, research continues into developing
better numerical techniques for computational hydraulics. The issues
most often addressed by researchers consider the application of faster
and more accurate numerical methods, many of which were originally
developed for gas dynamics problems. There has been a growing trend
in favour of Riemann based methods constructed within the finite
volume framework. Such methods are noted for their good conservation
and shock capturing capabilities. However, the computational cost
of employing these algorithms can lead to excessively long run times,
particularly when higher order mathematical models are used. This
often is as a result of stability constraints placed upon explicit
schemes, which require the smallest possible time step permitted
throughout the grid, to be applied globally. One possibillility for
improving this situation is to use local time stepping, whereby individual
cells are advanced by their own maximum allowable time steps. To
incorporate this concept into a transient model requires the development
of a suitable integration strategy, to ensure that the solution remains
accurate in time. Two such strategies developed for the Euler equations
are considered within this thesis for application to the Saint Venant
equations of open channel flow. Both techniques have been demonstrated
to reduce run times and improve the quality of solutions in the regions
of discontinuities. The investigation considers the first order scheme
of Roe, together with a second order extension constructed using
a flux limiter approach. The effects of using an upwind based source
term treatment, specifically developped for Roe's scheme, are also
considered, and the source term calculations are incorporated into
the LTS framework. Results are presented for a series of steady state
and transient test cases, wich illustrate how local time stepping
can lead to reduced run times and improved solution accuracy. The
results also highlight the benefits of using an upwind source term
treatment, particularly when variations in the channel geometry occur.},
file = {Crossley99.pdf:Crossley99.pdf:PDF},
owner = {olivier},
timestamp = {2008.05.04}
}
@ARTICLE{vanDam00,
author = {van Dam, J.C. and Feddes, R.A.},
title = {Numerical simulation of infiltration, evaporation and shallow groundwater
levels with the Richards equation},
journal = {Journal of Hydrology},
year = {2000},
volume = {233},
pages = {72--85},
abstract = {Analysis of water and solute movement in unsaturated±saturated soil
systems would greatly benefit from an accurate and efficient numerical
solution of the Richards equation. Recently the mass balance problem
has been solved by proper evaluation of the water capacity term.
However, the Darcy fluxes as calculated by various numerical schemes
still deviate significantly due to differences in nodal spacing and
spatial averaging of the hydraulic conductivity K. This paper discusses
a versatile, implicit, backward finite difference scheme which is
relatively easy to implement. Special attention is given to the selection
of a head or flux controlled top boundary condition during the iterative
solution of the Richards equation. The stability of the scheme is
shown for extreme events of infiltration, evaporation and rapidly
fluctuating, shallow groundwater levels in case of two strongly non-linear
soils. For nodal distances of 5 cm, arithmetic means of K overestimate
the soil water fluxes, while geometric means of K underestimate these
fluxes. At smaller nodal distances, arithmetic means of K converge
faster to the theoretical solution than geometric means. In case
of nodal distances of 1 cm and arithmetic averages of K, errors due
to numerical discretization are small compared to errors due to hysteresis
and horizontal spatial variability of the soil hydraulic functions.},
file = {vanDam00.pdf:vanDam00.pdf:PDF},
keywords = {infiltration; modelling; numerical analysis; permeability; Richards
equation; unsaturated flow},
owner = {olivier},
timestamp = {2010.06.06}
}
@BOOK{Danaila03,
title = {Simulation num\'erique en {C}++},
publisher = {Dunod},
year = {2003},
author = {Danaila, Ionut and Hecht, Fr\'ed\'eric and Pironneau, Olivier},
owner = {olivier},
timestamp = {2009.11.25}
}
@TECHREPORT{Darboux09,
author = {Darboux, F. and Razafison, U.},
title = {Quels cas tests expérimentaux pour l'étape 1~?},
year = {2009},
note = {9 pages},
file = {Darboux09.pdf:Darboux09.pdf:PDF},
keywords = {ANR METHODE, overland flow, laboratory experiment, furrow, tillage,
flow depth},
owner = {olivier},
timestamp = {2009.01.11}
}
@BOOK{Debauve93,
title = {Les travaux publics et les ing\'enieurs des ponts et chauss\'ees
depuis le {XVII}e si\`ecle},
publisher = {Vve {C}. {D}unod ({P}aris)},
year = {1893},
author = {Debauve, Alphonse},
file = {Debauve93.pdf:Debauve93.pdf:PDF},
owner = {olivier},
timestamp = {2010.03.15}
}
@PHDTHESIS{Decoene06,
author = {Decoene, Astrid},
title = {Modèle hydrostatique pour les écoulements à surface libre tridimensionnels
et schémas numériques},
school = {Universit\'e Pierre et Marie Curie, Paris 6},
year = {2007},
abstract = {Cette thèse a pour objectif l'approfondissement de l'étude des équations
régissant les écoulements à surface libre en dimension trois. Nous
proposons d'une part une nouvelle formulation variationnelle du problème
hydrostatique aboutissant à un problème semi-discretisé en temps
bien posé. Nous en faisons l'analyse mathématique et nous montrons
quelques résultats numériques obtenus après programmation de l'approximation
de ce problème dans le logiciel Telemac-3D développé au Laboratoire
National d'Hydraulique et Environnement (LNHE) d'edf. D'autre part,
nous étudions la réinterprétation dans le cadre ALE de la méthode
de discrétisation verticale de domaines tridimensionnels appelée
transformation sigma, et nous en proposons une généralisation permettant
d'améliorer la représentation des stratifications dans un écoulement
Finalement, nous présentons un schéma ALE-MURD conservatif pour la
résolution des équations de convection linéaires posées sur un domaine
mobile. Une condition particulière doit être vérifiée afin que le
schéma soit conservatif lorsque le domain bouge effectivement. Nous
montrons comment assurer cette contrainte dans le cas particulier
où le domaine est tridimensionnel et ne bouge que selon la verticale.
Ce résultat est illustré dans le cadre des écoulements à surface
libre en dimension trois.},
file = {Decoene06.pdf:Decoene06.pdf:PDF},
institution = {NDLTD Union Catalog [http://alcme.oclc.org/ndltd/servlet/OAIHandler]
(United States)},
keywords = {Mathematics, équations de Navier-Stokes à surface libre, écoulements
tridimensionnels, modèle hydrostatique, éléments finis, ALE, transformation
sigma, schémas distribués, lois de conservation géométrique},
location = {http://www.scientificcommons.org/24060204},
owner = {olivier},
publisher = {HAL - CCSD},
timestamp = {2009.07.19},
url = {http://tel.archives-ouvertes.fr/tel-00180003/en/}
}
@BOOK{Delannoy06,
title = {Programmer en {C}++},
publisher = {Eyrolles},
year = {2006},
author = {Delannoy, Claude},
owner = {olivier},
timestamp = {2009.11.25}
}
@ARTICLE{Delenne08,
author = {Delenne, Carole and Guinot, Vincent and Cappelaere, Bernard},
title = {Direct sensitivity computation for the Saint-Venant equations with
hydraulic jumps},
journal = {Comptes Rendus Mécanique},
year = {2008},
volume = {336},
pages = {766 - 771},
number = {10},
doi = {DOI: 10.1016/j.crme.2008.09.006},
file = {Delenne08.pdf:Delenne08.pdf:PDF},
issn = {1631-0721},
keywords = {Computational fluid mechanics},
owner = {olivier},
timestamp = {2009.07.21},
url = {http://www.sciencedirect.com/science/article/B6X1C-4TN5MJM-1/2/315de80490696185ec7e86b25eeab33e}
}
@PHDTHESIS{Delestre10b,
author = {Delestre, Olivier},
title = {Simulation du ruissellement d'eau de pluie sur des surfaces agricoles/
rain water overland flow on agricultural fields simulation},
school = {Universit\'e d'Orl\'eans (in French), available from TEL: tel.archives-ouvertes.fr/INSMI/tel-00531377/fr},
year = {2010},
month = Jul,
abstract = {In this work, we aim at developping both a model and a numerical method
adapted to the simulation of rainfall runoff on agricultural fields.
The model used is a system of partial differential equations for
shallow water flows: namely the system of Saint-Venant. Rain and
infiltration are treated as source terms and with a coupled model
of infiltration. Because of the hyperbolicity and conservativity
properties, we are using a finite volume scheme with the hydrostatic
reconstruction. This reconstruction allows us to deal with stationary
equilibria and wet/dry transitions due to rainfall events. First,
a systematic comparison on analytic solutions is achieved between
various numerical fluxes, two second order reconstructions (a MUSCL
and a modified ENO reconstructions) and different numerical treatment
of the friction term. This allows us to choose a numerical method
adapted to runoff simulation. Moreover it is able to catch roll waves
phenomenons. Then we are interested in the rain and infiltration
treatment. Infiltration is modeled thanks to the Green Ampt model.
This method is thereafter generalized to two dimensions and validated
on experimental results obtained by the INRA of Orl\'eans and the
IRD. The chosen numerical method has been implemented in an C++ open-source
software for rainfall runoff on agricultural fields simulations:
FullSWOF_2D.},
file = {Delestre10b.pdf:Delestre10b.pdf:PDF},
keywords = {obverland flow; Saint-Venant; well-balanced scheme; finite volume;
hydrostatic reconstruction; source term; friction; rain; infiltration;
C++; shallow water; numerical fluxes; roll waves; analytic solutions},
owner = {olivier},
timestamp = {2011.03.05}
}
@MASTERSTHESIS{Delestre08a,
author = {Delestre, O.},
title = {Ecriture d'un code C++ pour la simulation en hydrologie},
school = {Universit{\'e} d'Orl{\'e}ans, disponible sur : http://dumas.ccsd.cnrs.fr/dumas-00446163/fr/},
year = {2008},
month = {septembre},
note = {Encadrant : Fr\'ed\'eric Darboux},
abstract = {Shallow water system is a typical model for the simulation of overland
flow. We had a 1d fortran program to simulate one dimension flow,
based on a well-balanced method. This code was validated on several
analytical and experimental test cases. Nevertheless, this code was
ill-structured and did not allow for the development of modules.
As such this code became difficult to develop further. During this
internship, we developed a c++ code for overland flow. First developed
in one dimension, with then develop a code simulating the overland
flow over a surface. An analysis of the mathematical model allowed
us to point out the programming constraints that we will have to
face. Simulations based on the c++ 1d program were compared with
the simulations of the fortran program. Some differences in the results
remaind to be explained before the c++ 1d code could be considered
as validated. The changes carried out on the c++ 1d code will be
directly implemented into the c++ 2d code.},
file = {Delestre08a.pdf:Delestre08a.pdf:PDF},
keywords = {Numerical modelling; overland flow, C++; shallow-flow equations; well-balanced
scheme; 2D},
owner = {olivier},
timestamp = {2008.10.01}
}
@INPROCEEDINGS{Delestre09b,
author = {Delestre, Olivier and Cordier, St\'ephane and James, Fran\c{c}ois
and Darboux, Fr\'ed\'eric},
title = {Simulation of rain-water overland-flow},
booktitle = {Proceedings of the 12th International Conference on Hyperbolic Problems,
\rm University of Maryland, College Park (USA), 2008, E. Tadmor,
J.-G. Liu and A. Tzavaras Eds., Proceedings of Symposia in Applied
Mathematics 67, Amer. Math. Soc., 537--546},
year = {2009},
file = {Delestre09b.pdf:Delestre09b.pdf:PDF},
owner = {olivier},
timestamp = {2009.07.21}
}
@INPROCEEDINGS{Delestre09,
author = {Delestre, Olivier and James, Fran\c{c}ois},
title = {Simulation of rainfall events and overland flow},
booktitle = {Proceedings of X International Conference Zaragoza-Pau on Applied
Mathematics and Statistics, \rm Jaca, Spain, september 2008, Monograf\'ias
Matem\'aticas Garc\'ia de Galdeano},
year = {2009},
file = {Delestre09.pdf:Delestre09.pdf:PDF},
owner = {olivier},
timestamp = {2009.07.21}
}
@UNPUBLISHED{Delestre11,
author = {Delestre, Olivier and Lagr\'ee, Pierre-Yves},
title = {A "well balanced" finite volume scheme for blood flow simulation},
note = {submitted},
file = {Delestre11.pdf:Delestre11.pdf:PDF},
owner = {olivier},
timestamp = {2011.04.21}
}
@ARTICLE{Delestre10,
author = {Delestre, Olivier and Marche, Fabien},
title = {A Numerical Scheme for a Viscous Shallow Water Model with Friction},
journal = {J. Sci. Comput.},
year = {2010},
volume = {DOI 10.1007/s10915-010-9393-y},
file = {Delestre10.pdf:Delestre10.pdf:PDF},
keywords = {Shallow water; source term; friction; eddy viscosity; analytic solutions;
finite volume; MUSCL reconstruction; well-balanced scheme},
owner = {olivier},
timestamp = {2010.06.28}
}
@ARTICLE{Delfs09,
author = {Delfs, J.-O. and Park, C.-H. and Kolditz, O.},
title = {A sensitivity analysis of Hortonian flow},
journal = {Advances in Water Resources},
year = {2009},
volume = {32},
pages = {1386--1395},
abstract = {We present a sensitivity analysis for inﬁltration excess (Hortonian)
overland ﬂow based on a classic laboratory experiment by Smith and
Woolhiser [Smith RE, Woolhiser DA. Overland ﬂow on an inﬁltrating
surface. Water Resour Res 1971;7(4):899–913]. The model components
of the compartment approach are comprised of a diffusive wave approximation
to the Saint–Venant equations for overland ﬂow, a Richards model
for ﬂow in the variably saturated zone, and an interface coupling
concept that combines the two components. In the coupling scheme
a hydraulic interface is introduced to allow the deﬁnition of an
exchange ﬂux between the surface and the unsaturated zone. The effects
of friction processes, soil capillarity, hydraulic interface, and
vertical soil discretization on both inﬁltration and runoff prediction
are investigated in detail. The corresponding sensitivity analysis
is conducted using a small-perturbation method. As a result the importance
of the hydraulic processes and related parameters are evaluated for
the coupled hydrosystem.},
file = {Delfs09.pdf:Delfs09.pdf:PDF},
keywords = {diffusion wave; Richards; interface coupling; sensitivity analysis;
Smith and Woolhiser experiment; coupled hydrosystem modeling; infiltration
excess overland flow},
owner = {olivier},
timestamp = {2010.06.12}
}
@ARTICLE{Delis03,
author = {Delis, A. I.},
title = {Improved application of the {HLLE} {R}iemann solver for the shallow
water equations with source terms},
journal = {Communications in {N}umerical {M}ethods in {E}ngineering},
year = {2003},
volume = {19},
pages = {59-83},
file = {Delis03.pdf:Delis03.pdf:PDF},
owner = {olivier},
timestamp = {2010.04.01}
}
@ARTICLE{Delis05,
author = {Delis, A.~I. and Katsaounis, Th.},
title = {Numerical solution of the two-dimensional shallow water equations
by the application of relaxation methods},
journal = {Applied Mathematical Modelling},
year = {2005},
volume = {29},
pages = {754-783},
abstract = {A generalization and extension of a ﬁnite diﬀerence method for calculating
numerical solutions of the two dimensional shallow water system of
equations is investigated. A previously developed non-oscillatory
relaxation scheme is generalized as to included problems with source
terms in two dimensions, with emphasis given to the bed topography,
resulting to a class of methods of ﬁrst- and second-order in space
and time. The methods are based on classical relaxation models combined
with TVD Runge–Kutta time stepping mechanisms where neither Riemann
solvers nor characteristic decompositions are needed. Numerical results
are presented for several test problems with or without the source
term present. The wetting and drying process is also considered.
The presented schemes are veriﬁed by comparing the results with documented
ones.},
doi = {DOI: 10.1016/j.apm.2004.11.001},
file = {Delis05.pdf:Delis05.pdf:PDF},
issn = {0307-904X},
keywords = {Two-dimensional shallow water equations; Relaxation schemes; Finite
diﬀerences; TVD; Source terms; minmod; Van Leer; superbee; MC},
owner = {olivier},
timestamp = {2010.01.25},
url = {http://www.sciencedirect.com/science/article/B6TYC-4F2MG2W-2/2/887ec12c4d762cf855b5efdabe3507d2}
}
@ARTICLE{Delis09,
author = {Delis, A.~I. and Mathioudakis, E.~N.},
title = {A finite volume method parallelization for the simulation of free
surface shallow water flows},
journal = {Mathematics and Computers in Simulation},
year = {2009},
volume = {79},
pages = {3339-3359},
abstract = {We construct a parallel algorithm, suitable for distributed memory
architectures, of an explicit shock-capturing ﬁnite volume method
for solving the two-dimensional shallow water equations. The ﬁnite
volume method is based on the very popular approximate Riemann solver
of Roe and is extended to second order spatial accuracy by an appropriate
TVD technique. The parallel code is applied to distributed memory
architectures using domain decomposition techniques and we investigate
its performance on a grid computer and on a Distributed Shared Memory
supercomputer. The effectiveness of the parallel algorithm is considered
for speciﬁc benchmark test cases. The performance of the realization
measured in terms of execution time and speedup factors reveals the
efﬁciency of the implementation.},
doi = {DOI: 10.1016/j.matcom.2009.05.010},
file = {Delis09.pdf:Delis09.pdf:PDF},
issn = {0378-4754},
keywords = {Shallow water equations; Finite volume; Domain decomposition; Distributed
memory parallel architectures; Grid computing},
owner = {olivier},
timestamp = {2010.01.25},
url = {http://www.sciencedirect.com/science/article/B6V0T-4WKKTSC-1/2/89b455536a276aa3cc5268bb197a8aa6}
}
@ARTICLE{Delis00,
author = {Delis, A.~I. and Skeels, C.~P. and Ryrie, S.~C.},
title = {Implicit high-resolution methods for modelling one-dimensional open
channel flow},
journal = {Journal of Hydraulic Research},
year = {2000},
volume = {38},
pages = {369--382},
number = {5},
abstract = {Three implicit high-resolution total variation diminishing (TVD) schemes
are presented for solving the Saint-Venant equations. The applicability,
performance and validity of these methods are investigated. Recently
created benchmark solutions are reproduced for a wide range of cases,
which include friction, nonuniform bed slopes, transitions between
subcritical and supercritical flow, nonprismatic cross sections and
hydraulic jumps. The tests produce satisfactory results without resorting
to excessively fine grids. All the methods also produce satisfactory
results for an idealized dambreak problem.},
file = {Delis00.pdf:Delis00.pdf:PDF},
owner = {olivier},
timestamp = {2008.05.04}
}
@ARTICLE{Deng05,
author = {Deng, Zhi-Qiang and de Lima, J. L. M. P. and Singh, V. P.},
title = {Transport rate-based model for overland flow and solute transport:
Parameter estimation and process simulation},
journal = {Journal of Hydrology},
year = {2005},
volume = {315},
pages = {220--235},
abstract = {A one-dimensional mathematical model, termed a transport rate-based
model, is developed for solute transport over inﬁltrating soil slopes
under constant rainfall and declining sources. The model is comprised
of (1) the kinematic-wave equation for overland ﬂow, (2) a transport
rate-based advection equation for overland solute transport, (3)
a moment-based method for estimation of the parameters involved in
the ﬂow and solute transport equations, and (4) a semi-Lagrangian
algorithm for numerical solution of the solute transport equation.
Data from a single soil ﬂume experiment under constant rainfall established
the proof-of-concept for this new model. Sodium chloride was applied
to the soil surface to simulate the presence of a declining diffuse
pollutant. The parameters involved in the ﬂow equation were found
to take on the values that correspond to turbulent ﬂow. With these
turbulent ﬂow parameters the simulated hydrograph displayed an initial
rising limb, followed by a constant ﬂow discharge. The proﬁle of
solute concentration exhibits a steep receding limb transitioning
into an elongated tail. The solute transport rate follows a non-Gaussian
distribution that does not appear to have been derived before. These
theoretical hydrographs and pollutographs are in good agreement with
those measured in laboratory, demonstrating the laboratory proof-
of-concept for the transport rate-based model on soil and pavement
blocks.},
file = {Deng05.pdf:Deng05.pdf:PDF},
keywords = {overland flow; solute transport rate; numerical model; parameter estimation;
kinematic wave; hydrograph},
owner = {olivier},
timestamp = {2010.06.12}
}
@INPROCEEDINGS{Desconnets96,
author = {Desconnets, J.C. and Galle, S. and Leduc, C. and Peugeot, C.},
title = {Les processus de redistribution des eaux en r\'egion sah\'elienne:
l'hydrologie dans l'exp\'erience Hapex-Sahel},
booktitle = {L'hydrologie tropicale: g\'eoscience et outil pour le d\'eveloppement
(Actes de la conf\'erence de Paris, mai 1995) IAHS Publ. no. 238},
year = {1996},
file = {Desconnets96.pdf:Desconnets96.pdf:PDF},
owner = {olivier},
timestamp = {2010.05.17}
}
@MISC{Desveaux05,
author = {Desveaux, Vivien},
title = {Mod{\'e}lisation et {\'e}tude num{\'e}rique de l'infiltration de
l'eau de pluie dans le sol},
howpublished = {Rapport de stage de licence - ENS Lyon},
month = {@sep},
year = {2005},
note = {Encadrants : St{\'e}phane Cordier et Fran\c{c}ois James},
file = {Desveaux05.pdf:Desveaux05.pdf:PDF},
keywords = {infiltration, soil, Richards, Green-Ampt, 1d, ANR METHODE},
owner = {Fred. DARBOUX},
timestamp = {2008.08.08}
}
@PHDTHESIS{Devauchelle07,
author = {Devauchelle, Olivier},
title = {\'Ecoulements de surface et \'erosion},
school = {Universit\'e Pierre et Marie Curie},
year = {2007},
abstract = {When water ﬂows over a granular substrate at low Reynolds number,
erosion may generate various patterns (bars, braids, ripples or meanders),
sometimes surprisingly similar to those naturally encountered in
turbulent rivers. In a simple theoretical frame (shallow-water equations
and bedload transport), this study aims to tackle this geomorphological
problem using both analytical and numerical methods. A mass-conservative
bank condition is established for micro-rivers, which allows one
to model the widening of a small ﬂume of constant outﬂow through
erosion. The linear stability of the same micro-rivers is performed
in two dimensions. It is shown that the inﬂuence of the erodible
bank conditions can inﬂuence strongly the evolution of the bank instability.
The eﬀects of non-linearity on the bank instability are studied by
means of a ﬁnite-elements numerical scheme. Under certain circumstances,
diamond-shaped erosion fronts can develop. The stability of sand
ripples when the free surface aﬀects the ﬂow is brieﬂy studied. Finally,
the lubrication theory is used to demonstrate that a moving contact
line may stand on a porous plate, even for a vanishing contact angle,
provided the de-wetting process is slow enough. Furthermore, above
a critical withdrawal velocity, a Landau-Levich-Derjagin ﬁlm forms.},
file = {Devauchelle07.pdf:Devauchelle07.pdf:PDF},
owner = {olivier},
timestamp = {2009.07.21}
}
@ARTICLE{Dewals08,
author = {Dewals, B.~J. and Kantoush, S.~A. and Erpicum, S. and Pirotton, M.
and Schleiss, A.~J.},
title = {Experimental and numerical analysis of flow instabilities in rectangular
shallow basins},
journal = {Environmental Fluid Mechanics},
year = {2008},
volume = {8},
pages = {31--54},
abstract = {Free surface flows in several shallow rectangular basins have been
analysed experimentally, numerically and theoretically. Different
geometries, characterized by different widths and lengths, are considered
as well as different hydraulic conditions. First, the results of
a series of experimental tests are briefly depicted. They reveal
that, under clearly identified hydraulic and geometrical conditions,
the flow pattern is found to become non-symmetric, in spite of the
symmetrical inflow conditions, outflow conditions and geometry of
the basin. This non-symmetric motion results from the growth of small
disturbances actually present in the experimental initial and boundary
conditions. Second, numerical simulations are conducted based on
a depth-averaged approach and a finite volume scheme. The simulation
results reproduce the global pattern of the flow observed experimentally
and succeed in predicting the stability or instability of symmetric
flow pattern for all tested configurations. Finally, an analytical
study provides mathematical insights into the conditions under which
the symmetric flow pattern becomes unstable and clarifies the governing
physical processes.},
doi = {10.1007/s10652-008-9053-z},
file = {Dewals08.pdf:Dewals08.pdf:PDF},
keywords = {depth-averaged model; finite volume; reservoir hydrodynamics; shallow
flow; stability analysis},
owner = {olivier},
timestamp = {2008.04.30}
}
@ARTICLE{Dholakia98,
author = {Dholakia, Mrugen and Misra, Rajeev and Zaman, M.~S.},
title = {Simulation of border irrigation system using explicit MacCormack
finite difference method},
journal = {Agricultural Water Management},
year = {1998},
volume = {36},
pages = {181 - 200},
number = {3},
abstract = {The hydrodynamic, zero-inertia and kinematic wave models for simulating
all phases of the border irrigation event are presented. The explicit
second-order accurate MacCormack method is used for solving the governing
equations. A technique for implementing the boundary conditions that
are consistent with the numerical scheme is discussed. All the three
models do not require a special treatment such as moving grid, deformable
grid, subgrid technique, etc., to accurately simulate the advancing
and receding fronts. The results of all the three models namely hydrodynamic
finite difference model (HDFD), zero-inertia finite difference model
(ZIFD) and kinematic wave finite difference model (KWFD) are compared
with observed advance and recession times for four border irrigation
events available in literature. A very good comparison of results
is observed. The relative merits and demerits of the models are discussed.
The HDFD model is found to be more suitable for simulation of all
the four phases of border irrigation events.},
doi = {DOI: 10.1016/S0378-3774(97)00058-9},
file = {Dholakia98.pdf:Dholakia98.pdf:PDF},
issn = {0378-3774},
keywords = {Border irrigation},
owner = {olivier},
timestamp = {2009.11.29},
url = {http://www.sciencedirect.com/science/article/B6T3X-3T6RX0G-1/2/1e8fd61381ce545a375eac0ba8662771}
}
@ARTICLE{DiCristo09,
author = {Di Cristo, Cristiana and Iervolino, Michele and Vacca, Andrea and
Zanuttigh, Barbara},
title = {Roll-waves prediction in dense granular flows},
journal = {Journal of Hydrology},
year = {2009},
volume = {377},
pages = {50-58},
abstract = {This paper analyses conditions for roll-waves formation in homogeneous
granular ﬂows with the aim of predicting their occurrence in ﬁnite
length channels. With reference to a wide class of constitutive equations
of the ﬂowing medium, the response of the linearized one-dimensional
ﬂow model to a pointwise instantaneous disturbance is studied and
a closed form of the Green’s function, in both stable and unstable
conditions, is provided. The exponential growth of the disturbance
peak is used to predict the spatial evolution of roll-waves in dry
ﬂows of dense granular materials and a criterion for the minimum
channel length necessary to appreciate roll-wave development is proposed.
The comparison among theoretical and experimental data available
in the literature appears promising.},
file = {DiCristo09.pdf:DiCristo09.pdf:PDF},
keywords = {Roll-waves; Granular ﬂow; Open channel ﬂow; Stability; Green’s function;
Channel length},
owner = {olivier},
timestamp = {2010.01.25}
}
@ARTICLE{DiGiammarco96,
author = {Di Giammarco, P. and Todini, E. and Lamberti, P.},
title = {A conservative finite elements approach to overland flow: the control
volume finite element formulation},
journal = {Journal of Hydrology},
year = {1996},
volume = {175},
pages = {267--291},
abstract = {This paper proposes the control volume finite element (CVFE) method,
a locally conservative formulation of the better known finite elements
(FE) approach, to deal more effectively with overland flow. The two-dimensional
overland flow problem is introduced and several approaches available
in the literature are briefly reported. The partial differential
equations describing overland and channel processes are then presented
and a consistent two-dimensional formulation for the head losses
is introduced. The derivation of the CVFE discrete formulation is
preceded by a discussion on the classical integrated finite difference
(IFD) and FE approaches, together with their advantages and disadvantages.
The CVFE formulation is shown to improve on both approaches, resulting
in a better representation of the gradients than that of the IFD
approach and, in contrast to the FE, allows for the conservation
of mass at local scale. The preliminary results obtained with a CVFE
computer code are presented and compared with analytical solutions.
Finally, several computational aspects are discussed, such as the
formulation of the time integration, the representation of the water
volumes pertaining to each node of the space discretization mesh
and the explicit imposition of the local mass balance.},
file = {DiGiammarco96.pdf:DiGiammarco96.pdf:PDF},
keywords = {diffusive wave; hydrograph},
owner = {olivier},
timestamp = {2010.06.12}
}
@INPROCEEDINGS{Djadel06,
author = {Djadel, K. and Ern, A. and Piperno, S.},
title = {A discontinuous Galerkin method for the shallow-water equations with
bathymetric terms and dry areas},
booktitle = {European Confeence on Computational Fluid Dynamics ECCOMAS CFD 2006,
Wesseling, P.; O\~nate, E. and P\'eriaux, J. (Eds)},
year = {2006},
abstract = {Abstract. We develop a Runge-Kutta Discontinuous Galerkin method to
approximate the two-dimensional Shallow-Water Equations with bathymetric
terms and dry areas. We introduce a ﬂux modiﬁcation technique to
ensure a well-balanced scheme (i.e. that preserves steady-states
at rest) and a slope modiﬁcation technique to deal with dry areas.
Numerical results are presented to illustrate the performance of
the proposed method in various test cases.},
file = {Djadel06.pdf:Djadel06.pdf:PDF},
keywords = {discontinuous Galerkin methods; shallow-water equations; well-balanced
schemes; dry areas},
owner = {olivier},
timestamp = {2010.11.12}
}
@ARTICLE{Dressler54,
author = {Dressler, Robert~F.},
title = {Comparison of theories and experiments for the hydraulic dam-break
wave},
journal = {Int. Assoc. Sci. Hydraul.},
year = {1954},
volume = {38},
pages = {319-328},
file = {Dressler54.pdf:Dressler54.pdf:PDF},
owner = {olivier},
timestamp = {2009.07.30}
}
@ARTICLE{Dressler52,
author = {Dressler, R.~F.},
title = {Hydraulic resistance effect upon the dam-break},
journal = {Journal of Research of the National Bureau of Standards},
year = {1952},
volume = {49},
pages = {217--225},
number = {3},
month = sep,
abstract = {The dam-break solution, a known centered simple-wave when resistance
is neglected, is studied with the Chezy resistance formula added
to the nonlinear shallow-water equations. Resistance transforms the
wavefront from a characteristic curve into an envelope of characteristics.
The flow near the tip differs from the other parts, due to a distinct
boundary-layer type of region adjacent to the wavefront envelope.
Then a perturbation leads to a system of partial differential equations
with variable coefficients. Initial conditions are derived for the
singularity at the origin. By studying its characteristic equations,
this system is solved explicitly for the correction functions. Except
at the tip, resistance raises the water surface and lowers velocities.
These functions, no longer simple-waves, possess concurrent straight
characteristic lines that map into another set of the same type.
The critical flow locus moves downstream, faster for more resistance,
and discharge rates are reduced. The method fails in the tip layer
because the asymptotic expansions for the first derivatives lose
validity there. Estimates are made indirectly for the wavefront velocity
by observing where the boundary-layer effect becomes predominant.},
file = {Dressler52.pdf:Dressler52.pdf:PDF},
owner = {olivier},
timestamp = {2008.05.07}
}
@ARTICLE{Dressler49,
author = {Dressler, Robert~F.},
title = {Mathematical Solution of the Problem of Roll-Waves in Inclined Open
Channels},
journal = {Communications on Pure and Applied Mathematics},
year = {1949},
volume = {2},
pages = {149-194},
file = {Dressler49.pdf:Dressler49.pdf:PDF},
owner = {olivier},
timestamp = {2009.08.03}
}
@ARTICLE{Dressler53,
author = {Dressler, R. F. and Pohle, F. V.},
title = {Resistance effects on hydraulic instability},
journal = {Communications on Pure and Applied Mathematics},
year = {1953},
volume = {6},
pages = {93--96},
number = {1},
abstract = {For almost two centuries many quantitative experiments have been made
concerning the flow of water down an inclined open channel. Hydraulicians
have evolved empirical laws in confusing multiplicity to describe
a uniform flow as a function of the slope and the resistance caused
by friction with the channel walls and by turbulence. Each of the
laws has its own best range of applicability, but most are of the
same basic, viz. the effective resistance is considered in the momentum
equation as an opposing body force of form -\lambda u^n/y^m, u being
the velocity, y the "hydraulic radius" and \lambda a coefficient
describing the channel roughness, which in this notation is independent
of u and y. The exponents m, n >0 have specific values characteristic
of the different formulas. For a wide rectangular channel, y will
be also the depth of the water.},
doi = {10.1002/cpa.3160060103},
file = {Dressler53.pdf:Dressler53.pdf:PDF},
issn = {1097-0312},
keywords = {roll waves; Manning; Chezy},
owner = {olivier},
publisher = {Wiley Subscription Services, Inc., A Wiley Company},
timestamp = {2011.03.03},
url = {http://dx.doi.org/10.1002/cpa.3160060103}
}
@ARTICLE{Dunkerley02,
author = {Dunkerley, D.},
title = {Surface tension and friction coefficients in shallow, laminar overland
flow through organic litter},
journal = {Earth Surface Processes and Landforms},
year = {2002},
volume = {27},
pages = {45--58},
file = {Dunkerley02.pdf:Dunkerley02.pdf:PDF},
keywords = {laminar flow; surface tension; organic litter; interrill flow; surface
runoff; Darcy-Weisbach friction coefficient},
owner = {olivier},
timestamp = {2009.01.11}
}
@BOOK{Dupin05,
title = {Le langage C++},
publisher = {{C}ampus{P}ress},
year = {2005},
author = {Dupin, St\'ephane},
owner = {olivier},
timestamp = {2009.11.25}
}
@ARTICLE{Dutykh09,
author = {Dutykh, Denys},
title = {Visco-potential free-surface flows and long wave modelling},
journal = {European Journal of Mechanics - B/Fluids},
year = {2009},
volume = {28},
pages = {430 - 443},
number = {3},
doi = {DOI: 10.1016/j.euromechflu.2008.11.003},
file = {Dutykh09.pdf:Dutykh09.pdf:PDF},
issn = {0997-7546},
keywords = {Free-surface flows},
owner = {olivier},
timestamp = {2009.07.21},
url = {http://www.sciencedirect.com/science/article/B6VKX-4V1KMM7-1/2/3036b9f42197da685b70978882f678d2}
}
@PHDTHESIS{Dutykh07,
author = {Dutykh, Denys},
title = {Mod\'elisation math\'ematique des tsunamis},
school = {\'Ecole normale sup\'erieure de Cachan},
year = {2007},
abstract = {This thesis is devoted to tsunami wave modelling. The life of tsunami
waves can be conditionally divided into three parts: generation,
propagation and inundation (or run-up). In the ﬁrst part of the manuscript
we consider the generation process of such extreme waves. We examine
various existing approaches to its modelling. Then we propose a few
alternatives. The main conclusion is that the seismology/hydrodynamics
coupling is poorly understood at the present time.
The second chapter essentially deals with Boussinesq equations which
are often used to model tsunami propagation and sometimes even run-up.
More precisely, we discuss the importance, nature and inclusion of
dissipative eﬀects in long wave models.
In the third chapter we slightly change the subject and turn to two-phase
ﬂows. The main purpose of this chapter is to propose an operational
and simple set of equations in order to model wave impacts on coastal
structures. Another important application includes wave sloshing
in liquiﬁed natural gas carriers. Then, we discuss the numerical
discretization of governing equations in the ﬁnite volume framework
on unstructured meshes.
Finally, this thesis deals with a topic which should be present in
any textbook on hydrodynamics but it is not. We mean visco-potential
ﬂows. We propose a novel and suﬃciently simple approach for weakly
viscous ﬂow modelling. We succeeded in keeping the simplicity of
the classical potential ﬂow formulation with the addition of viscous
eﬀects. In the case of ﬁnite depth we derive a correction term due
to the presence of the bottom boundary layer. This term is nonlocal
in time. Hence, the bottom boundary layer introduces a memory eﬀect
to the governing equations.},
file = {Dutykh07.pdf:Dutykh07.pdf:PDF},
keywords = {Water waves; tsunami generation; Boussinesq equations; two-phase ﬂows;
visco-potential ﬂows; ﬁnite volumes},
owner = {olivier},
timestamp = {2009.07.19}
}
@ARTICLE{Ekvall93,
author = {Ekvall, Anders G. C.},
title = {Evolution of roll waves running down an inclined plane},
journal = {Chemical Engineering Science},
year = {1993},
volume = {48},
pages = {69--80},
number = {1},
abstract = {The method of fluid sheets is used to study the flow of a linear viscous
fluid down an inclined plane. The linear stability of the steady
Nusselt flow and the nonlinear evolution of large-amplitude waves
are examined. The results from linear stability anaiysis agree very
well with experimental data and other theoretical investigations.
A finite-difference scheme is used to examine the evolution of nonlinear
finite-amplitude waves. The dynamic nonlinear behavior seen experimentally
is predicted, including phenomena not previously reported in other
theoretical investigations, such as decreasing wave heights, wave
breaking and the breakdown of an initially solitary disturbance into
a series of waves. The computed wave forms include large-amplitude
waves and capillary ripples running in front of them.},
file = {Ekvall93.pdf:Ekvall93.pdf:PDF},
keywords = {roll-waves; linear stability; non-linear stability; fluid sheet method},
owner = {olivier},
timestamp = {2010.06.12}
}
@MASTERSTHESIS{Elbouajaji07,
author = {El Bouajaji, Mohamed},
title = {Mod{\'e}lisation des {\'e}coulements \`{a} surface libre~: {\'e}tude
du ruissellement des eaux de pluie},
school = {Universit{\'e} Louis Pasteur, disponible sur : http://dumas.ccsd.cnrs.fr/dumas-00459336/fr/},
year = {2007},
address = {Strasbourg},
note = {Encadrants~: Fabrice Dupros et Olivier Cerdan},
file = {Elbouajaji07.pdf:Elbouajaji07.pdf:PDF},
keywords = {Shallow flow equations; 2d; infiltration; Saint-Venant; ANR METHODE;
Green-Ampt; hydrostatic reconstruction; finite volume; well-balanced
scheme},
owner = {Fred. DARBOUX},
timestamp = {2008.08.08}
}
@BOOK{Karniadakis03,
title = {Parallel {S}cientific {C}omputing in {C}++ and {MPI}},
publisher = {Cambridge {U}niversity {P}ress},
year = {2003},
author = {Em Karniadakis, George and Kirby II, Rober {M}.},
owner = {olivier},
timestamp = {2009.11.25}
}
@ARTICLE{Endreny06,
author = {Endreny, Theodore A.},
title = {Simulation of {S}oil {W}ater {I}nfiltration with {I}ntegration, {D}ifferentiation,
{N}umerical {M}ethods and {P}rogramming {E}xercises},
journal = {Int. J. Engng. Ed.},
year = {2006},
volume = {0},
pages = {1--10},
number = {0},
abstract = {Students in a water resources engineering course consider the infiltration
of water into soils, a topic through which instructors can reinforce
many fundamental engineering principles. In this paper, undergraduates
used two 80 minute classes to explore Green-Ampt infiltration through
integration, differentiation, Newton-Raphson numerical methods and
Visual Basic programming. Students used
calculus software to check solved problems, programming software to
modify and execute model code, and spreadsheet software to examine
model outputs. Outputs included tables and graphs showing infiltration
for a single precipitation event. Student assessment of the lesson
is used to complement measurement of curricula outcomes and satisfy
the US Accreditation Board of Engineering Technology criteria.},
file = {Endreny06.pdf:Endreny06.pdf:PDF},
keywords = {MathCAD; Excel; Visual Basic for Applications; Student Assessment
of Learning Gains},
owner = {olivier},
timestamp = {2010.04.23}
}
@ARTICLE{Erduran02,
author = {Erduran, K.~S. and Kutija, V. and Hewett, C.~J.~M.},
title = {Performance of finite volume solutions to the shallow water equations
with shock-capturing schemes},
journal = {International Journal for Numerical Methods in Fluids},
year = {2002},
volume = {40},
pages = {1237--1273},
number = {10},
abstract = {Numerical methods have become well established as tools for solving
problems in hydraulic engineering. In recent years the finite volume
method (FVM) with shock capturing capabilities has come to the fore
because of its suitability for modelling a variety of types of flow;
subcritical and supercritical; steady and unsteady; continuous and
discontinuous and its ability to handle complex topography easily.This
paper is an assessment and comparison of the performance of finite
volume solutions to the shallow water equations with the Riemann
solvers; the Osher, HLL, HLLC, flux difference splitting (Roe) and
flux vector splitting. In this paper implementation of the FVM including
the Riemann solvers, slope limiters and methods used for achieving
second order accuracy are described explicitly step by step. The
performance of the numerical methods has been investigated by applying
them to a number of examples from the literature, providing both
comparison of the schemes with each other and with published results.
The assessment of each method is based on five criteria; ease of
implementation, accuracy, applicability, numerical stability and
simulation time. Finally, results, discussion, conclusions and recommendations
for further work are presented. Copyright {\copyright} 2002 John
Wiley \& Sons, Ltd.},
address = {WRSRL, Department of Civil Engineering, University of Newcastle,
Newcastle upon Tyne, NE1 7RU, U.K.},
citeulike-article-id = {2465841},
citeulike-linkout-0 = {http://dx.doi.org/10.1002/fld.402},
citeulike-linkout-1 = {http://www3.interscience.wiley.com/cgi-bin/abstract/101019669/ABSTRACT},
doi = {10.1002/fld.402},
file = {Erduran02.pdf:Erduran02.pdf:PDF},
keywords = {finite-volume, riemann-problem, shallow-water-eqs, shock-capturing},
owner = {olivier},
posted-at = {2008-03-04 17:07:41},
priority = {0},
timestamp = {2009.07.19},
url = {http://dx.doi.org/10.1002/fld.402}
}
@ARTICLE{Erduran05,
author = {Erduran, K.~S. and Kutija, V. and MacAlister, C.~R.},
title = {{Finite volume solution to integrated shallow surface-saturated groundwater
flow}},
journal = {International Journal for Numerical Methods in Fluids},
year = {2005},
volume = {49},
pages = {763-783},
month = nov,
abstract = {This paper describes development of an integrated shallow surface
and saturated groundwater model (GSHAW5). The surface flow motion
is described by the 2-D shallow water equations and groundwater movement
is described by the 2-D groundwater equations. The numerical solution
of these equations is based on the finite volume method where the
surface water fluxes are estimated using the Roe shock-capturing
scheme, and the groundwater fluxes are computed by application of
Darcy's law. Use of a shock-capturing scheme ensures ability to simulate
steady and unsteady, continuous and discontinuous, subcritical and
supercritical surface water flow conditions. Ground and surface water
interaction is achieved by the introduction of source-sink terms
into the continuity equations. Two solutions are tightly coupled
in a single code. The numerical solutions and coupling algorithms
are explained. The model has been applied to 1-D and 2-D test scenarios.
The results have shown that the model can produce very accurate results
and can be used for simulation of situations involving interaction
between shallow surface and saturated groundwater flows.},
adsnote = {Provided by the SAO/NASA Astrophysics Data System},
adsurl = {http://adsabs.harvard.edu/abs/2005IJNMF..49..763E},
doi = {10.1002/fld.1030},
file = {Erduran05.pdf:Erduran05.pdf:PDF},
keywords = {shallow water equations, saturated groundwater equation, finite volume,
shock-capturing scheme, surface and groundwater coupling},
owner = {olivier},
timestamp = {2009.07.19},
url = {http://dx.doi.org/10.1002/fld.1030}
}
@MASTERSTHESIS{Esclaffer03,
author = {Esclaffer, T.},
title = {Etude th{\'e}orique de la formation des d{\'e}bits de crues {\`a}
l'{\'e}chelle du versant},
school = {Universit{\'e} Paris XII--ENGREF--ENPC},
year = {2003},
abstract = {Experiences of isotopic separation have demonstrated the important
contribution of subsurface flows to flood discharge. Saturated source
areas near the streamflow seem to constitute a priviledged generation
area of overland and subsurface flows on the hillslope. In order
to permit a detailed analysis of the functioning of such areas, a
numeric hillsplope model coupling overland (diffusive wave) and subsurface
flows (Richards' equations) has been developed. In order to validate
the model, we performed simulations based on experimental data of
reduced models taken from the litterature. Respective contributions
of direct runoff and water table exfiltration are correctively reproduced
in equilibrium. On the other hand, due to incomplete knowledge of
soil hydrodynamic parameters, response kinetics are not well represented.
Trials realized on different soil types demonstrate the important
sensitivity of the hillslope response relatively to soil hydrodynamic
properties. In the future, the developped model will serve as basis
for an exhaustive study on the influence of different parameters
(hydrodynamic properties, soil thickness, slope, rain intensity,
initial conditions) on the hillslope's hydrological response.},
file = {Esclaffer03.pdf:Esclaffer03.pdf:PDF},
keywords = {floods; hydrological model; hillslope; satured source area; overland
flow; subsurface flow; capillary fringe},
owner = {olivier},
timestamp = {2008.05.05}
}
@ARTICLE{Eskilsson05,
author = {Eskilsson, C. and Sherwin, S.J.},
title = {Discontinuous Galerkin Spectral/hp Element Modelling of Dispersive
Shallow Water Systems},
journal = {Journal of Scientific Computing},
year = {2005},
volume = {22--23},
pages = {269--288},
abstract = {Two-dimensional shallow water systems are frequently used in engineering
practice to model environmental ﬂows. The beneﬁt of these systems
are that, by integration over the water depth, a two-dimensional
system is obtained which approximates the full three-dimensional
problem. Nevertheless, for most applications the need to propagate
waves over many wavelengths means that the numerical solution of
these equations remains particularly challenging. The requirement
for an accurate discretization in geometrically complex domains makes
the use of spectral/hp elements attractive. However, to allow for
the possibility of discontinuous solutions the most natural formulation
of the system is within a discontinuous Galerkin (DG) framework.
In this paper we consider the unstructured spectral/hp DG formulation
of (i) weakly nonlinear dispersive Boussinesq equations and (ii)
nonlinear shallow water equations (a subset of the Boussinesq equations).
Discretization of the Boussinesq equations involves resolving third
order mixed derivatives. To efﬁciently handle these high order terms
a new scalar formulation based on the divergence of the momentum
equations is presented. Numerical computations illustrate the exponential
convergence with regard to expansion order and ﬁnally, we simulate
solitary wave solutions.},
doi = {10.1007/s10915-004-4140-x},
file = {Eskilsson05.pdf:Eskilsson05.pdf:PDF},
keywords = {Boussinesq equation; shallow water equations; spectral/hp; discontinuous
Galerkin method; HLL; HLLC},
owner = {olivier},
timestamp = {2010.11.12}
}
@ARTICLE{Esteves00,
author = {Esteves, M. and Faucher, X. and Galle, S. and Vauclin, M.},
title = {Overland flow and infiltration modelling for small plots during unsteady
rain : numerical results versus observed values},
journal = {Journal of Hydrology},
year = {2000},
volume = {228},
pages = {265--282},
abstract = {This paper reports the development and application of a two-dimensional
model based on an explicit finite difference scheme coupling overland
flow and infiltration processes for natural hillslopes represented
by topographic elevation and soil hydraulics parameters. This model
allows modelling of hortonian overland flow and infiltration during
complex rainfall events. Original procedures have been developed
in order to simulate complex rainfall events on natural slopes. The
accuracy of the results is tested by comparison with experimental
field data on the basis of calibrated soil and surface friction parameters.
Good agreement between the calculated result and the measured data
was found. The scheme proposed was found to be appropriate. The results
of tests presented illustrate the effect of microtopography on the
distribution of the flow depths, the magnitude and direction of flow
velocities and infiltration depths.},
file = {Esteves00.pdf:Esteves00.pdf:PDF},
keywords = {Overland flow; two-dimensional modelling; Green-Ampt equation; runoff
generation; microrelief},
owner = {olivier},
timestamp = {2008.04.28}
}
@ARTICLE{Esteves03,
author = {Esteves, M. and Lapetite, J.~M.},
title = {A multi-scale approach of runoff generation processes in a sahelian
gully catchment : a case study in Niger},
journal = {Catena},
year = {2003},
volume = {50},
pages = {255-271},
file = {Esteves03.pdf:Esteves03.pdf:PDF},
owner = {olivier},
timestamp = {2009.09.09}
}
@PHDTHESIS{Estupina04,
author = {Estupina Borrel, V.},
title = {Vers une mod{\'e}lisation hydrologique adapt{\'e}e {\`a} la pr{\'e}vision
op{\'e}rationnelle des crues {\'e}clair--Application {\`a} de petits
bassins versants du sud de la France},
school = {INP de Toulouse},
year = {2004},
abstract = {La pr\'esente th\`ese traite de la pr\'evision des crues d\'evastatrices
engendr\'ees par des al\'eas extr\^emes et se situant principalement
dans des r\'egions m\'editerran\'eennes fran\c{c}aises, souvent qualifi\'ees
de crues "\'eclair". Une analyse des diff\'erents processus hydrologiques
principalement responsables de la gen\`ese et de la propagation de
telles crues montre qu'une mod\'elisation distribu\'ee \`a base physique
\`a l'\'echelle temporelle de la crue (moins de 2 jours) et \`a l'\'echelle
spatiale de petits bassins versants m\'editerran\'eens (moins de
1 000 km2) appara\^it comme pertinente. Parmi les mod\`eles d\'ej\`a
existants, r\'epondant au moins partiellement aux crit\`eres requis
et disponibles au moment de l'\'etude, TOPMODEL et HECHMS ont \'et\'e
mis en oeuvre. Les r\'esultats obtenus ne sont pas pleinement satisfaisants,
soit car ces mod\`eles n\'ecessitent des chroniques pluie - d\'ebit
correspondant \`a ces \'ev\'enements particuliers -chroniques rarement
disponibles-, soit car la variabilit\'e spatiale et les caract\'eristiques
des processus physiques influents ne sont pas suffisamment prises
en compte par ces mod\`eles. Afin de palier ces inconv\'enients,
un mod\`ele (MARINE pour Mod\'elisation pour l'Anticipation du Ruissellement
et des Inondations pour des \'ev\'eNements Extr\^emes) a \'et\'e
con\c{c}u dans le cadre de cette th\`ese. Il s'agit d'un mod\`ele
pluie - d\'ebit qui int\`egre l'imagerie satellitale et les pluies
issues du RADAR m\'et\'eorologique et qui ne n\'ecessite pas de longues
chroniques pluie - d\'ebit pour son calage. Afin que MARINE puisse
\^etre adapt\'e d'une part aux \'echelles des donn\'ees issues de
l'imagerie satellitale et d'autre part \`a l'\'echelle objectif \`a
laquelle les pr\'evisions doivent \^etre r\'ealis\'ees, diff\'erentes
mod\'elisations hydrologiques ont d\^u \^etre mises en cascades pour
franchir, par une m\'ethode agr\'egative, ce saut d'\'echelles. Ce
mod\`ele a fourni des r\'esultats tr\`es encourageants sur la crue
de l'Aude de novembre 1999 pour diff\'erents sous bassins et \`a
l'\'echelle du bassin entier, mais aussi pour des crues survenues
dans le d\'epartement du Gard en 1995. Son impl\'ementation en 2002
dans un service d'annonce des crues fran\c{c}ais (dans le cadre du
projet PACTES) et sa future implantation op�rationnelle au SCHAPI
offrent de r\'eelles applications temps r\'eel de ce code.},
file = {Estupina04.pdf:Estupina04.pdf:PDF},
keywords = {hydrologie; pr{\'e}vision op{\'e}rationnelle; t{\'e}l{\'e}d{\'e}tection;
crues {\'e}clair; mod{\'e}lisation; {\'e}chelles},
owner = {olivier},
timestamp = {2008.05.05}
}
@ARTICLE{Fahs09,
author = {Fahs, Marwan and Younes, Anis and Lehmann, Fran\c{c}ois},
title = {An easy and efficient combination of the Mixed Finite Element Method
and the Method of Lines for the resolution of Richards' Equation},
journal = {Environmental Modelling \& Software},
year = {2009},
volume = {24},
pages = {1122--1126},
abstract = {In this work, the Mixed Hybrid Finite Element (MHFE) method is combined
with the Method Of Lines (MOL) for an accurate resolution of the
Richard’s Equation (RE). The combination of these methods is often
complicated since hybridization requires a discrete approximation
of the time derivative whereas with the MOL, it should remain continuous.
In this paper, we use the new mass lumping technique developed in
Younes et al. [Younes, A., Ackerer, P., Lehmann, F., 2006. A new
mass lumping scheme for the mixed hybrid ﬁnite element method. International
Journal for Numerical Methods in Engineering 67, pp. 89–107.] for
the MHFE method. With this formulation, the MOL is easily implemented
and sophisticated time integration packages can be used without signiﬁcant
amount of work. Numerical simulations are performed on both homogeneous
and heterogeneous porous media to show the efﬁciency and robustness
of the developed scheme.},
file = {Fahs09.pdf:Fahs09.pdf:PDF},
keywords = {Richards' equation; unsaturated flow; mixed hybrid finite element
method; mass lumping; method of lines; ODE/DAE time integrator},
owner = {olivier},
timestamp = {2010.06.06}
}
@ARTICLE{Fassino98,
author = {Fassino, Claudia and Manzini, Gianmarco},
title = {Fast-secant algorithms for the non-linear Richards equation},
journal = {Communications in Numerical Methods in Engineering},
year = {1998},
volume = {14},
pages = {921--930},
abstract = {Groundwater flow in partially saturated porous media is modelled by
using the non-linear Richards equation, which is discretized in the
present work by using linear mixed-hybrid finite elements. The discretization
produces an algebraic non-linear system, which can be solved by an
iterative fixed-point algorithm, the Picard method. The convergence
rate is linear, and may be too poor for practical applications. A
superlinear convergence rate is obtained by considering a Broyden-type
approach, based on the Shermann±Morrison formula. The local character
of the Broyden method can be overcome by an accurate estimate of
the initial solution, that is by appropriately initializing the computation
via some (relaxed) Picard iterations. This strategy needs a convergence
criterion to decide when switching from the Picard to the quasi-Newton
method, which is crucial for the effectiveness of the scheme, as
illustrated by some numerical experiments. We also consider the non-linear
algebraic problem from a different viewpoint. Instead of applying
the quasi-Newton method directly to such a non-linear system, we
applied it to the non-linear function tied to the Picard scheme.
Each function evaluation requested by such an algorithm corresponds
to a local step of the Picard method, which is then used to compute
a Broyden displacement. The present technique can be seen as an accelerated
Picard algorithm. We compare the performances of these algorithms
when applied to a stationary and a time-dependent benchmark problem.},
file = {Fassino98.pdf:Fassino98.pdf:PDF},
keywords = {non-linear Richards equation; mixed-hybrid finite elements; quasi-Newton
methods; fast-secant methods; Darcy's law},
owner = {olivier},
timestamp = {2010.06.13}
}
@PHDTHESIS{Faug04,
author = {Faug, T.},
title = {Simulation sur mod{\`e}le r{\'e}duit de l'influence d'un obstacle
sur un {\'e}coulement {\`a} surface libre--Application aux ouvrages
de protection contre les avalanches de neiges},
school = {Universit{\'e} Joseph Fourier},
year = {2004},
file = {Faug04.pdf:Faug04.pdf:PDF},
keywords = {snow avalanches; defence structures; granular flow; density currents;
obstacle; experimentation; small-scale models; deposition processes;
jet; run-out shortening; local pressure losses},
owner = {olivier},
timestamp = {2008.05.07}
}
@ARTICLE{Fernandez07,
author = {Fern\'andez, M. A. and Gerbeau, J.-F. and Grandmont, C.},
title = {A projection semi-implicit scheme for the coupling of an elastic
structure with an incompressible fluid},
journal = {International Journal for Numerical Methods in Engineering},
year = {2007},
volume = {69(4)},
pages = {794--821},
abstract = {We address the numerical simulation of ﬂuid-structure systems involving
an incompressible viscous ﬂuid. This issue is particularly diﬃcult
to face when the ﬂuid added-mass acting on the structure is strong,
as it happens in hemodynamics for example. Indeed, several works
have shown that, in such situations, implicit coupling seems to be
necessary in order to avoid numerical instabilities. Although signiﬁcant
improvements have been achieved during the last years, solving implicit
coupling often exhibits a prohibitive computational cost. In this
work, we introduce a semi-implicit coupling scheme which remains
stable for a reasonable range of the discretization parameters. The
ﬁrst idea consists in treating implicitly the added-mass eﬀect, whereas
the other contributions (geometrical non-linearities, viscous and
convective eﬀects) are treated explicitly. The second idea, relies
on the fact that this kind of explicit-implicit splitting can be
naturally performed using a Chorin-Temam projection scheme in the
ﬂuid. We prove (conditional) stability of the scheme for a fully
discrete formulation. Several numerical experiments point out the
eﬃciency of the present scheme compared to several implicit approaches.},
doi = {10.1002/nme.1792},
file = {Fernandez07.pdf:Fernandez07.pdf:PDF},
keywords = {fluid-structure interaction; semi-implicit coupling; added-mass effect;
projection scheme; blood flows},
owner = {olivier},
timestamp = {2011.03.16}
}
@TECHREPORT{Fernandez04b,
author = {Fern\'andez, Miguel~Angel and Milisi\'c, Vuk and Quarteroni, Alfio},
title = {Analysis of a geometrical multiscale blood flow model based on the
coupling of ODE's and hyperbolic PDE's},
institution = {INRIA},
year = {2004},
number = {5127},
month = Feb,
abstract = {For the numerical simulation of the circulatory system, geometrical
multiscale models based on the coupling of systems of differential
equations with different spatial dimensions is becoming common practice.
In this work we address the mathematical analysis of a coupled multiscale
system involving a zero-dimensional model, describing the global
characteristics of the circulatory system, and a one-dimensional
model giving the pressure propagation along a straight vessel. We
provide a local-in-time existence and uniqueness of classical solutions
for this coupled problem. To this purpose we reformulate the original
problem in a general abstrct framework by splitting it into subproblems
(the 0D system of ODE's and the 1D hyperbolic system of PDE's), then,
we use fixed-point techniques. The abstract result is then applied
to the original blood flow case under very realistic hypotheses on
the data. This work represents the 1D-0D counterpart of the 3D-0D
mathematical analysis reported in [SIAM J. on Multiscale Model. Simul.,
1(2) (2003) 173].},
file = {Fernandez04b.pdf:Fernandez04b.pdf:PDF},
keywords = {multiscale modelling; hyperbolic systems; lumped parameters models;
blood flow modelling; fixed-point techniques; modelisation multi-echelle;
systemes hyperboliques; modeles 0D; ecoulements sanguins; techniques
de point fixe},
owner = {olivier},
timestamp = {2010.11.30}
}
@ARTICLE{FernandezNieto08,
author = {Fern\'andez-Nieto, Enrique~D. and Bresch, Didier and Monnier, J\'er\^ome},
title = {A consistent intermediate wave speed for a well-balanced {HLLC} solver},
journal = {C. R. Acad. Sci. Paris, Ser. I},
year = {2008},
volume = {346},
pages = {795-800},
abstract = {In this work, we present a HLLC scheme modiﬁcation for application
to non-homogeneous shallow-water equations with pollutant transport.
This new version is related to the deﬁnition of a consistent approximation
of the intermediate wave speed. Numerical results are presented to
illustrate the importance of such approximation to get appropriate
pollutant concentration proﬁles.},
file = {FernandezNieto08.pdf:FernandezNieto08.pdf:PDF},
owner = {olivier},
timestamp = {2010.01.25}
}
@INPROCEEDINGS{Fernandez04,
author = {Fernandez-Feria, R.},
title = {Dam-break flow for arbitrary slope of the bottom},
booktitle = {Mechanics of the 21st Century. Proceedings of the 21st International
Congress of Theoretical and Applied Mechanics},
year = {2004},
editor = {Witolda Gutkowski and Tomasz A. Kowalewski},
address = {Warsaw, Poland},
month = aug # { 15-21},
abstract = {The dam-break flow problem in the shallow-water approximation on an
inclined bed for arbitrary slopes of the bottom is considered. An
analytical solution for the spreading of the water fronts at the
initial stages is given. A self-similar solution asymptotically valid
for large times is also found. For intermediate times the problem
is solved numerically by the method of characteristics.},
file = {Fernandez04.pdf:Fernandez04.pdf:PDF},
keywords = {dam-break},
owner = {Fred. DARBOUX},
timestamp = {2008.07.24}
}
@TECHREPORT{Fezoui88,
author = {Fezoui, Loula and Steve, Herv\'e},
title = {D\'ecomposition de flux de Van Leer en \'el\'ements finis/A finite
element method relying on Van Leer flux splitting},
institution = {INRIA},
year = {1988},
number = {830},
month = Apr,
abstract = {Nous pr\'esentons dans ce rapport une m\'ethode de r\'esolution num\'erique
d'\'ecoulements compressibles r\'egis par les \'equations d'Euler
bidimensionnelles. Le sch\'ema repose une formulation mixte El\'ements
Finis (triangles) / Volumes Finis. Diff\'erentes approches de type
MUSCL sont utilis\'ees pour calculer des solutions stationnaires
avec une bonne pr\'ecision \`a l'aide d'un sch\'ema implicite lin\'earis\'e
robuste et efficace. L'originalit\'e de ce travail est l'utilisation
du flux de van Leer et de son Jacobien dans le sch\'ema implicite,
ce qui permet d'obtenir une m\'ethode de Newton pour de grands pas
de temps. Des comparaisons num\'eriques avec un autre sch\'ema sur
un calcul d'\'ecoulement \`a grand nombre de Mach y sont pr\'esent\'ees.
This paper deals with numerical simulations of 2-D Euler compressible
flows. MUSCL Finite Volume approach with a Finite Element triangulation
is used to solve steady accurate solutions with a robust and efficient
implicit linearized scheme. We choose the van Leer flux-vector splitting
and its jacobian in order to get the Newton method when large time
steps are used. Comparisons are made with an other scheme: Osher's
flux for explicit step and Steger-Warming's flux for implicit step;
we present calculations with the two methods for a complex flow with
high Mach numbers.},
file = {Fezoui88.pdf:Fezoui88.pdf:PDF},
keywords = {Euler; flux de van Leer; tube \`a choc; \'ecoulement transsonique;
\'ecoulement supersonique; limiteur de van Leer;},
owner = {olivier},
timestamp = {2010.11.12}
}
@ARTICLE{Fiedler00,
author = {Fiedler, R.~F. and Ramirez, J.~A.},
title = {A numerical method for simulating discontinuous shallow flow over
an infiltrating surface},
journal = {International Journal for Numerical Methods in Fluids},
year = {2000},
volume = {32},
pages = {219--240},
abstract = {A numerical method based on the MacCormack finite difference scheme
is presented. The method was developed for simulating two-dimensional
overland flow with spatially variable infiltration and microtopography
using the hydrodynamic flow equations. The basic MacCormack scheme
is enhanced by using the method of fractional step to simplify application;
treating the friction slope, a stiff source term, point-implicitly,
plus, for numerical oscillation control and stability, upwinding
the convective acceleration term. A higher-order smoothing operator
is added to aid oscillation control when simulating flow over highly
variable surfaces. Infiltration is simulated with the Green-Ampt
model coupled to the surface water component in a manner that allows
dynamic interaction. The developed method will also be useful for
simulating irrigation, tidal flat and wetland circulation, and floods.},
file = {Fiedler00.pdf:Fiedler00.pdf:PDF},
keywords = {shallow water equations; finite difference; MacCormack scheme; upwind;
point-implicit},
owner = {olivier},
timestamp = {2008.04.28}
}
@BOOK{Flamant91,
title = {M\'ecanique appliqu\'ee. Hydraulique},
publisher = {Librairie polytechnique},
year = {1891},
author = {Flamant, A.},
series = {Encyclop\'edie des travaux publics},
address = {Paris, France},
file = {Flamant91.pdf:Flamant91.pdf:PDF},
keywords = {hydrology, Manning},
owner = {olivier},
timestamp = {2008.08.20}
}
@BOOK{Flamant91b,
title = {M\'ecanique appliqu\'ee - {H}ydraulique},
publisher = {{B}audry et Cie},
year = {1891},
editor = {coll. "{E}ncyclop\'edie des travaux publics", {P}aris},
author = {Flamant, Alfred-Aim\'e},
file = {Flamant91b.pdf:Flamant91b.pdf:PDF},
owner = {olivier},
timestamp = {2010.03.15}
}
@ARTICLE{Formaggia06,
author = {Formaggia, Luca and Lamponi, Daniele and Tuveri, Massimiliano and
Veneziani, Alessandro},
title = {Numerical Modeling of 1D Arterial Networks Coupled with a Lumped
Parameters Description of the Heart},
journal = {Computer Methods in Biomechanics and Biomedical Engineering},
year = {2006},
volume = {9},
pages = {273--288},
abstract = {The investigation on the pressure wave propagation along the arterial
network and its relationship with vascular physiopathologies can
be supported nowadays by numerical simulations. One dimensional (1D)
mathematical models, based on systems of two partial differential
equations for each arterial segment suitably matched at bifurcations,
can be simulated with low computational costs and provide useful
insights into the role of wave reflections. For instance, those induced
by stiffening of the arterial walls or a vascular endoprosthesis
and their influence on the cardiac work. Some recent works have indeed
moved in this direction.
The specific contribution of the present paper is to illustrate a
1D numerical model in which there is an effective coupling between
the heart action and the 1D system. Often, the action of the heart
on the arterial system is modelled as a boundary condition at the
entrance of the aorta. However, it is well known that the left ventricle
and the vascular network are a strongly coupled single mechanical
system. This coupling can be relevant in the numerical description
of pressure waves propagation, particularly when dealing with pathological
situations. In this work we propose a simple lumped parameter model
for the heart and show how it can be coupled numerically with a 1D
model for the arteries. Numerical results actually confirm the relevant
impact of the heart-arteries coupling in realistic simulations.},
file = {Formaggia06.pdf:Formaggia06.pdf:PDF},
keywords = {blood flow; 1D; network},
owner = {olivier},
timestamp = {2011.03.10}
}
@ARTICLE{Freeze69,
author = {Freeze, R. Allan and Harlan, R.L.},
title = {Blueprint for a physically-based, digitally-simulated hydrologic
response model},
journal = {Journal of Hydrology},
year = {1969},
volume = {9},
pages = {237--258},
abstract = {In recent years hydrologists have subjected the various subsystems
of the hydrologic cycle to intensive study, designed to discover
the mechanisms of flow and to arrive at physical and mathematical
descriptions of the flow processes. As a consequence, meaningful
results are now available in the form of numerical solutions to mathematical
boundary value problems for groundwater flow, unsaturated porous
media flow, overland flow, and channel flow. These developments in
physical hydrology, together with the tremendous advance in digital
computer technology, should provide the impetus for a necessary redirection
of research in hydrologic simulation. In this paper, a blueprint
for the development of physically-based hydrologic response models
is presented; the level of sophistication that can be achieved with
presently available methodology is discussed; and areas for necessary
future research are pinpointed.},
file = {Freeze69.pdf:Freeze69.pdf:PDF},
keywords = {Darcy; Richards; Saint-Venant; Manning},
owner = {olivier},
timestamp = {2010.06.14}
}
@ARTICLE{Fullana09,
author = {Fullana, Jose-Maria and Zaleski, St\'ephane},
title = {A branched one-dimensional model of vessel networks},
journal = {J. Fluid. Mech.},
year = {2009},
volume = {621},
pages = {183--204},
abstract = {We introduce a model representing the venous network of the leg. The
network consists of a coupled system of elastic tubes. The ﬂow through
each elastic tube is assumed to be unsteady, incompressible and one-dimensional.
The network topology, as well as the lengths and diameters of the
tubes, is based on literature data. As in the human leg the network
is composed of two sub-networks, deep and superﬁcial, which are connected
by transverse segments. We introduce a new model for conﬂuences or
branching points, as well as models of the valvular system and of
the muscular activity. We perform a numerical study of the transmission
and reﬂection of waves at a conﬂuence. Our model valvular system
imposes a privileged direction of the ﬂow towards the heart. Muscular
activity is modelled using a modiﬁcation of the tube law of the vessel
and through an inﬂow of blood when muscle contraction pushes blood
from the microcirculation to the veins. The model is capable of simulating
several motions such as walking, dorsal ﬂexion and tiptoe. Numerical
tests show the physical relevance of the model, and in particular
demonstrate that when the system is excited at the foot level, a
two-frequency response appears. These frequencies are closely related
to the characteristic lengths of the typical segments of the deep
and of the superﬁcial networks. We ﬁnd good qualitative agreement
between experimental and numerical ﬂow rates, using clinical data
corresponding to a single ‘tiptoe’ motion. We make numerical predictions
of the internal venous pressure at the foot level in a valvular-incontinent
system which agree with clinical observations.},
file = {Fullana09.pdf:Fullana09.pdf:PDF},
keywords = {blood flow},
owner = {olivier},
timestamp = {2011.03.16}
}
@ARTICLE{Furman07,
author = {Furman, Alex},
title = {Modeling {C}oupled {S}urface-{S}ubsurface {F}low {P}rocesses: {A}
{R}eview},
journal = {Vadose Zone Journal},
year = {2007},
volume = {7},
pages = {741--756},
number = {2},
month = May,
abstract = {Surface and subsurface ﬂow systems are inherently uniﬁed systems that
are often broken into sections for logical (e.g., me scales) and
technical (e.g., analytical and computational solvability) reasons.
While the basic physical laws are common to surface and subsurface
systems, spa al and temporal dimensions as well as the continuum
approach used for the subsurface lead to diﬀerent formulations of
the governing par al diﬀerential equations. While in most applications
such decoupling of the systems works well and allows a very accurate
and eﬃcient description of the individual system by treating the
adjacent system as a boundary condition, in the case of water ﬂow
over a porous medium, it does not. Therefore coupled models are in
increasing use in this ﬁeld, led mostly by watershed and surface
irrigation modelers. The governing equations of each component of
the coupled system and the coupling physics and mathematics are
reviewed ﬁrst. Three diﬀerent coupling schemes are iden ﬁed, namely
the uncoupled (with the degenerated uncoupled scheme being a special
case of the uncoupled), the iteratively coupled, and the fully coupled.
Next, the diﬀerent applications of the diﬀerent coupling schemes,
sorted by ﬁeld of applica on, are reviewed. Finally, some research
gaps are discussed, led by the need to include vertical momentum
transfer and to expand the use of fully coupled models toward surface
irrigation applications.},
file = {Furman07.pdf:Furman07.pdf:PDF},
keywords = {Saint-Venant; Darcy; Richards},
owner = {olivier},
timestamp = {2010.04.23}
}
@ARTICLE{Furman06,
author = {Furman, A. and Warrick, A. W. and Zerihun, D. and Sanchez, C. A.},
title = {Modified {K}ostiakov {I}nfiltration {F}unction: {A}ccounting for
{I}nitial and {B}oundary {C}onditions},
journal = {Journal of Irrigation and Drainage Engineering},
year = {2006},
volume = {132},
pages = {587--596},
number = {6},
month = Dec,
abstract = {Abstract: The effect of speciﬁc initial and boundary conditions is
generally not considered when applying the Kostiakov inﬁltration
functions. A methodology is developed to account for changes in water
levels and initial soil moisture. First, Richards’ equation is solved
numerically to generate a database of one-dimensional inﬁltration
values, with varying initial ͑water content or pressure head͒ and
boundary ͑ponding depth͒ conditions for three contrasting soils.
These are then used to calibrate corresponding coefﬁcients for modiﬁed
Kostiakov models and, by considering linear regressions, to obtain
simple correction factors. Results show that the correction factors
are not universally valid, and only the correction to the Kostiakov
k parameter shows statistically consistent applicability. However,
examples demonstrate potentially signiﬁcant improvement in the accuracy
of irrigation models by correcting the Kostiakov equation to account
for initial and boundary conditions.},
doi = {10.1061/͑ASCE͒0733-9437͑2006͒132:6͑587͒},
file = {Furman06.pdf:Furman06.pdf:PDF},
keywords = {Surface irrigation; Moisture content; Hydrologic models; Water ﬂow;
Boundaries; Inﬁltration},
owner = {olivier},
timestamp = {2010.04.23}
}
@ARTICLE{Galbiati95,
author = {Galbiati, G. and Savi, F.},
title = {Evaluation of the {C}omparative {I}nfluence of {S}oil {H}ydraulic
{P}roperties and {R}oughness on {O}verland {F}low at the {L}ocal
{S}cale},
journal = {J. agric. Engng Res.},
year = {1995},
volume = {61},
pages = {183--190},
file = {Galbiati95.pdf:Galbiati95.pdf:PDF},
keywords = {Manning; shallow water; Saint-Venant; Green-Ampt; Philip; Smith and
Parlange; wave front advance},
owner = {olivier},
timestamp = {2010.04.24}
}
@ARTICLE{Gallouet03,
author = {Gallou\"et, T. and H\'erard, J.-M. and Seguin, N.},
title = {Some approximate Godunov schemes to compute shallow-water equations
with topography},
journal = {Computers \& Fluids},
year = {2003},
volume = {32},
pages = {479--513},
abstract = {We study here the computation of shallow-water equations with topography
by Finite Volume methods, in a one-dimensional framework (though
all methods introduced may be naturally extended in two dimensions).
All methods are based on a discretisation of the topography by a
piecewise function constant on each cell of the mesh, from an original
idea of Le Roux et al. Whereas the Well-Balanced scheme of Le Roux
is based on the exact resolution of each Riemann problem, we consider
here approximate Riemann solvers. Several single step metods are
derived from this formalism, and numerical results are compared to
a fractional step method. Some test cases are presented : convergence
towards steady states in subcritical and supercritical configurations,
occurence of dry area by a drain over a bump and occurence of vacuum
by a double rarefaction wave over a step. Numerical schemes, combined
with an appropriate high-order extension, provide accurate and convergent
approximations.},
file = {Gallouet03.pdf:Gallouet03.pdf:PDF},
owner = {olivier},
timestamp = {2008.04.28}
}
@ARTICLE{Gandolfi00,
author = {Gandolfi, C. and Savi, F.},
title = {A {M}athematical {M}odel for the {C}oupled {S}imulation of {S}urface
{R}unoff and {I}nfiltration},
journal = {J. agric. Engng Res.},
year = {2000},
volume = {75},
pages = {49--55},
abstract = {The simulation of the unsteady free-surface flow on infiltrating surfaces
has many hydrological applications, including the study of overland
flow, soil erosion and conservation, surface irrigation and contaminant
transportation. The surface runoff is strictly connected to the infiltration
through the soil surface, so, an independent simulation of the two
processes, although very often adopted, may be unrealistic. This
paper presents a mathematical model for simulating these interdependent
surface and subsurface processes. The model is based on the two-dimensional
shallow water equations, coupled with the one-dimensional Richards
equation. These equations are integrated jointly, following the MacCormack
scheme, which is an explicit, finite-difference scheme, accurate
to the second order. The model can simulate initially dry surface
conditions and variable initial soil water content, and can deal
with space-variable characteristics (slope, roughness and soil hydraulic
properties). The accuracy of the model is tested by comparing its
results with analytical solutions and with experimental data. Finally,
a numerical experiment carried out on a simple hypothetical catchment,
both using the complete model and a simplified version, in which
the Richards equation and the shallow water equations are solved
in cascade, is discussed.},
file = {Gandolfi00.pdf:Gandolfi00.pdf:PDF},
keywords = {MacCormack; Richards; experimental data},
owner = {olivier},
timestamp = {2010.04.24}
}
@ARTICLE{Garcia-Navarro99,
author = {Garcia-Navarro, P. and Fras, A. and Villanueva, I.},
title = {Dam-break flow simulation: some results for one-dimensional models
of real cases},
journal = {Journal of Hydrology},
year = {1999},
volume = {216},
pages = {227 - 247},
number = {3-4},
abstract = {In many countries, the determination of the parameters of the wave,
likely to be produced after the failure of a dam, is required by
law, and systematic studies are mandatory. There is a necessity to
develop adequate numerical solvers which are able to reproduce situations
originated from the irregularities of a non-prismatic bed and to
model the complete equations that progress despite the irregular
character of the data. Many hydraulic situations can be described
by means of a one-dimensional (1D) model, either because a more detailed
resolution is unnecessary or because the flow is markedly 1D. Many
techniques have been developed recently for systems of conservation
laws in 1D (in the context of gas dynamics). Some years after their
adoption for solving problems in gas dynamics, upwind and total variation
diminishing (TVD) numerical schemes have been successfully used for
the solution of the shallow water equations, with similar advantages.
Their use is nevertheless only gradually gaining acceptance in this
sector. The performance of some of these techniques for practical
applications in river flow is reported in this work.},
doi = {DOI: 10.1016/S0022-1694(99)00007-4},
file = {Garcia-Navarro99.pdf:Garcia-Navarro99.pdf:PDF},
issn = {0022-1694},
keywords = {Flood routing},
owner = {olivier},
timestamp = {2009.09.16},
url = {http://www.sciencedirect.com/science/article/B6V6C-3W1YCMC-6/2/6662988f601707b1075af4142a74e612}
}
@ARTICLE{Garcia-Navarro00,
author = {Garcia-Navarro, P. and Vazquez-Cendon, M.~E.},
title = {On numerical treatment of the source terms in the shallow water equations},
journal = {Computers \& Fluids},
year = {2000},
volume = {29},
pages = {951--979},
abstract = {Upwind schemes are very well adapted to advection dominated flows
and have become popular for applications involving the Euler system
of equations. Recently, Riemann solver-based techniques such as Roe's
scheme have become a successful tool for numerical simulation of
other conservation laws like the shallow water equations. One of
the disadvantages of this technique is related to the treatment of
the source terms of the equations. The conservativity of the scheme
can be seriously damaged if a careless treatment is applied. Previous
papers studied the way to treat the terms arising from bed level
changes. This paper deals with the analysis of the main reasons leading
to a correct treatment of the geometrical source terms, that is,
those representing the changes in cross-section which may be linked
to the specific dependence of the flux function on the geometry.},
doi = {DOI: 10.1016/S0045-7930(99)00038-9},
file = {Garcia-Navarro00.pdf:Garcia-Navarro00.pdf:PDF},
issn = {0045-7930},
keywords = {source terms; shallow water equations; Roe's scheme; channel with
irregular geometries; shallow water equations;},
owner = {olivier},
timestamp = {2008.05.04},
url = {http://www.sciencedirect.com/science/article/B6V26-40NNKXP-5/2/49f42eb4adafafa7da73d97f1575d38b}
}
@ARTICLE{George08,
author = {George, D.~L.},
title = {Augmented Riemann solvers for the shallow water equations over variable
topography with steady states and inundation},
journal = {Journal of Computational Physics},
year = {2008},
volume = {227},
pages = {3089--3113},
abstract = {We present a class of augmented approximate Riemann solvers for the
shallow water equations in the presence of a variable bottom surface.
These belong to the class of simple approximate solvers that use
a set of propagating jump discontinuities, or waves, to approximate
the true Riemann solution. Typically, a simple solver for a system
of m conservation laws uses m such discontinuities. We present a
four wave solver for use with the the shallow water equations ---
a system of two equations in one dimension. The solver is based on
a decomposition of an augmented solution vector --- the depth, momentum
as well as momentum flux and bottom surface. By decomposing these
four variables into four waves the solver is endowed with several
desirable properties simultaneously. This solver is well-balanced:
it maintains a large class of steady states by the use of a properly
defined steady state wave --- a stationary jump discontinuity in
the Riemann solution that acts as a source term. The form of this
wave is introduced and described in detail. The solver also maintains
depth non-negativity and extends naturally to Riemann problems with
an initial dry state. These are important properties for applications
with steady states and inundation, such as tsunami and flood modeling.
Implementing the solver with LeVeque's wave propagation algorithm
[R.J. LeVeque, Wave propagation algorithms for multi-dimensional
hyperbolic systems, J. Comput. Phys. 131 (1997) 327-335] is also
described. Several numerical simulations are shown, including a test
problem for tsunami modeling.},
doi = {10.1016/j.jcp.2007.10.027},
file = {George08.pdf:George08.pdf:PDF},
keywords = {shallow water equations; hyperbolic conservation laws; finite volume
methods; Godunov methods; Riemann solvers; wave propagation; shock
capturing methods; tsunami modeling},
owner = {olivier},
timestamp = {2008.05.04}
}
@PHDTHESIS{George06,
author = {George, D.~L.},
title = {Finite volume methods and adaptive refinement for tsunami propagation
and inundation},
school = {University of Washington},
year = {2006},
abstract = {The shallow water equations are a commonly accepted governing system
for tsunami propagation and inundation. In their most generally valid
form, the equations are a set of hyperbolic integral conservation
laws --- a general class of systems for which an extensive body of
numerical theory exists. In this thesis, finite volume wave propagation
methods --- high resolution Godunov-type methods --- are extended
to this form of the shallow water equations in the context of tsunami
modeling. A novel approximate Riemann solver is developed in order
to handle the diverse flow regimes exhibited by tsunamis. This solver
provides well-balanced source term inclusion required for accurate
resolution of near steady state solutions --- a necessity when modeling
transoceanic tsunami propagation. The solver also preserves nonnegative
water depths and accurately captures discontinuities and moving shorelines,
making it appropriate for inundation modeling. Adaptive refinement
algorithms are extended to this application. These algorithms allow
evolving sub-grids of various resolutions to move with features in
the solution. Extending the adaptive algorithms to tsunami modeling
requires some new interpolation and integrating strategies in order
to preserve steady states. Finally, the methods are extended to solution
on a sphere or idealized earthfitted reference ellipsoids. Together,
the methods developed allow modeling transoceanic tsunami propagation
as well as coastal inundation in single global-scale simulations.},
file = {George06.pdf:George06.pdf:PDF},
owner = {olivier},
timestamp = {2008.05.05}
}
@MASTERSTHESIS{George04,
author = {George, D.~L.},
title = {Numerical approximation of the nonlinear shallow water equations
with topography and dry beds},
school = {University of Washington},
year = {2004},
file = {George04.pdf:George04.pdf:PDF},
owner = {olivier},
timestamp = {2008.05.05}
}
@ARTICLE{Gerbeau03,
author = {Gerbeau, J.-F. and Leli\`evre, T. and Le Bris, C.},
title = {Simulations of {MHD} flows with moving interfaces},
journal = {Journal of Computational Physics},
year = {2003},
volume = {184},
pages = {163--191},
abstract = {We report on the numerical simulation of a two-fluid magnetohydrodynamics
problem arising in the industrial production of aluminium. The motion
of the two non-miscible fluids is modeled through the incompressible
Navier-Stokes equations coupled with the Maxwell equations. Stabilized
finite elements techniques and an arbitrary Lagrangian-Eulerian formulation
(for the motion of the interface separating the two fluids) are used
in the numerical simulation. With a view to justifying our strategy,
details on the numerical analysis of the problem, with a special
emphasis on conservation and stability properties and on the surface
tension discretization, as well as results on tests cases are provided.
Examples of numerical simulations of the industrial case are eventually
presented.},
file = {Gerbeau03.pdf:Gerbeau03.pdf:PDF},
keywords = {magnetohydrodynamic; free interface; two-fluids flow; surface tension;
geometric conservation law; ALE formulation},
owner = {olivier},
timestamp = {2008.04.28}
}
@ARTICLE{Gerbeau01,
author = {Gerbeau, J.-F. and Perthame, B.},
title = {Derivation of viscous {S}aint-{V}enant system for laminar shallow
water; numerical validation},
journal = {Discrete Contin. Dyn. Syst. Ser. B},
year = {2001},
volume = {1},
pages = {89--102},
number = {1},
file = {Gerbeau01.pdf:Gerbeau01.pdf:PDF},
fjournal = {Discrete and Continuous Dynamical Systems. Series B. A Journal Bridging
Mathematics and Sciences},
issn = {1531-3492},
mrclass = {76D05 (35Q30 35Q35)},
mrnumber = {MR1821555 (2001m:76029)},
owner = {olivier},
timestamp = {2009.08.26}
}
@TECHREPORT{Gerbeau00,
author = {Gerbeau, J.-F. and Perthame, B.},
title = {Derivation of viscous {S}aint-{V}enant system for laminar water;
numerical validation},
institution = {INRIA},
year = {2000},
number = {4084},
month = dec,
abstract = {We derive the Saint-Venant system for the shallow waters including
small friction, viscosity and Coriolis-Boussinesq factor departing
from the Navier-Stokes system with a free moving boundary. This derivation
relies on the hydrostatic approximation where we follow the role
of viscosity and friction on the bottom. Numerical comparison between
the limiting Saint-Venant system and direct Navier-Stokes simulation
allow to validate this derivation.},
file = {Gerbeau00.pdf:Gerbeau00.pdf:PDF},
keywords = {Navier-Stokes equations; Saint-Venant equations; shallow water; free
surface; asymptotic analysis; viscosity; friction},
owner = {olivier},
timestamp = {2008.04.28}
}
@ARTICLE{vandeGiesen05,
author = {van de Giesen, Nick and Stomph, Tjeerd Jan and de Ridder, Nico},
title = {Surface runoff scale effects in {W}est {A}frican watersheds: modeling
and management options},
journal = {Agricultural Water Management},
year = {2005},
volume = {72},
pages = {109-130},
abstract = {Measurements of surface runoff from uniform slopes of different lengths
in West Africa have shown that longer slopes tend to have less runoff
per unit of length than short slopes. The main reason for this scale
effect is that once the rain stops, water on long slopes has more
opportunity time to inﬁltrate than water on short slopes. A validated
simple model is put forward that quantiﬁes the scale effects and
predicts under which circumstances they can be expected to be most
signiﬁcant. An overview is given of management options that are available
to farmers to reduce runoff at the ﬁeld and slope level. The potential
effects of these management options on the hydraulic conductivity,
Ksat, and Manning’s roughness coefﬁcient, n, are qualiﬁed. The model
is subsequently used to calculate the effect of changes in Ksat and
n on the runoff from slopes under rainfall conditions found in West
Africa. Finally, two design examples are given, namely maximum ﬁeld
lengths and dimensioning of interceptor drains.},
file = {vandeGiesen05.pdf:vandeGiesen05.pdf:PDF},
keywords = {Surface runoff; Scale effects; Erosion management; West Africa},
owner = {olivier},
timestamp = {2010.01.25}
}
@ARTICLE{Gilding83,
author = {Gilding, B. H.},
title = {The soil-moisture zone in a physically-based hydrologic model},
journal = {Advances in Water Resources},
year = {1983},
volume = {6},
pages = {36--43},
number = {1},
abstract = {The present paper describes an approach to modelling the unsaturated
soil-moisture zone in the framework of an integrated physically-based
hydrologic response model. It is supposed that the subsurface flow
regime may be viewed as two separate entities -- a saturated flow
system which may be modelled by standard two-dimensional regional
techniques, and a single overlying unsaturated zone in which the
flow is essentially vertical. Coupling takes place via the definition
of saturation at the lower boundary of the unsaturated zone, and
via a conservative water balance. Attention is focused on the computational
procedure for the unsaturated zone as a self-contained module. The
major difficulties are the definition of the interface between the
saturated and unsaturated zones, the nonlinear character of the equation
used to describe unsaturated flow, the inclusion of realistic atmospheric
boundary conditions, and, the interaction between water uptake by
plants and available soil-moisture. Each of these points is discussed,
in turn, with the emphasis on mathematically formulating the problem
in such a way that the most important physical features are reproduced
with a minimal amount of computational effort. The text concludes
with a few illustrative examples.},
doi = {DOI: 10.1016/0309-1708(83)90077-5},
file = {Gilding83.pdf:Gilding83.pdf:PDF},
issn = {0309-1708},
keywords = {Darcy; Richards},
owner = {olivier},
timestamp = {2010.06.15},
url = {http://www.sciencedirect.com/science/article/B6VCF-4888G6H-38/2/8927c7e1923798942bfd073fb5955287}
}
@ARTICLE{Gill77,
author = {Gill,A. E.},
title = {The hydraulics of rotating-channel flow},
journal = {Journal of Fluid Mechanics},
year = {1977},
volume = {80},
pages = {641-671},
number = {04},
abstract = {ABSTRACT Flow of a homogeneous inviscid fluid down a rotating channel
of slowly varying crosssection is considered, with particular reference
to conditions under which the flow is ‘hydraulically controlled’.
This problem is a member of a general class of problems of which
gas flow through a nozzle and flow over a broad-crested weir are
examples (Binnie 1949). A general discussion of such problems gives
the means for determining the position of the control section (which
is generally flow dependent) and shows that at this position there
always exist long-wave disturbances with zero phase speed (i.e. disturbances
are always ‘critical’ at the control section). The general
theory is applied to the rotating-channel problem for the case of
uniform potential vorticity. For this problem, three parameters are
needed to specify the upstream flow, and the control theory gives
a relationship between these parameters which depends on the geometry
of the channel.},
doi = {10.1017/S0022112077002407},
eprint = {http://journals.cambridge.org/article_S0022112077002407},
file = {Gill77.pdf:Gill77.pdf:PDF},
keywords = {bump; rotating channel; control section; analyrical solution},
owner = {olivier},
timestamp = {2010.06.18},
url = {http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=387360&fulltextType=RA&fileId=S0022112077002407}
}
@ARTICLE{Gimenez08,
author = {Gim\'enez, Rafael and Govers, Gerard},
title = {Effects of freshly incorporated straw residue on rill erosion and
hydraulics},
journal = {CATENA},
year = {2008},
volume = {72},
pages = {214 - 223},
number = {2},
abstract = {Rill hydraulics (and hence, flow detachment) are modified by the presence
of incorporated vegetation residue. Typically, water flow in the
rill is retarded due to the extra shear stress generated by the residue.
The main objective of this study was to develop an approach to predict
soil detachment by rill flow in the presence of freshly incorporated
vegetation residue that is compatible with our current understanding
of rill hydraulics and requires no additional information on rill
geometry. Laboratory experiments were carried out to collect a dataset
on rill flow detachment on surfaces with incorporated straw that
was compatible with existing dataset on bare soils (Giménez and Govers,
2001). Interaction between bed roughness and flow hydraulics in eroding
rills. Water Resources Research, Vol. 37 No. 3, 791-799). We found
that effective unit length shear force, [Gamma]e, is well related
to soil detachment when incorporated residue is present. The determination
of [Gamma]e is based on the recalculation of the wetted cross-section
area for a given flow velocity and slope, a hypothetical wetted cross-section
area is estimated using empirical relationships defined for rills
formed in bare soils. This procedure was also successfully applied
to data from former field experiments. The procedure allows estimating
erosion rates when flow characteristics (velocity and hydraulic radius)
are known. However, the prediction of these flow characteristics
remains uncertain.},
doi = {DOI: 10.1016/j.catena.2007.05.004},
file = {Gimenez08.pdf:Gimenez08.pdf:PDF},
issn = {0341-8162},
keywords = {Rill erosion},
owner = {olivier},
timestamp = {2009.11.14},
url = {http://www.sciencedirect.com/science/article/B6VCG-4P3TYM9-1/2/16152f714bda277bf78c6fa234b54dfe}
}
@MASTERSTHESIS{Gineau10,
author = {Gineau, Audrey},
title = {Propagation of pulsated waves in viscoelastic tubes: application
in arterial flows},
school = {UPMC},
year = {2010},
abstract = {We formulate a simple one-dimensional model for steady and pulsated
flows in straight and viscoelastic tube. With a numerical simulation,
we paid attention to the contributions of wall non-linear an viscous
parameters presents in this model. We validate the theoretical analysis
thanks to the simulation of the flows with the software COMSOL 3.4.
Experimental measurements has been carried out for the same configuration
of flows. Taking in account the different observed effects, we find
a good agreement between experimental and numerical results, and
we can confirm the predominant behaviour of the wall viscoelasticity.
We introduce a biomechanical issue with the simulation of the pulsated
flow in a viscoelastic tube that represents an aneurysm.
Nous pr\'esentons un mod\`ele int\'egral simple mono dimensionnel
en vue d’application pour les \'ecoulements biom\'ecaniques dans
les art\`eres. En pratique nous comparerons \`a une exp\'erience
d’\'ecoulement dans un tube droit visco\'elastique. Nous discutons
la contribution des termes de viscosit\'e fluide, de visco\'elasticit\'e
et de non lin\'éarit\'e de fluide et de paroi. Nous comparons num\'eriquement
cette approche 1D \`a la r\'esolution "compl\`ete” en axi-sym\'etrique
de l’int\'eraction fluide structure r\'esolue avec le code commercial
COMSOL. Ayant tenu compte de ces ph\'enom\`enes principaux, nous
observons un bon accord entre l’exp\'erience et la simulation. Notamment,
la visco\'elasticit\'e du tuyau a un r\^ole pr\'edominant. En perspective,
nous pr\'esentons un premier calcul dans une configuration pathologique
d’une art\`ere: l’an\'evrisme.},
file = {Gineau10.pdf:Gineau10.pdf:PDF},
keywords = {blood flow; artery},
owner = {olivier},
timestamp = {2010.11.26}
}
@TECHREPORT{Ginzburg08,
author = {Ginzburg, Irina and N\'ed\'elec, Yves},
title = {Exact solutions of one-dimensional steady-state shallow water equation},
institution = {Cemagref},
year = {2008},
month = {20 @jun},
abstract = {We present the analytical solutions for surface profiles on the flat,
arbitrary
inclined bottom bed. These solutions satisfy the one-dimensional shallow
water
equations (Saint-Venant equation) for the Darcy-Weisbach and Manning-Strickler
friction laws in inifinitely large channels, or without friction.
They express naturaly
the deviation of the surface profile from the constant water level,
in function of the
non-dimensional governing parameters. Obtained solutions are illustrated
for a
large range of the possible configurations and verified with the help
of the direct
numerical integration of the steady state Saint-Venant equation.},
file = {Ginzburg08.pdf:Ginzburg08.pdf:PDF},
keywords = {shallow flow equations; analytic solution; ANR METHODE; Saint-Venant;
direct method},
owner = {Fred. DARBOUX},
timestamp = {2008.08.11}
}
@ARTICLE{Ginzburg03,
author = {Ginzburg, I. and Steiner, K.},
title = {Lattice Boltzmann model for free-surface flow and its application
to filling process in casting},
journal = {Journal of Computational Physics},
year = {2003},
volume = {185},
pages = {61--99},
abstract = {A generalized lattice Boltzmann model to simulate free-surface is
constructed in both two and three dimensions. The proposed model
satisfies the interfacial boundary conditions accurately. A distinctive
feature of the model is that the collision processes is carried out
only on the points occupied partially or fully by the fluid. To maintain
a sharp interfacial front, the method includes an anti-diffusion
algorithm. The unknown distribution functions at the interfacial
region are constructed according to the first-order Chapman-Enskog
analysis. The interfacial boundary conditions are satisfied exactly
by the coefficients in the Chapman-Enskog expansion. The distribution
functions are naturally expressed in the local interfacial coordinates.
The macroscopic quantities at the interface are extracted from the
least-square solutions of a locally linearized system obtained from
the known distribution functions. The proposed method does not require
any geometric front construction and is robust for any interfacial
topology. Simulation results of realistic filling process are presented
: rectangular cavity in two dimensions and Hammer box, Campbell box,
Sheffield box, and Motorblock in three dimensions. To enhance the
stability at high Reynolds numbers, various upwind-type schemes are
developed. Free-slip and no-slip boundary conditions are also discussed.},
doi = {10.1016/S0021-9991(02)00048-7},
file = {Ginzburg03.pdf:Ginzburg03.pdf:PDF},
keywords = {Lattice Boltzmann models; free-surface phenomena; interface boundary
conditions; filling processes; injection molding; volume of fluid
method; interface boundary conditions; advection-schemes; upwind-schemes},
owner = {olivier},
timestamp = {2008.04.30}
}
@BOOK{Godlewski96,
title = {Numerical approximations of hyperbolic systems of conservation laws},
publisher = {Springer-Verlag, New York},
year = {1996},
author = {Godlewski, Edwige and Raviart, Pierre-Arnaud},
volume = {Applied Mathematical Sciences 118},
owner = {olivier},
timestamp = {2010.03.14}
}
@ARTICLE{Godoy10,
author = {Godoy, William F. and DesJardin, Paul E.},
title = {On the use of flux limiters in the discrete ordinates method for
3D radiation calculations in absorbing and scattering media},
journal = {Journal of Computational Physics},
year = {2010},
volume = {229},
pages = {3189--3213},
abstract = {The application of ﬂux limiters to the discrete ordinates method (DOM),
SN , for radiative transfer calculations is discussed and analyzed
for 3D enclosures for cases in which the intensities are strongly
coupled to each other such as: radiative equilibrium and scattering
media. A Newton–Krylov iterative method (GMRES) solves the ﬁnal systems
of linear equations along with a domain decomposition strategy for
parallel computation using message passing libraries in a distributed
memory system. Ray effects due to angular discretization and errors
due to domain decomposition are minimized until small variations
are introduced by these effects in order to focus on the inﬂuence
of ﬂux limiters on errors due to spatial discretization, known as
numerical diffusion, smearing or false scattering. Results are presented
for the DOM-integrated quantities such as heat ﬂux, irradiation and
emission. A variety of ﬂux limiters are compared to ‘‘exact” solutions
available in the literature, such as the integral solution of the
RTE for pure absorbing-emitting media and isotropic scattering cases
and a Monte Carlo solution for a forward scattering case. Additionally,
a non-homogeneous 3D enclosure is included to extend the use of ﬂux
limiters to more practical cases. The overall balance of convergence,
accuracy, speed and stability using ﬂux limiters is shown to be superior
compared to step schemes for any test case.},
file = {Godoy10.pdf:Godoy10.pdf:PDF},
keywords = {Radiative transfer equation; discrete ordinates method; flux limiters;
TVD schemes; radiation heat transfer; non-homogeneous 3D media; Newton-Krylov
GMRES; MC; minmod; Ospre; superbee; Sweby; UMIST, van Albada; van
Leer; Chakravarthy-Osher; Koren},
owner = {olivier},
timestamp = {2010.06.09}
}
@ARTICLE{GonzalezSanchis09,
author = {Gonz\'alez-Sanch\'is, M. and Murillo, J. and L\'opez-Barrera, D.
and Latorre, B. and Com\'in, F. and Garc\'ia-Navarro, P.},
title = {Application of numerical models to real problems: {S}imulation of
flood events with ecological interest in the {E}bro {R}iver},
journal = {Monograf\'ias de la {R}eal {A}cademia de {C}iencias de {Z}aragoza},
year = {2009},
volume = {31},
pages = {121-135},
abstract = {The application of a ﬁnite volume numerical scheme for 2D shallow-water
equations to ﬂood events in the Ebro River is presented. The area
of interest is a Natural Reserve playing an important role in protecting
human settlements from ﬂooding events and developing important biological
functions like water quality improvement, wildlife refuge, landscape
heterogeneity, etc. The hydraulic model used is based in the 2D transient
shallow water equations on irregular bed solved with an explicit
ﬁnite volume upwind scheme able to compute ﬂow advance over dry bed.
This model has been calibrated during the last years in a wide range
of real and academic cases giving an eﬃcient result. This study involves
the reliable simulation of, not only the ﬂood event itself but the
drying processes. It is necessary to remark the importance of the
correct characterisation of the roughness coeﬃcient and the topography.
The former is estimated from a previous classiﬁcation of structurally
homogeneous habitats and the latter is deﬁned by merging the DTM
data with the ﬁeld-measured ones. The calibration of the suitability
of the model to solve this problem is based on diﬀerent sets of ﬁeld
measurements: ﬂooded area and water levels measured during a ﬂood
event and time series of point-wise measurements of
water-depth and velocity during diﬀerent situations along the year.
Hydrological connectivity is highly related to the exchange processes
of nutrients and particulate matter between the river and the ﬂoodplain.
It represents an indicator of the dynamics of the ecological processes
in the ﬂoodplain and, consequently, is a key factor to be considered
for the restoration of degraded habitats of ﬂoodplains. The model
presented is a tool that helps to analyse the surface processes involved.},
file = {GonzalezSanchis09.pdf:GonzalezSanchis09.pdf:PDF},
keywords = {Hydrological connectivity; Unsteady surface ﬂow; wetting/drying; Finite
volume; Shallow-water},
owner = {olivier},
timestamp = {2010.01.30}
}
@ARTICLE{Gosse00,
author = {Gosse, L.},
title = {A well-balanced flux-vector splitting scheme designed for hyperbolic
systems of conservation laws with source terms},
journal = {Computers \& Mathematics with Applications},
year = {2000},
volume = {39},
pages = {135 - 159},
number = {9-10},
doi = {DOI: 10.1016/S0898-1221(00)00093-6},
file = {Gosse00.pdf:Gosse00.pdf:PDF},
issn = {0898-1221},
keywords = {Conservation laws},
owner = {olivier},
timestamp = {2009.07.21},
url = {http://www.sciencedirect.com/science/article/B6TYJ-40NFTJN-D/2/320458e48d7fbefdf910aaf251d7255c}
}
@ARTICLE{Gottardi08,
author = {Gottardi, G. and Venutelli, M.},
title = {An accurate time integration method for simplified overland flow
models},
journal = {Advances in Water Resources},
year = {2008},
volume = {31},
pages = {173--180},
month = aug,
abstract = {An accurate time integration method for the diffusion-wave and kinematic-wave
approximated models for the overland flow is pro- posed. The discretization
of the first- and second-order spatial derivatives in the basic equation
is obtained by using the second-order Lax-Wendroff and the three-point
centred finite difference schemes, respectively. For the solution
in time, the system of ordinary differ- ential equations, obtained
by the linearization of the celerity and of the hydraulic diffusivity
by Taylor series expansions, is integrated analytically. The stability
and the numerical dissipation and dispersion are investigated by
the Fourier analysis. A proper Courant num- ber, and the corresponding
time step for the numerical simulations can be established. In addition,
the proposed diffusion-wave and kine- matic-wave models are straightforwardly
extended to the two-dimensional flow. Test cases for both one- and
two-dimensional problems, compare the solutions of the diffusion-wave
and kinematic-wave models with analytical solutions, with experimental
results and with numerical solutions obtained by the Saint-Venant
equations. These simulations show that the proposed numerical-analytical
models accurately predict the overland flow for several situations,
in particular for unsteady rainfall rate and for spatial variations
of the surface roughness.},
doi = {10.1016/j.advwatres.2007.08.004},
file = {Gottardi08.pdf:Gottardi08.pdf:PDF},
keywords = {Overland flow; Diffusion and kinematic wave models; Finite difference
method; Stability and accuracy},
owner = {olivier},
timestamp = {2008.07.24}
}
@ARTICLE{Gottardi01,
author = {G. Gottardi and M. Venutelli},
title = {UPF: two-dimensional finite-element groundwater flow model for saturated-unsaturated
soils},
journal = {Computers \& Geosciences},
year = {2001},
volume = {27},
pages = {179 - 189},
number = {2},
abstract = {A finite-element program for modeling water flow in saturated-unsaturated
soils is presented. The program can handle non-uniform flow regions
having irregular boundaries and local anisotropy. The flow domain
can be either in a vertical or in a horizontal plane, or in a three
dimensional system with radial symmetry. The flow equation is solved
by using either a Galerkin finite-element (GFE), or a control-volume
finite-element (CVFE) method. The discretization of the flow domain
is obtained by using triangular finite elements and linear shape
functions; the integration in time is performed by a finite-difference
(FD) Picard scheme. Different schemes of the [`]upstream' and [`]lumping'
procedures in computing, respectively, the conductivity and capacity
matrices are compared, taking as evaluation parameters the global
mass balance errors and the stability of the solutions. The listing
of the FORTRAN 77 source code, along with the user manual, the description
of the subroutines used in the code, and four input files for four
test cases are available by anonymous FTP from ftp.iamg.org site
or may be downloaded by Internet from http://www.iamg.org/CGEditor/index.htm.},
doi = {DOI: 10.1016/S0098-3004(00)00082-0},
file = {Gottardi01.pdf:Gottardi01.pdf:PDF},
issn = {0098-3004},
keywords = {Numerical code; Unsaturated flow; Galerkin formulation; Control-volume
finite-element model; Richards},
owner = {olivier},
timestamp = {2010.06.04},
url = {http://www.sciencedirect.com/science/article/B6V7D-4234894-6/2/95acb3f2185f01208dcf4a23a0f89a1a}
}
@ARTICLE{Gottardi97,
author = {Gottardi, G. and Venutelli, M.},
title = {Landflow: Computer program for the numerical simulation of two-dimensional
overland flow},
journal = {Computers \& Geosciences},
year = {1997},
volume = {23},
pages = {77--89},
number = {1},
file = {Gottardi97.pdf:Gottardi97.pdf:PDF},
owner = {olivier},
timestamp = {2008.04.22}
}
@ARTICLE{Gottardi93,
author = {Gottardi, G. and Venutelli, M.},
title = {Richards: Computer program for the numerical simulation of the one-dimensional
infiltration into unsaturated soil},
journal = {Computers \& Geosciences},
year = {1993},
volume = {9},
pages = {1239--1266},
abstract = {Flow into unsaturated soil is governed by the Richards partial differential
equation expressing the mass conservation law for the water. Numerical
approximations based on different forms of this one-dimensional (1-D)
nonlinear partial differential equation can lead to significantly
different results for unsaturated flow problems. The Richards equation
may be written in three standard forms: the "h-based"
form, the "0-based" form, and the "mixed" form. Documentation is presented
for a program which integrates the three standard forms of this equation
using finite difference and finite-elementtechniques. Boundary conditions
at prefixed pressure head and prefixed injection rate are allowed;
moreover, mass balance errors are computed for controlling the accuracy
of the results and for comparing the performances of the three standard
forms. The listing of the computer code written in FORTRAN 77 is
included along with the user manual and some illustrative infiltration
tests in homogeneous and in layered soils.},
file = {Gottardi93.pdf:Gottardi93.pdf:PDF},
keywords = {numerical code; unsaturated flow; Richards' equations; finite difference
method; finite-element method; FORTRAN 77},
owner = {olivier},
timestamp = {2010.06.06}
}
@ARTICLE{Gottardi93b,
author = {Gottardi, G. and Venutelli, M.},
title = {A control-volume finite-element model for two-dimensional overland
flow},
journal = {Advances in Water Resources},
year = {1993},
volume = {16},
pages = {277--284},
abstract = {A control-volume finite-element (CVFE) formulation for the numerical
integration of the two-dimensional diffusion hydrodynamic model is
presented. Three different methods for computing the transmissivity
terms are compared on the basis of the global boundary-outflow error
for both the finite-clement (FE) and the CVFE formulation of the
model. As is well known, the two-dimensional diffusion-hydrodynamic
model (DHM) is obtained from the more general overland-flow mode],
based on momentum and mass-balance equations, with inertia terms
neglected. The applied CVFE technique uses linear triangular finite-element
shape functions to estimate the value of the variables at the boundaries
of the subcontrol volume of each node. The use of linear-interpolation
functions allows the elemental matrices of the model to be expressed
in a simple polynomial form. Integration in time is obtained by a
fiuite-difference (FD) Picard scheme. Some numerical examples are
presented to compare, on the basis of global-outflow errors and analytical
solution, the performances of six schemes of the
CVFE method with that of the equivalent Galerkin FE formulations.},
file = {Gottardi93b.pdf:Gottardi93b.pdf:PDF},
keywords = {overland unsteady flow; two-dimensional diffusion model; control-volume
finite-element model},
owner = {olivier},
timestamp = {2010.06.09}
}
@ARTICLE{Gourgue09,
author = {Gourgue, Olivier and Comblen, Richard and Lambrechts, Jonathan and
K\¨arn\¨a and Legat, Vincent and Deleersnijder, Eric},
title = {A flux-limiting wetting-drying method for finite-element shallow-water
models with application to the Scheldt Estuary},
journal = {Advances in Water Resources},
year = {2009},
volume = {32},
pages = {1726--1739},
abstract = {We present a flux-limiting wetting–drying approach for finite-element
discretizations of the shallow-water equations using discontinuous
linear elements for the elevation. The key ingredient of the method
is the use of limiters for generalized nodal fluxes. This method
is implemented into the Second-generation Louvain-la-Neuve Ice-ocean
Model (SLIM), and is verified against standard test cases. The method
is further applied to the wetting and drying of sand banks in the
Scheldt Estuary, which is located in northern Belgium and the southern
Netherlands. The results obtained for both the benchmarks and the
realistic problem illustrate the accuracy of the method in describing
the hydrodynamics in the vicinity of dry areas. In particular, the
method strictly conserves mass, and there is no transport through
dry areas.},
doi = {10.1016/j.advwatres.2009.09.005},
file = {Gourgue09.pdf:Gourgue09.pdf:PDF},
keywords = {wetting-drying; tidal flat; estuary; Scheldt; finite element; Discontinuous
Galerkin; Balzano; Thacker},
owner = {olivier},
timestamp = {2010.11.24}
}
@ARTICLE{Goutal02,
author = {Goutal, N. and Maurel, F.},
title = {A finite volume solver for 1{D} shallow-water equations applied to
an actual river},
journal = {International Journal for Numerical Methods in Fluids},
year = {2002},
volume = {38},
pages = {1--19},
doi = {10.1002/fld.201},
file = {Goutal02.pdf:Goutal02.pdf:PDF},
keywords = {shallow-water equations; river; source terms; finite volume; Roe scheme},
owner = {olivier},
timestamp = {2008.05.03}
}
@TECHREPORT{Goutal97,
author = {Goutal, N. and Maurel, F.},
title = {Proceedings of the 2nd workshop on dam-break wave simulation},
institution = {EDF-DER},
year = {1997},
abstract = {Dans le cadre du groupe de travail AIRH sur les simulations num\'eriques
d'onde de submersion, ce rapport est une compilation des r{\'e}sultats
sur les cas-tests analytiques pr{\'e}sent{\'e}s {\`a} Lisbonne en
Novembre 1996.},
file = {Goutal97.pdf:Goutal97.pdf:PDF},
owner = {olivier},
timestamp = {2008.05.01}
}
@ARTICLE{Govers07,
author = {Govers, Gerard and Gim\'enez, Rafael and Van Oost, Kristof},
title = {Rill erosion: Exploring the relationship between experiments, modelling
and field observations},
journal = {Earth-Science Reviews},
year = {2007},
volume = {84},
pages = {87 - 102},
number = {3-4},
abstract = {Predicting rill erosion rates for a given discharge and slope minimally
requires a model for rill hydraulics that allows the prediction of
hydraulic parameters and a model for sediment detachment. Several
relationships that describe rill hydraulics and/or sediment detachment
within an eroding rill have been proposed and are incorporated into
state of the art soil erosion models. In this paper a critical review
of the theoretical concepts that are underpinning current rill flow
and sediment detachment models is made in the light of recent experimental
results. Approaches to define detachment-hydraulics relationship
are generally based on developments in alluvial river hydraulics.
However, experimental evidence to support the use of these concepts
in models of rill erosion is scarce and recent experimental findings
suggest that the basic assumptions used to model rill erosion are
to some extent flawed. An analysis of empirically collected data
on rill hydraulics conclusively shows that the empirical Manning
equation does not hold for rill flow and should therefore not be
used in rill erosion models. An empirical power law relationship
relating velocity to discharges is much better in agreement with
available experimental data, both for soils with and without rock
fragments. In the absence of vegetation residue and/or other macroscopic,
immobile elements such as rock fragments, total shear stress and
unit length shear force can be used to predict soil detachment. The
use of unit length shear force has the advantage that no information
about rill geometry is necessary. The evidence for sediment load
and rill flow detachment interaction is somewhat conflicting: the
presence of a heavy sediment load appears to restrict rill flow detachment,
but the exact form of the relationship between detachment rate and
sediment load remains unclear. The effect of the presence of a sediment
load on flow detachments under natural conditions is also limited
by the nature of the detachment and transporting capacity relationships:
on a rectilinear hillslope, transporting capacity increases much
more rapidly with discharge than detachment capacity. We propose
modifications to the theoretical formulations used in rill erosion
models so that they are in better agreement with experimental evidence.
Finally, we illustrate the potential of simplified models and conclude
that the combination of empirical equations for flow detachment and
rill hydraulics leads to results that are consistent with empirical
data relating rill erosion rates to topography.},
doi = {DOI: 10.1016/j.earscirev.2007.06.001},
file = {Govers07.pdf:Govers07.pdf:PDF},
issn = {0012-8252},
keywords = {rill erosion},
owner = {olivier},
timestamp = {2009.11.14},
url = {http://www.sciencedirect.com/science/article/B6V62-4P6VDS8-1/2/ecff216085e2b4a1f89f664e40f15f30}
}
@ARTICLE{Govindaraju95,
author = {Govindaraju, Rao~S.},
title = {Non-dimensional analysis of a physically based rainfall-runoff-erosion
model over steep slopes},
journal = {Journal of Hydrology},
year = {1995},
volume = {173},
pages = {327 - 341},
number = {1-4},
abstract = {A non-dimensional analysis is undertaken to study the rainfall-runoff-erosion
process over steep slopes. This analysis leads to a reduction in
the number of parameters required for modeling erosion by overland
flow. Two important parameters are identified: the dimensionless
erodibility [sigma]* denoting the average erodibility over the whole
slope, and G which partitions the sediment transport dynamics into
detachment, deposition and equilibrium regimes. Analytical solutions
are presented for the non-dimensional equations. It is observed that
G remains practically time-invariant but has a marked spatial variation
along the slope. The dimensionless sediment discharge along the slope
shows strong dependence on both [sigma]* and G. Some asymptotic results
are also discussed along with practical applications of this work.},
doi = {DOI: 10.1016/0022-1694(95)02738-B},
file = {Govindaraju95.pdf:Govindaraju95.pdf:PDF},
issn = {0022-1694},
owner = {olivier},
timestamp = {2009.11.14},
url = {http://www.sciencedirect.com/science/article/B6V6C-3Y6PG7K-K/2/0452a8897a74ecdd7eb274a62ab4095c}
}
@ARTICLE{Govindaraju91,
author = {Govindaraju, Rao S. and Kavvas, M. L.},
title = {Modeling the erosion process over steep slopes: approximate analytical
solutions},
journal = {Journal of Hydrology},
year = {1991},
volume = {127},
pages = {279--305},
abstract = {Analytical expressions are developed for the rainfall-runoff-erosion
process on steep hillslopes subjected to time-varying rainfall events.
The erosion equation is essentially represented as a first-order
reaction with the reaction rate being represented by the soil erodibility.
The analytical transient solutions are based upon the assumption
that the flow and sediment discharge have a constant relationship
as during steady-state conditions. The analytical solution for the
sediment discharge performs well when compared with numerical and
experimental results. The approximate analytical solution for the
concentration profile is the asymptotic limit of the transient numerical
solutions. An error analysis shows that the analytical solutions
improve with increasing slope length and that the solution model
presented here is applicable to a wide range of physical situations.},
file = {Govindaraju91.pdf:Govindaraju91.pdf:PDF},
keywords = {diffusion wave; sediment transport dynamics; analyrical; hydrograph},
owner = {olivier},
timestamp = {2010.06.14}
}
@ARTICLE{Govindaraju96,
author = {Govindaraju, R. S. and Kavvas, M. L. and Jones, S. E. and Rolston,
D. E.},
title = {Use of Green-Ampt model for analyzing one-dimensional convective
transport in unsaturated soils},
journal = {Journal of Hydrology},
year = {1996},
volume = {178},
pages = {337 - 350},
number = {1-4},
abstract = {A general analytical solution to the equation describing purely convective
vertical transport of a conservative solute under transient water
flow conditions is presented. Richards equation does not yield analytical
solutions for the flow field, except under restrictive choices of
hydraulic properties relating water content, hydraulic conductivity
and the soil matric potential. The utility of the Green-Ampt model
for homogeneous unsaturated soils is investigated as an alternative
to Richards equation. This model, though approximate, provides analytical
solutions to the flow field. It is found that the flow quantities
required for the analytical solution of convective transport (specifically
the soil water storage) are predicted accurately by the Green-Ampt
model. Comparisons of numerical and analytical solutions of solute
concentration profiles suggest that the Green-Ampt water flow model
is adequate for convective solute transport predictions, and that
the flow field need not be computed by the more numerically expensive
Richards equation for this problem.},
doi = {DOI: 10.1016/0022-1694(95)02796-3},
file = {Govindaraju96.pdf:Govindaraju96.pdf:PDF},
issn = {0022-1694},
keywords = {Green-Ampt; infiltration; transport; analytical},
owner = {olivier},
timestamp = {2010.06.06},
url = {http://www.sciencedirect.com/science/article/B6V6C-3VW297J-1M/2/0e89f7feaffe97652faa5501180334aa}
}
@ARTICLE{Gowdish09,
author = {Gowdish, L. and Mu\~noz-Carpena, R.},
title = {An {I}mproved {G}reen-{A}mpt {I}nfiltration and {R}edistribution
{M}ethod for {U}n {M}ultistorm {S}eries},
journal = {Vadose Zone Journal},
year = {2009},
volume = {8},
pages = {470--479},
number = {2},
month = May,
file = {Gowdish09.pdf:Gowdish09.pdf:PDF},
keywords = {Green-Ampt; infiltration; modified Green-Ampt},
owner = {olivier},
timestamp = {2010.04.24}
}
@ARTICLE{Grant97,
author = {Grant, Gordon~E.},
title = {Critical flow constrains flow hydraulics in mobile-bed streams: {A}
new hypothesis},
journal = {Water Resources Research},
year = {1997},
volume = {33},
pages = {349-358},
number = {2},
month = feb,
abstract = {A new hypothesis predicts that in mobile-bed river channels, interactions
between the channel hydraulics and bed conﬁguration prevent the Froude
number (Fr)
from exceeding 1 for more than short distances or periods of time.
Flow conditions in many steep, competent streams appear to be close
to critical. Froude numbers of steep (slope ~ 0.01) sand-bed streams
with considerable freedom to adjust boundaries oscillate between
0.7 and 1.3 over 20- to 30-s cycles, with an average of 1.0 at the
channel thalweg. Critical ﬂow in these streams is maintained by the
interaction between the mobile bed and free water surface at high
Fr, which results in a cyclical pattern of creation and destruction
of bed forms. Field observations support that a similar mechanism
of ﬂow– bed form interaction constrains Fr <= 1 in active-bed braided
gravel rivers, step-pool streams, laboratory rills, lahar-runout
channels, and even some bedrock channels. Empirical and analytical
results show that as slope increases, competent ﬂows tend to asymptotically
approach critical ﬂow. An assumption of critical ﬂow would dramatically
simplify paleohydraulic ﬂow reconstructions and modeling of ﬂow hydraulics
in high gradient streams.},
file = {Grant97.pdf:Grant97.pdf:PDF},
owner = {olivier},
timestamp = {2009.11.29}
}
@ARTICLE{Greco96,
author = {Greco, Massimo},
title = {Evoluzione di onde a fronte ripido di altezza finita},
journal = {Scritti in onore di Mario Ippolito},
year = {1996},
volume = {Napoli, 16 e 17 maggio 1996},
pages = {349--361},
file = {Greco96.pdf:Greco96.pdf:PDF},
keywords = {roll waves; Chezy; Gauckler-Strickler; Froude; Saint-Venant},
owner = {olivier},
timestamp = {2010.05.02}
}
@ARTICLE{Green11,
author = {Green, W.~H. and Ampt, G.~A.},
title = {Studies on soil physics},
journal = {The Journal of Agricultural Science},
year = {1911},
volume = {4},
pages = {1-24},
file = {Green11.pdf:Green11.pdf:PDF},
owner = {olivier},
timestamp = {2008.05.07}
}
@ARTICLE{Greenberg96,
author = {Greenberg, J.~M. and Le{R}oux, A.-Y.},
title = {A well-balanced scheme for the numerical processing of source terms
in hyperbolic equation},
journal = {SIAM Journal on Numerical Analysis},
year = {1996},
volume = {33},
pages = {1--16},
file = {Greenberg96.pdf:Greenberg96.pdf:PDF},
owner = {olivier},
timestamp = {2008.04.28}
}
@ARTICLE{Grifoll96,
author = {Grifoll, Jordi and Cohen, Yoram},
title = {Contaminant migration in the unsaturated soil zone: the effect of
rainfall and evapotranspiration},
journal = {Journal of Contaminant Hydrology},
year = {1996},
volume = {23},
pages = {185 - 211},
number = {3},
abstract = {The potential effect of rainfall and evapotranspiration on contaminant
migration in the unsaturated soil zone was studied using a deterministic
dynamic modeling approach. The contaminant mass transfer equation
was solved along with Richards' equation for water transport subject
to dynamic surface boundary conditions that consider rainfall and
evapotranspiration. As an illustration of the effect of rainfall
and evapotranspiration on various transport mechanisms, test cases
are presented for the transport and volatilization of benzene, 1,1,2,2-tetrachloroethane
and methanol for a loam-type soil using self-consistent dynamic rainfall
and evapotranspiration weather sequences. The present study suggests
that transport mechanisms such as diffusion, dispersion and convection
can all be significant, to varying degrees, during various parts
of the year. The temporal variability of both the volatilization
flux and the amount of chemical remaining in the unsaturated soil
zone are significantly impacted by the dynamics of rainfall and the
period of initial contamination.},
doi = {DOI: 10.1016/0169-7722(95)00086-0},
file = {Grifoll96.pdf:Grifoll96.pdf:PDF},
issn = {0169-7722},
keywords = {Richards; pollutant; analytical},
owner = {olivier},
timestamp = {2010.06.03},
url = {http://www.sciencedirect.com/science/article/B6V94-3VWG0D4-9/2/af6ca7ea54ee912a6ce0ba54e9a22551}
}
@MASTERSTHESIS{Grigis08,
author = {Grigis, Lucas},
title = {Mesure de champs de vitesse pour la modélisation du ruissellement
sur surfaces rugueuses},
school = {Master 1 ``Sciences de la Terre, de l'Univers et de l'Environnement''
- Université Joseph Fourier},
year = {2008},
address = {Grenoble},
note = {Encadrant : Cédric Legout},
file = {Grigis08.pdf:Grigis08.pdf:PDF},
keywords = {ANR METHODE, metrology, overland flow, laboratory experiment, Particle
Image Velocimetry, PIV, velocity},
owner = {olivier},
timestamp = {2008.10.16}
}
@ARTICLE{Guinot09b,
author = {Guinot, V.},
title = {Upwind finite volume solution of sensitivity equations for hyperbolic
systems of conservation laws with discontinuous solutions},
journal = {Computers \& Fluids},
year = {2009},
volume = {38},
pages = {1697 - 1709},
number = {9},
doi = {DOI: 10.1016/j.compfluid.2009.03.002},
file = {Guinot09b.pdf:Guinot09b.pdf:PDF},
issn = {0045-7930},
owner = {olivier},
timestamp = {2009.07.21},
url = {http://www.sciencedirect.com/science/article/B6V26-4VW551C-1/2/3a28c519ab53e638055c478554abf0cb}
}
@ARTICLE{Guinot09,
author = {Guinot, Vincent and Cappelaere, Bernard},
title = {Sensitivity analysis of 2D steady-state shallow water flow. Application
to free surface flow model calibration},
journal = {Advances in Water Resources},
year = {2009},
volume = {32},
pages = {540 - 560},
number = {4},
doi = {DOI: 10.1016/j.advwatres.2009.01.005},
file = {Guinot09.pdf:Guinot09.pdf:PDF},
issn = {0309-1708},
keywords = {Model sensitivity},
owner = {olivier},
timestamp = {2009.07.21},
url = {http://www.sciencedirect.com/science/article/B6VCF-4VGXC8N-3/2/5435fedcd80025cc4e5e8715a1cfff5c}
}
@ARTICLE{Guy09c,
author = {Guy, Brian~T. and Dickenson, W.~Trevor and Sohrabi, Teymour~M. and
Rudra, Ramesh~P.},
title = {Development of an empirical model for calculating sediment-transport
capacity in shallow overland flows: Model calibration},
journal = {Biosystems Engineering},
year = {2009},
volume = {103},
pages = {245 - 255},
number = {2},
doi = {DOI: 10.1016/j.biosystemseng.2009.02.013},
file = {Guy09c.pdf:Guy09c.pdf:PDF},
issn = {1537-5110},
owner = {olivier},
timestamp = {2009.07.21},
url = {http://www.sciencedirect.com/science/article/B6WXV-4W1BFPK-1/2/fae324074f2622493d7b1b7300a5b7ba}
}
@ARTICLE{Guy09a,
author = {Guy, Brian~T. and Rudra, Ramesh~P. and Dickenson, W.~Trevor and Sohrabi,
Teymour~M.},
title = {Empirical model for calculating sediment-transport capacity in shallow
overland flows: Model development},
journal = {Biosystems Engineering},
year = {2009},
volume = {103},
pages = {105 - 115},
number = {1},
doi = {DOI: 10.1016/j.biosystemseng.2009.02.002},
file = {Guy09a.pdf:Guy09a.pdf:PDF},
issn = {1537-5110},
owner = {olivier},
timestamp = {2009.07.21},
url = {http://www.sciencedirect.com/science/article/B6WXV-4VV1B9W-2/2/21087ecb3e51f24e710c12c0a07b64ec}
}
@ARTICLE{Guy09b,
author = {Guy, Brian~T. and Sohrabi, Teymour~M. and Rudra, Ramesh~P. and Dickinson,
W.~Trevor},
title = {An empirical model development for the sediment transport capacity
of shallow overland flow: model validation},
journal = {Biosystems Engineering},
year = {2009},
volume = {In Press, Corrected Proof},
pages = { - },
doi = {DOI: 10.1016/j.biosystemseng.2009.03.004},
file = {Guy09b.pdf:Guy09b.pdf:PDF},
issn = {1537-5110},
owner = {olivier},
timestamp = {2009.07.21},
url = {http://www.sciencedirect.com/science/article/B6WXV-4WNWW70-1/2/2006e5eccf7a2d2b4fe4ea67ea6978ba}
}
@INPROCEEDINGS{Harterich05,
author = {H\"arterich, J.},
title = {Existence of rollwaves in a viscous shallow water equation},
booktitle = {Proceedings Equadiff 2003, World Scientific, p.511--516},
year = {2005},
abstract = {In the present paper we consider a shallow water equation with Chezy
friction term. It is well-known that this hyperbolic PDE admits a
one-parameter family of discontinuous periodic roll wave solutions
parametrized by their wavelength as well as a discontinuous homoclinic
wave.
We show that analogous traveling waves exist when small viscous terms
of size \epsilon are added to the equation and determine how the
velocity of the viscous homoclinic waves diﬀers from the velocity
of the inviscid waves. The correponding traveling wave equation leads
to a singularly perturbed problem involving points on the slow manifold
which are not normally hyperbolic. The periodic roll waves follow
stable
and unstable parts of the slow manifold and are therefore of “canard”
type.},
file = {Harterich05.pdf:Harterich05.pdf:PDF},
keywords = {roll waves; viscosity},
owner = {olivier},
timestamp = {2010.05.02}
}
@ARTICLE{Habibzadeh09,
author = {Habibzadeh, Alireza and Omid, Mohammad Hossein},
title = {Bedload resistance in supercritical flow},
journal = {International Journal of Sediment Research},
year = {2009},
volume = {24},
pages = {400--409},
number = {4},
abstract = {The movement of bedload in subcritical flow produces additional roughness
as compared to flow in a rigid bed. The magnitude of this bed load
roughness is proportional to the thickness of the sediment layer
moving along the bed, the particle size and the sediment concentration.
In a supercritical flow, however, further resistance is expected
due to the momentum absorption by the high flow velocity. In this
study the effect of sediment movement on the flow resistance in supercritical
flow was experimentally investigated. The experiments included flows
over smooth and rough beds carrying sediment of mean diameters D50=2.80,
5.42 and 7.06 mm in a rigid rectangular channel. The results show
that the sediment transport may increase the friction factor by up
to 90% and 60% in smooth and rough beds, respectively. Bedload extracts
its momentum from the flow, which causes a reduction of near bed
flow velocity and steeper velocity gradient near the bed resulting
in an increase in shear velocity as well as in roughness height.
The increase in friction factor is directly related to bedload concentration
and particle size.},
file = {Habibzadeh09.pdf:Habibzadeh09.pdf:PDF},
keywords = {hydraulic resistance; friction factor; bedload transport; supercritical
flow},
owner = {olivier},
timestamp = {2011.02.24}
}
@ARTICLE{Hall89,
author = {Hall, M. J. and Johnston, P.~M. and Wheater, H.~S.},
title = {Evaluation of overland flow models using laboratory catchment data:
{I}. An apparatus for laboratory catchment studies},
journal = {Hydrological Sciences Journal},
year = {1989},
volume = {34},
pages = {277--288},
number = {3},
abstract = {A laboratory catchment provides experimental control over hydrological
variables which is notably absent in the monitoring of experimental
and representative basins. In designing an apparatus for laboratory
catchment studies, particular attention must be paid to the methods
of simulating rainfall over, and of measuring discharge from, the
artificial catchments. The former should reflect the importance of
the several characteristics of natural rainfall to the purpose of
the experiments, while the latter should be capable of registering
instantaneous rates of runoff directly. Moreover, every effort should
be made to employ the most efficient and economical methods of setting-up
and recording the results of experiments. Data from such a facility
at Imperial College, London, have been employed for the development
and intercomparison of numerical models of overland flow.},
file = {Hall89.pdf:Hall89.pdf:PDF},
owner = {olivier},
timestamp = {2008.05.04}
}
@ARTICLE{Haque02,
author = {Haque, A.},
title = {Study of surface runoff using physical models},
journal = {Environmental Geology},
year = {2002},
volume = {41},
pages = {797--805},
doi = {10.1007/s00254-001-0455-1},
file = {Haque02.pdf:Haque02.pdf:PDF},
keywords = {surface runoff; kinematic wave approximations; Darcy-Weisbach resistance
formula; laminar flow; constant slope; constant rainfall-excess},
owner = {olivier},
timestamp = {2008.05.01}
}
@ARTICLE{Harten87,
author = {Harten, Ami and Engquist, Bjorn and Osher, Stanley and Chakravarthy,
Sukumar~R.},
title = {Uniformly {H}igh {O}rder {A}ccurate {E}ssentially {N}on-oscillatory
{S}chemes, {III}},
journal = {Journal of Computational Physics},
year = {1987},
volume = {71},
pages = {231-303},
month = aug,
abstract = {We continue the construction and the analysis of essentially non-oscillatory
shock capturing methods for the approximation of hyperbolic conservation
laws. We present an hierarchy of uniformly high-order accurate schemes
which generalizes Godunov’s scheme and its second-order accurate
MUSCL extension to an arbitrary order of accuracy. The design involves
an essentially non-oscillatory piecewise polynomial reconstruction
of the solution from its cell averages, time evolution through an
approximate solution of the resulting initial value problem, and
averaging of this approximate solution over each cell. The reconstruction
algorithm is derived
from a new interpolation technique that, when applied to piecewise
smooth data, gives high-order accuracy whenever the function is smooth
but avoids a Gibbs phenomenon at discontinuities. Unlike standard
ﬁnite difference methods this procedure uses an adaptive stencil
of grid points and, consequently, the resulting schemes are highly
nonlinear.},
file = {Harten87.pdf:Harten87.pdf:PDF},
owner = {olivier},
timestamp = {2009.11.04}
}
@ARTICLE{Harten83,
author = {Harten, Amiram and Lax, Peter D. and van Leer, Bram},
title = {On upstream differencing and Godunov-type schemes for hyperbolic
conservation laws},
journal = {SIAM Review},
year = {1983},
volume = {25},
pages = {35--61},
number = {1},
month = Jan,
abstract = {This paper reviews some of the recent developments in upstream difference
schemes through a unified representation, in order to enable comparison
between the various schemes. Special attention is given to the Godunov-type
schemes that result from using an approximate solution of the Riemann
problem. For schemes based on flux splitting, the approximate Riemann
solution can be interpreted as a solution of the collisionless Boltzmann
equation.},
file = {Harten83.pdf:Harten83.pdf:PDF},
keywords = {HLL},
owner = {olivier},
timestamp = {2011.03.06}
}
@ARTICLE{Harten86,
author = {Harten, Ami and Osher, Stanley and Engquist, Bjorn and Chakravarthy,
Sukumar~R.},
title = {Some results on uniformly high-order accurate essentially nonoscillatory
schemes},
journal = {Applied Numerical Mathematics},
year = {1986},
volume = {2},
pages = {347 - 377},
number = {3-5},
note = {Special Issue in Honor of Milt Rose's Sixtieth Birthday},
abstract = {We continue the construction and the analysis of essentially nonoscillatory
shock capturing methods for the approximation of hyperbolic conservation
laws. These schemes share many desirable properties with total variation
diminishing schemes, but TVD schemes have at most first-order accuracy
in the sense of truncation error, at extrema of the solution. In
this paper we construct an hierarchy of uniformly high-order accurate
approximations of any desired order of accuracy which are tailored
to be essentially nonoscillatory. This means that, for piecewise
smooth solutions, the variation of the numerical approximation is
bounded by that of the true solution up to O(hR - 1), for 0 Kc for reduced tillage > Kc for
no tillage) but not [tau]cr. It was concluded that Kc and [tau]cr
are not related to each other and that soil and macro-environmental
properties affecting the foremost do not necessarily affect the latter
as well and vise versa. Often Kc seems to be a more appropriate parameter
than [tau]cr to represent the differences in soil erosion resistance
under various soil and environmental conditions (e.g. bulk density,
moisture content, consolidation, tillage). The two parameters represent
different quantities and are therefore both needed to characterize
the soil's resistance to concentrated flow erosion.},
doi = {DOI: 10.1016/j.earscirev.2006.08.001},
file = {Knapen07.pdf:Knapen07.pdf:PDF},
issn = {0012-8252},
keywords = {soil erosion resistance},
owner = {olivier},
timestamp = {2009.11.14},
url = {http://www.sciencedirect.com/science/article/B6V62-4M57HBS-1/2/d3954edab16e397245585bfb504023dd}
}
@ARTICLE{Kollet06,
author = {Kollet, Stefan J; and Maxwell, Reed M.},
title = {Integrated surface-groundwater flow modeling: A free-surface overland
flow boundary condition in a parallel groundwater flow model},
journal = {Advances in Water Resources},
year = {2006},
volume = {29},
pages = {945--958},
abstract = {Interactions between surface and groundwater are a key component of
the hydrologic budget on the watershed scale. Models that honor these
interactions are commonly based on the conductance concept that presumes
a distinct interface at the land surface, separating the surface
from the subsurface domain. These types of models link the subsurface
and surface domains via an exchange ﬂux that depends upon the magnitude
and direction of the hydraulic gradient across the interface and
a proportionality constant (a measure of the hydraulic connectivity).
Because experimental evidence of such a distinct interface is often
lacking in ﬁeld systems, there
is a need for a more general coupled modeling approach. A more general
coupled model is presented that incorporates a new two-dimensional
overland ﬂow simulator into the parallel three-dimensional variably
saturated subsurface ﬂow code ParFlow [Ashby SF, Falgout RD. A parallel
multigrid preconditioned conjugate gradient algorithm for groundwater
ﬂow simulations. Nucl Sci Eng 1996;124(1):145–59; Jones JE, Woodward
CS. Newton–Krylov-multigrid solvers for large-scale, highly heterogeneous,
variably saturated ﬂow problems. Adv Water Resour 2001;24:763–774].
This new overland ﬂow simulator takes the form of an upper boundary
condition and is, thus, fully integrated without relying on the conductance
concept. Another important advantage of this approach is the eﬃcient
parallelism incorporated into ParFlow, which is exploited by the
overland ﬂow simulator.
Several veriﬁcation and simulation examples are presented that focus
on the two main processes of runoﬀ production: excess inﬁltration
and saturation. The model is shown to reproduce an analytical solution
for overland ﬂow, replicates a laboratory experiment for surface–subsurface
ﬂow and compares favorably to other commonly used hydrologic models.
The inﬂuence of heterogeneity of the shallow subsurface on overland
ﬂow is also examined. The results show the propagation of uncertainty
due to subsurface heterogeneity to the overland ﬂow predictions and
demonstrate the usefulness of our approach. Both the overland ﬂow
component and the coupled model are evaluated in a parallel scaling
study and show to be eﬃcient.},
file = {Kollet06.pdf:Kollet06.pdf:PDF},
keywords = {-groundwater interactions; overland flow boundary condition; integrated
parallel modeling; subsurface heterogeneity; hydrograph uncertainty},
owner = {olivier},
timestamp = {2010.04.24}
}
@ARTICLE{Kool94,
author = {Kool, J.B. and Huyakorn, P.S. and Sudicky, E.A. and Saleem, Z.A.},
title = {A composite modeling approach for subsurface transport of degrading
contaminants from land-disposal sites},
journal = {Journal of Contaminant Hydrology},
year = {1994},
volume = {17},
pages = {69--90},
number = {1},
abstract = {A composite modeling approach is presented for simulating the three-dimensional
(3-D) subsurface transport of dissolved contaminants with transformation
products. The approach is based on vertical infiltration and contaminant
transport in the unsaturated zone and 3-D groundwater flow and contaminant
migration in the saturated zone. Moisture movement and groundwater
flow are considered to be steady, but contaminant transport is treated
as transient. The model allows for advection, dispersion, linear
or nonlinear equilibrium sorption, and first-order biochemical transformation
of either a single contaminant species, or a multi-species, straight
or branched, decay chain. The model is designed for regulatory decision
making using Monte Carlo analysis. For such applications considerable
emphasis is placed on computational efficiency and robustness of
the model. An efficient and robust semi-analytical method is used
to perform the steady-state solution for infiltration through the
unsaturated zone. A variety of transport solutions, corresponding
to transient or steady state, and linear or nonlinear sorption conditions,
are incorporated in the model. For transient linear transport, the
Laplace transform technique is used. The transformed unsaturated-zone
transport equation is solved analytically; the transformed saturated-zone
transport is solved numerically using the Laplace transform-Galerkin
(LTG) technique which permits a nonuniform groundwater flow field,
reflecting the influence of locally higher infiltration from the
waste source. The model contains fully 3-D solutions for flow and
transport in the saturated zone, as well as two-dimensional solutions
for vertical cross-sectional and areal scenarios. Model formulations
and solution schemes are verified by comparison against a fully 3-D,
variably saturated flow and transport code for a hypothetical problem
which represents a typical landfill. The model is applied also to
simulate a controlled release field experiment and the model predictions
compare well with groundwater monitoring data for the site.},
doi = {DOI: 10.1016/0169-7722(94)90078-7},
file = {Kool94.pdf:Kool94.pdf:PDF},
issn = {0169-7722},
keywords = {unsaturated zone; saturated zone},
owner = {olivier},
timestamp = {2010.06.15},
url = {http://www.sciencedirect.com/science/article/B6V94-487DT9F-5/2/aadcbd054adcaee5df7f88e8161e1bce}
}
@MASTERSTHESIS{Koop06,
author = {Koop, O.R.},
title = {Continuous and discontinuous Galerkin finite element methods of variational
Boussinesq water-wave models},
school = {University of Twente - Department of Applied Mathematics - Group
of Numerical Analysis and Computational Mechanics},
year = {2006},
month = Oct,
abstract = {There are many reasons to investigate the propagation of surface water
waves in the sea. In this report Boussinesq models are studied, that
can be applied for modeling free-surface waves propagating from the
deep sea up into the surf zone. These models can become fairly complex
and improving linear frequency dispersion properties of these Boussinesq
models often invoke diﬃcult higher-order terms in the resulting partial
diﬀerential equations [18].
Among others, Broer [7, 8], Broer et al.[9]and Klopman et al.[19]
propose, based on the variational principle for potential ﬂows proposed
by Luke [27], variational Boussinesq models to describe potential
ﬂows with dispersion. The advantage of these models is that energy
is conserved and guaranteed to be positive, while mixed higher order
spatial and temporal derivatives are avoided. The cost of this is
that we additional unknown quantities, with associated elliptic partial
diﬀerential equations, that are relatively simple to solve numerically
[20].
In this report three variational models are considered, namely those
of Luke [27], Klopman et al. [19] and Whitham [37], and they are
extended including surface tension eﬀects. Additionally, we integrated
the motion of the ﬂuid domain boundaries with our variational principles
describing the ﬂuid motion. We compare the linear dispersion relations
of the three models and draw the conclusions that the Klopman variational
Boussinesq model approximates the exact linear dispersion obtained
from Luke variational principle for potential ﬂow, better than the
Whitham model. We numerically solve the Whitham and Klopman variational
Boussinesq models in time using
a continuous Galerkin ﬁnite element method. To simulate the propagtion
of the discontinuous jump that occurs when waves are breaking, we
propose a discontinuous Galerkin ﬁnite element method. In this progress
of this report, a discontinuous Galerkin approach was succesfully
applied to the linear Klopman variational Boussinesq model. This
approach can be followed to formulate a discontinuous Galerkin ﬁnite
element discretization to solve the fully nonlinear model.
In this report it is shown that breaking waves do not occur in Whitham’s
variational Boussinesq model for waves propagating over a horizontal
seabed. Further, we consider the weakly nonlinear Klopman VBM, i.e.
neglecting higher-order waves-slope eﬀects, and it is shown that
waves described by this model can not break as well. Further research
on the fully nonlinear Klopman variational Boussinesq model is required.
In this report we draw some conclusions and state recommendations,
particularly on how to construct a discontinuous Galerkin FEM to
solve the fully nonlinear Klopman variational Boussinesq model numerically.},
file = {Koop06.pdf:Koop06.pdf:PDF},
keywords = {water waves; Boussinesq model; continuous Galerkin; discontinuous
Galerkin; shallow water; periodic wave},
owner = {olivier},
timestamp = {2010.11.12}
}
@ARTICLE{Korichi10,
author = {Korichi, K. and Hazzab, A. and Ghenaim, A.},
title = {Sch\'emas \`a captures de chocs pour la simulation num\'erique des
\'ecoulements \`a surface libre},
journal = {Larhyss Journal},
year = {2010},
volume = {8},
pages = {81--100},
month = Jun,
abstract = {La pr\'esente \'etude est une contribution \`a la simulation des \'ecoulements
de surface en r\'esolvant le syst\`eme d’\'equations hyperboliques
et non lin\'eaires de Saint-Venant. En effet, la r\'esolution analytique
de ces \'equations para\^it impossible, mais la r\'esolution num\'erique
est maintenant tout \`a fait courante gr\^ace au d\'eveloppement
de nouvelles m\'ethodes num\'eriques ainsi qu’\`a la capacit\'e de
plus en plus importante de la m\'emoire des calculateurs. Pour des
raisons de stabilit\'e et de pr\'ecision, la m\'ethode des volumes
finis a \'et\'e appliqu\'ee au cours de la pr\'esente \'etude. Une
classe de m\'ethodes, bas\'ees essentiellement sur la r\'esolution
du probl\`eme de Riemann, a \'et\'e retenue et concerne les sch\'emas
\`a capture de chocs. Les tests d’applications aux \'ecoulements
permanents et transitoires par cette approche num\'erique confirment
sa pertinence et sa stabilit\'e.},
file = {Korichi10.pdf:Korichi10.pdf:PDF},
keywords = {simulation d'\'ecoulement \`a surface libre; Saint-Venant; volumes
finis; probl\`eme de Riemann; sch\'ema de Roe; les limiteurs de flux;
sch\'ema de Godunov; Roe; minmod; superbee; monotonie centrale; MC;
van Leer},
owner = {olivier},
timestamp = {2010.11.12}
}
@ARTICLE{Kouznetsov07,
author = {Kouznetsov, M.Y. and Roodsari, R. and Pachepsky, Y.A. and Shelton,
D.R. and Sadeghi, A.M. and Shirmohammadi, A. and Starr, J.L.},
title = {Modeling manure-borne bromide and fecal coliform transport with runoff
and infiltration at a hillslope},
journal = {Journal of Environmental Management},
year = {2007},
volume = {84},
pages = {336 - 346},
number = {3},
abstract = {Hillslope vegetated buffers are recommended to prevent water pollution
from agricultural runoff. However, models to predict the efficacy
of different grass buffer designs are lacking. The objective of this
work was to develop and test a mechanistic model of coupled surface
and subsurface flow and transport of bacteria and a conservative
tracer on hillslopes. The testing should indicate what level of complexity
and observation density might be needed to capture essential processes
in the model. We combined the three-dimensional FEMWATER model of
saturated-unsaturated subsurface flow with the Saint-Venant model
for runoff. The model was tested with data on rainfall-induced fecal
coliforms (FC) and bromide (Br) transport from manure applied at
vegetated and bare 6-m long plots. The calibration of water retention
parameters was unnecessary, and the same manure release parameters
could be used both for simulations of Br and FC. Surface straining
rates were similar for Br and bacteria. Simulations of Br and FC
concentrations were least successful for the funnels closest to the
source. This could be related to the finger-like flow of the manure
from the strip along the bare slopes, to the transport of Br and
FC with manure colloids that became strained at the grass slope,
and to the presence of micro-ponds at the grassed slope. The two-dimensional
model abstraction of the actual 3D transport worked well for flux-averaged
concentrations. The model developed in this work is suitable to simulate
surface and subsurface transport of agricultural contaminants on
hillslopes and to evaluate efficiency of grass strip buffers, especially
when lateral subsurface flow is important.},
doi = {DOI: 10.1016/j.jenvman.2006.06.011},
file = {Kouznetsov07.pdf:Kouznetsov07.pdf:PDF},
issn = {0301-4797},
keywords = {Overland flow; infiltration; fecal coliforms; manure; modeling; Richards;
transport},
owner = {olivier},
timestamp = {2010.06.03},
url = {http://www.sciencedirect.com/science/article/B6WJ7-4KRY3Y2-1/2/55518df555e9660749e1f841819fa6c8}
}
@ARTICLE{Krause05,
author = {Krause, P. and Boyle, D. P. and B\¨ase, F.},
title = {Comparison of different efficiency criteria for hydrological model
assessment},
journal = {Advances in Geosciences},
year = {2005},
volume = {5},
pages = {89-97},
month = Dec,
abstract = {The evaluation of hydrologic model behaviour and performance is commonly
made and reported through comparisons of simulated and observed variables.
Frequently, comparisons are made between simulated and measured streamﬂow
at the catchment outlet. In distributed hydrological modelling approaches,
additional comparisons of simulated and observed measurements for
multi-response validation may be integrated into the evaluation procedure
to assess overall modelling performance. In both approaches, single
and multi-response, efﬁciency criteria are commonly used by hydrologists
to provide an objective assessment of the “closeness” of the simulated
behaviour to the observed measurements. While there are a few efﬁciency
criteria such as the Nash-Sutcliffe efﬁciency, coefﬁcient of determination,
and index of agreement that are frequently used in hydrologic modeling
studies and reported in the literature, there are a large number
of other efﬁciency criteria to choose from. The selection and use
of speciﬁc efﬁciency criteria and the interpretation of the results
can be a challenge for even the most experienced hydrologist since
each criterion may place different emphasis on different types of
simulated and observed behaviours. In this paper, the utility of
several efﬁciency criteria is investigated in three examples using
a simple observed streamﬂow hydrograph.},
file = {Krause05.pdf:Krause05.pdf:PDF},
owner = {olivier},
timestamp = {2010.02.06}
}
@ARTICLE{Kuiry10,
author = {Kuiry, Soumendra Nath and Ding, Yan and Wang, Sam S. Y.},
title = {Modelling coastal barrier breaching flows with well-balanced shock-capturing
technique},
journal = {Computers \& Fluids},
year = {2010},
volume = {39},
pages = {2051--2068},
abstract = {This paper presents a coastal hydrodynamic model for simulating coastal
barrier breaching ﬂows through an inlet which are mostly induced
by extreme hydrological conditions such as storm/hurricane surges,
waves and tides. In order to simulate wave ﬁeld and wave-induced
ﬂow ﬁeld in a coast, a wave action spectral model is coupled with
a hydrodynamic model. The Godunov-type shock-capturing technique
is used in the hydrodynamic model to simulate the supercritical ﬂows
and shocks driven by the extreme storm conditions. The hydrodynamic
model is based on the solution of depth-averaged non-linear shallow
water equations with all physical forcings common to coastal hydrological
conditions so that it is capable of simulating multiple ﬂow regimes,
in which subcritical, transcritical, or supercritical ﬂows may happen.
The bed slope terms in the system of equations are treated in such
a way that exact balance between ﬂux gradient and bed slope terms
is achieved under still water condition. The wave model readily provides
the radiation stresses that represent the shortwave-averaged forcings
in a water column and take into account wave-induced nearshore currents.
In the coupled system, the models are operated systematically. The
coastal hydrodynamic model is shown to accurately reproduce analytical
and benchmark numerical solutions. To further test the accuracy of
the model, ﬂow through a coastal inlet with a storm surge is simulated
and the results are compared with an established coastal ﬂow model.
Finally, the model is examined to simulate a severe storm surge that
develops supercritical ﬂows and the results are found to be encouraging.},
doi = {10.1016/j.compfluid.2010.07.015},
file = {Kuiry10.pdf:Kuiry10.pdf:PDF},
keywords = {shallow water equations; supercritical flow; radiation stress; storm
surge; coastal flow; process-based model; finite volume method; bump;
dam},
owner = {olivier},
timestamp = {2011.02.24}
}
@BOOK{Kundu08,
title = {Fluid Mechanics, Fourth Edition},
year = {2008},
editor = {Elsevier, Oxford},
author = {Kundu, Pijush K. and Cohen, Ira M.},
owner = {olivier},
timestamp = {2011.03.18}
}
@BOOK{Kundu04,
title = {Fluid Mechanics, Third Edition},
year = {2004},
editor = {Elsevier, Oxford},
author = {Kundu, Pijush K. and Cohen, Ira M.},
file = {Kundu04.pdf:Kundu04.pdf:PDF},
owner = {olivier},
timestamp = {2011.03.16}
}
@ARTICLE{Kuraz10,
author = {Kur\'az, Michal and Mayer, Petr and Leps, Matej and Trpkosov\'a,
Dagmar},
title = {An adaptive time discretization of the classical and the dual porosity
model of Richards' equation},
journal = {Journal of Computational and Applied Mathematics},
year = {2010},
volume = {233},
pages = {3167--3177},
abstract = {This paper presents a numerical solution to the equations describing
Darcian flow in a variably saturated porous medium—a classical Richards’
equation model Richards (1931) [1] and an extension of it that approximates
the flow in media with preferential paths—a dual
porosity model Gerke and van Genuchten (1993) [8]. A numerical solver
to this problem, the DRUtES computer program, was developed and released
during our investigation. A new technique which maintains an adaptive
time step, defined here as the Retention Curve
Zone Approach, was constructed and tested. The aim was to limit the
error of a linear approximation to the time derivative part. Finally,
parameter identification was performed in order to compare the behavior
of the dual porosity model with data obtained from a non-homogenized
fracture and matrix flow simulation experiment.},
file = {Kuraz10.pdf:Kuraz10.pdf:PDF},
keywords = {Darcy's law; variable saturation; retention curve; mass balance; adaptative
time discretization; preferential flow; homogenization; parameter
identification; multi-objective evolutionary algorithm; Richards},
owner = {olivier},
timestamp = {2010.06.07}
}
@ARTICLE{Kurganov02,
author = {Kurganov, A. and Levy, Doron},
title = {Central-Upwind Schemes for the Saint-Venant System},
journal = {Mathematical Modelling and Numerical Analysis},
year = {2002},
volume = {36},
pages = {397--425},
file = {Kurganov02.pdf:Kurganov02.pdf:PDF},
keywords = {Saint-Venant; well-balanced; shallow water},
owner = {olivier},
timestamp = {2011.03.10}
}
@ARTICLE{Lagree00,
author = {Lagr\'ee, P.~Y.},
title = {An inverse technique to deduce the elasticity of a large artery},
journal = {The European Physical Journal},
year = {2000},
volume = {9},
pages = {153--163},
abstract = {Our purpose is to build an inverse method which best fits a model
of artery flow and experimental measurements (we assume that we are
able to measure the displacement of the artery as a function of time
at three stations). Having no clinical data, we simulate these measurements
with the numerical computations from a “boundary layer” code. First,
we revisit the system of Ling and Atabek of boundary layer type for
the transmission of a pressure pulse in the arterial system for the
case of an elastic wall (but we solve it without any simplification
in the u∂u/∂x term). Then, using a method analogous to the well known
Von Karman-Pohlhausen method from aeronautics but transposed here
for a pulsatile flow, we build a system of three coupled non-linear
partial differential equations depending only on time and axial co-ordinate.
This system governs the dynamics of internal artery radius, centre
velocity and a quantity related to the presence of viscous effects.
These two methods give nearly the same numerical results. Second,
we construct an inverse method: the aim is to find for the simple
integral model, the physical parameters to put in the “boundary layer”
code (simulating clinical data). This is done by varying in the integral
model the viscosity and elasticity in order to fit best with the
data. To achieve this in a rational way, we have to minimise a cost
function, which involves the computation of the adjoint system of
the integral method. The good set of parameters (i.e. viscosity,
and two coefficients of a wall law) is effectively found again. It
opens the perspective for application in real clinical cases of this
new non-invasive method for evaluating the viscosity of the flow
and elasticity of the wall.},
file = {Lagree00.pdf:Lagree00.pdf:PDF},
keywords = {laminar flow; flow in ducts; channels; nozzles; conduits; blood flow},
owner = {olivier},
timestamp = {2010.11.26}
}
@ARTICLE{Lagree05,
author = {Lagr\'ee, Pierre-Yves and Lorthois, Sylvie},
title = {The RNS/Prandtl equations and their link with other asymptotic descriptions.
Application to the computation of the maximum value of the Wall Shear
Stress in a pipe},
journal = {Int. J. Eng. Sci.},
year = {2005},
volume = {43/3--4},
pages = {352--378},
abstract = {In this paper, a steady laminar axisymmetrical ﬂow in a straight constricted
pipe is considered. The RNS/Prandtl equations are presented as an
asymptotic limit of the Navier-Stokes equations. This set of equations
is shown to include at ﬁrst order several asymptotic descriptions
of the full Navier-Stokes equations: the Blasius regime, Interacting
Boundary Layer theory, Triple Deck theory, the Poiseuille regime
and Double Deck theory. These theories are all characterised by a
constant pressure in each cross section. Thus, these equations are
able to describe the transitions between ﬂow regions that correspond
to diﬀerent classical asymptotic descriptions or regimes that are
usually done with the full Navier-Stokes Equations. One potential
application is to predict the order of magnitude of the wall shear
stress in a constricted pipe. This prediction will be compared with
Navier-Stokes computations for a case of a severe constriction.},
file = {Lagree05.pdf:Lagree05.pdf:PDF},
keywords = {interacting boundary layer; triple deck; reduced Navier-Stokes; laminar
flows; flows in ducts; channels; nozzles; conduits; steady shear
flow},
owner = {olivier},
timestamp = {2011.03.16}
}
@ARTICLE{Lagree96,
author = {Lagr\'ee, Pierre-Yves and Rossi, Maurice},
title = {Etude de l'\'ecoulement du sang dans les art\`eres: effets nonlin\'eaires
et dissipatifs},
journal = {C. R. Acad. Sci. Paris, t322, S\'erie II b},
year = {1996},
pages = {401--408},
abstract = {blood flow in arteries: nonlinear and dissipative effects. We define
a model for the transmission of the pressure pulse in the arterial
system where dissipative effects (blood viscosity, vessel viscoelasticity),
nonlinear phenomema (nonlinear elasticity, convection e ect) are
included. Tapering of arteries are not considered. Using a method
analogous to the well known Von Karman-Pohlhausen method but transposed
here for a pulsatile flow, we end up with a system of three coupled
nonlinear partial differential equations depending only on time and
axial coordinate. This system governs the dynamics of internal artery
radius R(x t), center velocity U0 (x t) and q (x t) a quantity related
to the presence of boundary layer effects. Finally, we present some
numerical computations for this set of equations.},
file = {Lagree96.pdf:Lagree96.pdf:PDF},
keywords = {blood flow},
owner = {olivier},
timestamp = {2011.03.15}
}
@ARTICLE{Lamb84,
author = {Lamb,V. R. and Britter,R. E.},
title = {Shallow flow over an isolated obstacle},
journal = {Journal of Fluid Mechanics},
year = {1984},
volume = {147},
pages = {291--313},
number = {-1},
abstract = { ABSTRACT This is a study of how certain geometrical and flow parameters
affect the tendency of a fluid to flow around rather than over a
single obstacle of simple shape in a homogeneous non-rotating fluid.
A series of numerical experiments was conducted with a finite-difference
model of such a shallow flow, assuming a hydrostatic pressure distribution.
The results demonstrate how the flow over a three-dimensional obstacle
deviates from the patterns established for a two-dimensional ridge.
Measures are suggested for quantitative assessment of the tendency
to flow around as a function of relative hill height and Froude number.A
series of laboratory experiments was also performed, examining the
motions of two superposed homogeneous layers of fluid past an isolated
obstacle in a towing tank. The resulting motion of the interface
was found to agree with the results of the numerical experiments.
The laboratory experiments also extended the understanding gained
from the numerical experiments. Flow-visualization techniques were
employed to aid in the qualitative assessment of the flow around
the obstacles and its dependence on hill and flow parameters. In
particular, these techniques demonstrated the impingement of the
interface on the obstacle, and its dependence on flow speed and hill
height},
doi = {10.1017/S0022112084002093},
eprint = {http://journals.cambridge.org/article_S0022112084002093},
file = {Lamb84.pdf:Lamb84.pdf:PDF},
keywords = {hydrostatic pressure; bump; obstacle},
owner = {olivier},
timestamp = {2010.06.18},
url = {http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=377447&fulltextType=RA&fileId=S0022112084002093}
}
@ARTICLE{Lane77,
author = {Lane, L.J. and Woolhiser, D.A.},
title = {Simplifications of watershed geometry affecting simulation of surface
runoff},
journal = {Journal of Hydrology},
year = {1977},
volume = {35},
pages = {173 - 190},
number = {1-2},
abstract = {In formulating the equations describing the flow of water on the surface
of a watershed, geometric simplifications must be made. A geometric
simplification is the substitution of a simple geometry for a more
complex one. The problem is to examine techniques for and consequences
of such simplifications, and thereby develop objective procedures
for geometric simplification of complex watersheds. Watershed geometry
is represented by a series of planes and channels in cascade. When
overland flow and open-channel flow in the cascade are described
by the kinematic wave equations, the resulting mathematical model
is called the kinematic cascade model. Planes are fitted to coordinate
data from topographic maps by a least-squares procedure. Residuals
of this fit form a geometric goodness-of-fit statistic as the improvement
over using the mean elevation. Channel elements are determined, using
Gray's method, as the slope of the hypotenuse of a right triangle
with the same area as that under the observed stream profile. The
ratio of the altitude of this right triangle to the total relief
of a stream is the index of concavity, a channel goodness-of-fit
statistic. An overall goodness-of-fit statistic is the drainage density
ratio, the ratio of drainage density in the cascade of planes and
channels to drainage density of the watershed. The mean value of
a hydrograph goodness-of-fit statistic, as the improvement over using
the mean discharge, increases as the geometric goodness-of-fit statistic
increases but also decreases as the drainage density increases. A
combined goodness-of-fit statistic, the product of the drainage density
ratio and the geometric goodness-of-fit statistic, is related to
the degree of distortion in optimal-hydraulic roughness parameters.
Distortions in watershed geometry result in optimal roughness parameters
smaller than the corresponding empirically derived values for simple
watersheds where less distortion is involved. Given rainfall, runoff
and topographic data for a small watershed, it is possible to define
the simplest kinematic cascade geometry which when used in simulation
will, on the average, preserve selected hydrograph characteristics
to given degree of accuracy.},
doi = {DOI: 10.1016/0022-1694(77)90085-3},
file = {Lane77.pdf:Lane77.pdf:PDF},
issn = {0022-1694},
keywords = {kinematic wave; watershed; cascade},
owner = {olivier},
timestamp = {2010.06.18},
url = {http://www.sciencedirect.com/science/article/B6V6C-487F9N4-H1/2/cc1c0bf018d88a61573d484cd5cb7a43}
}
@ARTICLE{Langseth00,
author = {Langseth, Jan Olav and LeVeque, Randall J.},
title = {A Wave Propagation Method for Three-Dimensional Hyperbolic Conservation
Laws},
journal = {Journal of Computational Physics},
year = {2000},
volume = {165},
pages = {126 - 166},
number = {1},
abstract = {A class of wave propagation algorithms for three-dimensional conservation
laws and other hyperbolic systems is developed. These unsplit finite-volume
methods are based on solving one-dimensional Riemann problems at
the cell interfaces and applying flux-limiter functions to suppress
oscillations arising from second-derivative terms. Waves emanating
from the Riemann problem are further split by solving Riemann problems
in the transverse directions to model cross-derivative terms. With
proper upwinding, a method that is stable for Courant numbers up
to 1 can be developed. The stability theory for three-dimensional
algorithms is found to be more subtle than in two dimensions and
is studied in detail. In particular we find that some methods which
are unconditionally unstable when no limiter is applied are (apparently)
stabilized by the limiter function and produce good looking results.
Several computations using the Euler equations are presented including
blast wave and complex shock/vorticity problems. These algorithms
are implemented in the software, which is freely available.},
doi = {DOI: 10.1006/jcph.2000.6606},
file = {Langseth00.pdf:Langseth00.pdf:PDF},
issn = {0021-9991},
keywords = {-volume methods; high resolution; wave propagation; three dimensions;
Euler equations; software; minmod; superbee; MC},
owner = {olivier},
timestamp = {2010.06.02},
url = {http://www.sciencedirect.com/science/article/B6WHY-45FC8B5-10/2/dcf956390b5cfa01106dc96744f06d98}
}
@TECHREPORT{Lastoria08,
author = {Lastoria, Barbara},
title = {Hydrological processes on the land surfae: A survey of modelling
approaches},
institution = {FORALPS Technical Report, 9. {U}niversit\`a degli {S}tudi di {T}rento,
{D}ipartimento di {I}ngegneria {C}ivile e {A}mbientale, {T}rento,
{I}taly, 56 pp.},
year = {2008},
abstract = {The project FORALPS pursued improvements in the knowledge of weather
and climate processes in the Alps, required for a more sustainable
management of their water resources. The FORALPS Technical Reports
series presents the original achievements of the project, and provides
an accessible introduction to selected topics in hydro-meteorological
monitoring and analysis.},
file = {Lastoria08.pdf:Lastoria08.pdf:PDF},
keywords = {Horton; Kostiakov; Philip; Green-Ampt; SCS; Saint-Venant; kinematic
wave; diffusion wave; quasi-dynamic wave},
owner = {olivier},
timestamp = {2010.04.25}
}
@ARTICLE{Lawrence97,
author = {Lawrence, D.~S.~L.},
title = {Macroscale surface roughness and frictional resistance in overland
flow},
journal = {Earth Surface Processes and Landforms},
year = {1997},
volume = {22},
pages = {365--382},
abstract = {The hydraulics of overland flow on rough granular surfaces can be
modelled and evaluated using the inundation ratio rather than the
flow Reynolds number, as the primary dimensionless group determining
the flow behaviour. The inundation ratio describes the average degree
of submergence of the surface roughness and is used to distinguish
three flow regimes representing partially inundated, marginally inundated
and well-inundated surfaces. A heuristic physical model for the flow
hydraulics in each regime demonstrates that the three states of flow
are characterized by very different functional dependencies of frictional
resistance on the scaled depth of flow. At partial inundation, flow
resistance is associated with the drag force derived from individual
roughness elements and therefore increases with depth and percentage
cover. At marginal inundation, the size of the roughness elements
relative to the depth of flow controls the degree of vertical mixing
in the flow so that frictional resistance tends to decrease very
rapidly with increasing depth of flow. Well-inundated flows are described
using rough turbulent flow hydraulics previously developed for open
channel flows. These flows exhibit a much more gradual decrease in
frictional resistance with increasing depth than that observed during
marginal inundation. A data set compiled from previously published
studies of overland flow hydraulics is used to assess the functional
dependence of frictional resistance on inundation ratio over a wide
range of flow conditions. The data confirm the non-monotonic dependence
predicted by the model and support the differentiation of three flow
regimes based on the inundation ratio. Although the percentage cover
and the surface slope may be of importance in addition to the inundation
ratio in the partially and marginally inundated regimes, the Reynolds
number appears to be of significance only in describing well-inundated
flows at low to moderate Reynolds numbers. As these latter conditions
are quite rare in natural environments, the inundation ratio rather
than the Reynolds number should be used as the primary dimensionless
group when evaluating the hydraulics of overland flow on rough surfaces.},
file = {Lawrence97.pdf:Lawrence97.pdf:PDF},
keywords = {shallow flow hydraulics; inundation ratio; surface microtopography;
hillslope hydrology},
owner = {olivier},
timestamp = {2009.01.11}
}
@ARTICLE{Lazarovitch09,
author = {Lazarovitch, N. and Warrick, A.~W. and Furman, A. and Zerihun, D.},
title = {Subsurface {W}ater {D}istribution from {F}urrows {D}escribed by {M}oment
{A}nalyses},
journal = {Journal of Irrigation and Drainage Engineering},
year = {2009},
volume = {135},
pages = {7--12},
number = {1},
month = Feb,
abstract = {Abstract: Moment analysis techniques are applied to describe the spatial
and temporal subsurface wetting patterns resulting from furrow
inﬁltration and redistribution. These techniques are adapted from
previous work with drip irrigation. The water added is considered
as a
“plume” with the zeroth moment representing the total volume of water
applied to the domain. The ﬁrst moments lead to the location of
the center of the plume, and the second moments relate to the amount
of spreading about the mean position. Using moments, any fraction
of the applied water and its spatial extent, deﬁned by an ellipse,
can be related to a “probability” curve. Remarkably, the probability
curves are, for practical purposes, identical for all times and for
all of the soils considered in this study. The same observation was
made in
relation to the distribution of water under a dripper. The consistency
of the probability relationships can be exploited to pinpoint the
distribution of irrigation water under a furrow in a compact and
physically meaningful way. This approach is tested with numerically
generated data for inﬁltration from furrows in three contrasting
soils. The general conclusion is that moment analysis allows a straight-
forward, physically meaningful description of the general pattern
of moisture distribution. Potential applications of the results of
moment analyses include improved irrigation management, formulation
of the inﬁltration and redistribution process from a furrow in a
neural network setting, and parameter estimation of the soil hydraulic
properties.},
file = {Lazarovitch09.pdf:Lazarovitch09.pdf:PDF},
keywords = {Moments; Furrow irrigation; Soil water; Neural networks},
owner = {olivier},
timestamp = {2010.04.23}
}
@PHDTHESIS{LeDissez06,
author = {Le Dissez, Aur\'elie},
title = {Mod\'elisation num\'erique des \'ecoulements tidaux en milieux peu
profonds. Application \`a l'\'etude de l'hydrodynamique du bassin
d'Archachon.},
school = {Universit\'e de Bordeaux I},
year = {2006},
file = {LeDissez06.pdf:LeDissez06.pdf:PDF},
owner = {olivier},
timestamp = {2009.07.21}
}
@ARTICLE{Lebacque08,
author = {Lebacque, Jean Patrick and Louis, Xavier and Mammar, Salim and Schnetzler,
Bernard and Haj-Salem, Habib},
title = {Mod\'elisation du trafic autoroutier au second ordre},
journal = {C. R. Acad. Sci. Paris, Ser. I},
year = {2008},
volume = {346},
pages = {1203--1206},
abstract = {R\'esum\'e
Nous considérons un mod\`ele de traﬁc autoroutier au second ordre
que nous batirons \`a partir de consid\'erations comportementales
simples. L’analyse du probl\`eme de Riemann aff\'erent sera men\'ee.
Dans la seconde partie nous d\'evelopperons la d\'eﬁnition d’une
solution obtenue \`a la limite, issue d’une famille de probl\`emes
perturb\'es rendant le probl\`eme de Riemann toujours solvable. Nous
constaterons enﬁn les cons\'equences de cette extension en terme
de limite de compressibilit\'e et de conservation de quantit\'es
comportementales.
Abstract
Modelling of motorway trafﬁc to second order. In the ﬁrst part of
the Note, we introduce a second order trafﬁc ﬂow model,
which we derive from simple physical considerations. We consider the
related Riemann problem and solve it in any cases. In the
second part, we examine what is required for the construction of proper
analytical solutions to be always possible, and what the
extended model implies in term of incompressibility, and conservation
of physically meaningful quantities.},
doi = {10.1016/j.crma.2008.09.024},
file = {Lebacque08.pdf:Lebacque08.pdf:PDF},
owner = {olivier},
timestamp = {2011.02.24}
}
@ARTICLE{Lee10,
author = {Lee, Sang-Heon and Wright, Nigel G.},
title = {Simple and efficient solution of the shallow water equations with
source terms},
journal = {International Journal for Numerical Methods in Fluids},
year = {2010},
volume = {63},
pages = {313--340},
abstract = {A simple and efﬁcient method to solve the one-dimensional shallow
water equations with source terms is presented. To avoid a fractional
step method for the discretization of the source terms, a homogeneous
form of the shallow water equations is proposed and well-known conservative
numerical schemes are modiﬁed to solve the new form of the equations.
The modiﬁcation to the homogeneous form equations combines the source
terms with the ﬂux term and solves them by the same solution structure
of the numerical scheme. As a result, the source terms are automatically
discretized to achieve perfect balance with ﬂux terms without any
special treatment and the method does not introduce numerical errors.
The proposed method is veriﬁed against several benchmark tests and
shows good agreement with analytical solutions.},
doi = {10.1002/fld.2071},
file = {Lee10.pdf:Lee10.pdf:PDF},
keywords = {shallow water equations; source terms; Roe's solver; HLL solver; Lax-Wendroff
scheme; MacCormack scheme; Godunov; well-balanced; balance},
owner = {olivier},
timestamp = {2011.02.23}
}
@ARTICLE{Lei05,
author = {Lei, Tingwu and Xia, Weisheng and Zhao, Jun and Liu, Zhen and Zhang,
Qingwen},
title = {Method for measuring velocity of shallow water flow for soil erosion
with an electrolyte tracer},
journal = {Journal of Hydrology},
year = {2005},
volume = {301},
pages = {139--145},
number = {1-4},
month = jan,
abstract = {Measurement of the velocity of shallow water flow on a hill slope
is of great importance in soil erosion studies. Electrolyte tracers
have been tried to estimate mean velocity of water flow with the
velocity of the leading edge of the solute propagation multiplied
with a somewhat arbitrary correction factor. In this study, an analytical
solution of solute (tracer) transport was formulated to serve as
the mathematical foundation for measuring shallow water flow velocity.
To estimate the flow velocity,,. a procedure was advanced. In the
procedures. the analytical solution is fitted with the measured propagation
curve and given the 'the least square' estimation of velocity. A
detailed mathematical description is oulined for this purpose. Experimental
results are given to show the feasibility of the method. including
the analytical solution and the estimation procedures. This study
provides the theoretical foundation for measuring the velocity of
shallow water flow and for studies of overland solute transport.
(C) 2004 Elsevier B.V. All rights reserved.},
doi = {10.1016/j.jhydrol.2004.06.025},
file = {Lei05.pdf:Lei05.pdf:PDF},
keywords = {Flow velocity, Overland flow, Electrolyte pulse, The least square
method},
owner = {olivier},
timestamp = {2009.01.11}
}
@PHDTHESIS{Lemos02,
author = {Lemos, A.~C.},
title = {Numerical methods for singular differential equations arising from
steady flows in channels and ducts},
school = {university of Reading--department of mathematics},
year = {2002},
month = may,
abstract = {We study ordinary nonlinear differential equations which arise from
steady nonlinear conservation laws with source terms. Two examples
of conservation laws which lead to these equations are the Saint-Venant
and the Euler equations. In each case there is a reduction to a scalar
equation and we use the ideas of upwinding and discretisation of
source terms to devise methods for the solution. Numerical results
are presented with both the Engquist-Osher and the Roe scheme with
different strategies for discretising the source terms based on balance
ideas.},
file = {Lemos02.pdf:Lemos02.pdf:PDF},
owner = {olivier},
timestamp = {2008.05.04}
}
@ARTICLE{Lemos04,
author = {Lemos, A.~C. and Baines, M.~J. and Nichols, N.~K.},
title = {Upwind solution of singular differential equations arising from steady
channel flows},
journal = {Computers \& Fluids},
year = {2004},
volume = {33},
pages = {821--827},
abstract = {We study ordinary nonlinear singular differential equations which
arise from steady conservation laws with source terms. An example
of steady conservation laws which leads to those scalar equations
is the Saint-Venant equations. The numerical solution of these scalar
equations is sought by using the ideas of upwinding and discretisation
of source terms. Both the Engquist-Osher scheme and the Roe scheme
are used with different strategies for discretising the source terms.},
file = {Lemos04.pdf:Lemos04.pdf:PDF},
owner = {olivier},
timestamp = {2008.05.04}
}
@MASTERSTHESIS{Lequien03,
author = {Lequien, Alexandra},
title = {Analyse et \'evaluation des crues extr\^emes par mod\'elisation hydrologique
spatialis\'ee. Cas du bassin versant du Vidourle},
school = {Universit\'e Montpellier II, Sciences et Techniques du Languedoc,
DEA Sciences de l'Eau dans l'Environnement Continental},
year = {2003},
month = Jul,
abstract = {Le bassin versant du Vidourle, situé dans le Sud Est de la France,
est soumis à des crues éclairs particulièrement dangereuses. Face
à la récurrence de ces événements catastrophiques, la compréhension
et l’identification des processus hydrologiques mis en jeu lors du
passage de la normale à l’extrême, constitue un axe stratégique de
prévention contre les inondations. Des indicateurs de fonctionnement
du bassin ont été recherchés par modélisation pluie-débit spatialisée
sur l’épisode de septembre 2002 ainsi que sur différentes crues observées
en 1995 et 2001. L’étude a porté sur sept sous bassins versants du
Vidourle. La combinaison d’un schéma de type SCS aménagé avec une
vidange et d’un transfert de type Lag&Route a conduit à des résultats
satisfaisants. La paramétrisation de ces schémas varie peu entre
les sous bassins étudiés et reste relativement stable sur un sous
bassin donné, pour les crues majeures et mineures. La cohérence de
ces critères accrédite la modélisation retenue pour la prévision
de crues extrêmes; elle devra être validée sur d’autres bassins versants
régionaux.},
file = {Lequien03.pdf:Lequien03.pdf:PDF},
keywords = {Données hydro-pluviométriques; modélisation spatialisée; crues extrêmes;
radar, calage;
production; transfert; MERCEDES; Vidourle},
owner = {olivier},
timestamp = {2010.04.22}
}
@BOOK{LeVeque02,
title = {Finite volume methods for hyperbolic problems},
publisher = {Cambridge University Press},
year = {2002},
author = {LeVeque, Randall~J.},
pages = {xx+558},
series = {Cambridge Texts in Applied Mathematics},
address = {Cambridge},
abstract = {This is an excellent introduction into finite volume methods for solving
conservation laws. The book is divided into three main parts: Part
I deals with linear equations in predominately one spatial dimension,
Part II introduces nonlinear equations again in one spatial dimension,
while Part III introduces multidimensional problems. Beginning with
an introduction to the mathematics of these partial differential
equations, including all the basic hyperbolic theory for linear equations
(characteristics, Riemann problems, definition, and examples), LeVeque
then presents the basics of finite volume methods for the integration
of conservation laws. Extensions to these basics in terms of high
resolution methods such as the use of limiters in multidimensional
up-winding is then presented. The nonlinear portion of the book begins
with the mathematics of nonlinear scalar conservation laws, the application
of finite volume methods for their numerical solution, extensions
to systems of equations, the nonlinear Riemann problem, non-classical
hyperbolic systems, and finally concludes with a chapter on equations
with source terms. The third part of the book deals with multidimensional
hyperbolic problems and numerical methods both in scalar and vector
form.
The book is exceptionally well written and the problems are worth
subsequent study. If you work in the area of hyperbolic systems you
must read this book.
One of the great bonuses that this book contains is that it includes
a description and introduction on the use of the CLAWPACK software.
The CLAWPACK of codes is a large collection of FORTRAN 77 codes for
solving a large number of hyperbolic systems (both conservative and
nonconservative forms). Included is a "getting started" section which
can help new users become familiar with the codes and get them up
and solving problems very quickly.},
file = {LeVeque02.pdf:LeVeque02.pdf:PDF},
isbn = {0-521-81087-6; 0-521-00924-3},
mrclass = {65-01 (65M06 74S30 76M12)},
mrnumber = {MR1925043 (2003h:65001)},
mrreviewer = {Serge Piperno},
owner = {olivier},
timestamp = {2009.08.24}
}
@ARTICLE{LeVeque98,
author = {LeVeque, Randall J.},
title = {Balancing Source Terms and Flux Gradients in High-Resolution Godunov
Methods: The Quasi-Steady Wave-Propagation Algorithm},
journal = {Journal of Computational Physics},
year = {1998},
volume = {146},
pages = {346 - 365},
number = {1},
abstract = {Conservation laws with source terms often have steady states in which
the flux gradients are nonzero but exactly balanced by source terms.
Many numerical methods (e.g., fractional step methods) have difficulty
preserving such steady states and cannot accurately calculate small
perturbations of such states. Here a variant of the wave-propagation
algorithm is developed which addresses this problem by introducing
a Riemann problem in the center of each grid cell whose flux difference
exactly cancels the source term. This leads to modified Riemann problems
at the cell edges in which the jump now corresponds to perturbations
from the steady state. Computing waves and limiters based on the
solution to these Riemann problems gives high-resolution results.
The 1D and 2D shallow water equations for flow over arbitrary bottom
topography are used as an example, though the ideas apply to many
other systems. The method is easily implemented in the software package.},
doi = {DOI: 10.1006/jcph.1998.6058},
file = {LeVeque98.pdf:LeVeque98.pdf:PDF},
issn = {0021-9991},
keywords = {Godunov methods; shock capturing; source terms; conservation laws;
steady states; shallow water equations},
owner = {olivier},
timestamp = {2010.06.02},
url = {http://www.sciencedirect.com/science/article/B6WHY-45J58TW-22/2/72a8af8c9e23f63b0df9484475f7e2df}
}
@ARTICLE{LeVeque97,
author = {LeVeque, Randall J.},
title = {Wave Propagation Algorithms for Multidimensional Hyperbolic Systems},
journal = {Journal of Computational Physics},
year = {1997},
volume = {131},
pages = {327 - 353},
number = {2},
abstract = {A class of high resolution multidimensional wave-propagation algorithms
is described for general time-dependent hyperbolic systems. The methods
are based on solving Riemann problems and applying limiter functions
to the resulting waves, which are then propagated in a multidimensional
manner. For nonlinear systems of conservation laws the methods are
conservative and yield good shock resolution. The methods are generalized
to hyperbolic systems that are not in conservation form and to problems
that include a #capacity##function.# Several examples are included
for gas dynamics, acoustics in a heterogeneous medium, and advection
in a stratified flow on curvilinear grids. The software packageimplements
these algorithms in Fortran and is freely available on the Web. One
and two space dimensions are discussed here, although the algorithms
and software have also been extended to three dimensions.},
doi = {DOI: 10.1006/jcph.1996.5603},
file = {LeVeque97.pdf:LeVeque97.pdf:PDF},
issn = {0021-9991},
keywords = {minmod; superbee; MC; conservation laws},
owner = {olivier},
timestamp = {2010.06.02},
url = {http://www.sciencedirect.com/science/article/B6WHY-45KV05X-M/2/0ac77dff8185a978e5a84041f8197985}
}
@BOOK{LeVeque92,
title = {Numerical methods for conservation laws},
publisher = pub-BIRKHAUSER,
year = {1992},
author = {LeVeque, Randall~J.},
pages = {214},
series = {Lectures in mathematics ETH Zurich},
address = pub-BIRKHAUSER:adr,
acknowledgement = {#ack-nhfb#},
isbn = {3-7643-2464-3, 0-8176-2464-3 (U.S.)},
keywords = {conservation laws (mathematics); differential equations, hyperbolic
-- numerical solutions; shock waves},
lccn = {QA377 .L4157 1992},
owner = {olivier},
timestamp = {2009.09.28}
}
@ARTICLE{LeVeque88,
author = {LeVeque, Randall J.},
title = {High resolution finite volume methods on arbitrary grids via wave
propagation},
journal = {Journal of Computational Physics},
year = {1988},
volume = {78},
pages = {36 - 63},
number = {1},
abstract = {In previous work by the author, a generalization of Godunov's method
for systems of conservation laws has been developed and analyzed
that can be applied with arbitrary time steps on arbitrary grids
in one space dimension. Stability for arbitrary time steps is achieved
by allowing waves to propagate through more than one mesh cell in
a time step. In this paper the method is extended to second-order
accuracy and to a finite volume method in two space dimensions. This
latter method is based on solving one-dimensional normal and tangential
Riemann problems at cell interfaces and again propagating waves through
one or more mesh cells. By avoiding the usual time step restriction
of explicit methods, it is possible to use reasonable time steps
on irregular grids where the minimum cell area is much smaller than
the average cell. Boundary conditions for the Euler equations are
discussed and special attention is given to the case of a Cartesian
grid cut by an irregular boundary. In this case small grid cells
arise only near the boundary, and it is desirable to use a time step
appropriate for the regular interior cells. Numerical results in
two dimensions show that this can be achieved.},
doi = {DOI: 10.1016/0021-9991(88)90036-8},
file = {LeVeque88.pdf:LeVeque88.pdf:PDF},
issn = {0021-9991},
owner = {olivier},
timestamp = {2010.06.02},
url = {http://www.sciencedirect.com/science/article/B6WHY-4DD1RR2-4F/2/4e7cbfb8314a9203e5a2f6a9c5155203}
}
@ARTICLE{LeVeque01,
author = {LeVeque, Randall J. and Pelanti, Marica},
title = {A Class of Approximate Riemann Solvers and Their Relation to Relaxation
Schemes},
journal = {Journal of Computational Physics},
year = {2001},
volume = {172},
pages = {572 - 591},
number = {2},
abstract = {We show that a simple relaxation scheme of the type proposed by Jin
and Xin [Comm. Pure Appl. Math.48, 235 (1995)] can be reinterpreted
as defining a particular approximate Riemann solver for the original
system of m conservation laws. Based on this observation, a more
general class of approximate Riemann solvers is proposed which allows
as many as 2m waves in the resulting solution. These solvers are
related to more general relaxation systems and connections with several
other standard solvers are explored. The added flexibility of 2m
waves may be advantageous in deriving new methods. Some potential
applications are explored for problems with discontinuous flux functions
or source terms.},
doi = {DOI: 10.1006/jcph.2001.6838},
file = {LeVeque01.pdf:LeVeque01.pdf:PDF},
issn = {0021-9991},
owner = {olivier},
timestamp = {2010.06.02},
url = {http://www.sciencedirect.com/science/article/B6WHY-45BC26R-31/2/7fa6b11eb7d84a653c106cb8bef55c47}
}
@ARTICLE{LeVeque96,
author = {LeVeque, Randall J. and Shyue, Keh-Ming},
title = {Two-Dimensional Front Tracking Based on High Resolution Wave Propagation
Methods},
journal = {Journal of Computational Physics},
year = {1996},
volume = {123},
pages = {354 - 368},
number = {2},
abstract = {We present a fully conservative, high resolution approach to front
tracking for nonlinear systems of conservation laws in two space
dimensions. An underlying uniform Cartesian grid is used, with some
cells cut by the front into two subcells. The front is moved by solving
a Riemann problem normal to each segment of the front and using the
motion of the strongest wave to give an approximate location of the
front at the end of the time step. A high resolution finite volume
method is then applied on the resulting slightly irregular grid to
update all cell values. A #large##time##step# wave propagation algorithm
is used that remains stable in the small cut cells with a time step
that is chosen with respect to the uniform grid cells. Numerical
results on a radially symmetric problem show that pointwise convergence
with order between 1 and 2 is obtained in both the cell values and
location of the front. Other computations are also presented.},
doi = {DOI: 10.1006/jcph.1996.0029},
file = {LeVeque96.pdf:LeVeque96.pdf:PDF},
issn = {0021-9991},
owner = {olivier},
timestamp = {2010.06.02},
url = {http://www.sciencedirect.com/science/article/B6WHY-45NJMFV-10/2/88e4998c15ed3293cd3b95ef0dd71d93}
}
@BOOK{Levi95,
title = {The science of water - The foundation of modern hydraulics},
publisher = {American Society of Civil Engineers Press},
year = {1995},
author = {Levi, Enzo},
address = {New York, NW, USA},
note = {Translated from the Spanish ``El Agua Segun La Ciencia'' by Daniel
E. Medina},
file = {Levi95.pdf:Levi95.pdf:PDF},
keywords = {hydrology, Manning},
owner = {olivier},
timestamp = {2008.08.20}
}
@MISC{LeRoux09,
author = {Le{R}oux, A.-Y.},
title = {The linear appearance theorem for a class of non linear non homogeneous
hyperbolic systems involving a transport equation},
howpublished = {http://www.math.ntnu.no/conservation/2009/034.html},
month = Jun,
year = {2009},
note = {Preprint},
file = {LeRoux09.pdf:LeRoux09.pdf:PDF},
owner = {olivier},
timestamp = {2010.02.15}
}
@MISC{LeRoux02,
author = {Le{R}oux, A.-Y.},
title = {Several {A}pplications of {G}eneralized {S}olutions in {S}ome {E}xamples
of {W}ave {P}ropagation},
howpublished = {http://www.math.ntnu.no/conservation/2002/005.html},
month = Jan,
year = {2002},
note = {Preprint},
file = {LeRoux02.pdf:LeRoux02.pdf:PDF},
owner = {olivier},
timestamp = {2010.02.15}
}
@MISC{LeRoux01,
author = {Le{R}oux, A.-Y.},
title = {Conditions aux limites et {P}robl\`emes {H}yperboliques: un point
de vue num\'erique},
howpublished = {Workshop Conditions Limites Num\'eriques pour les Syst\`emes {H}yperboliques,
I.H.P., Paris, Juin 2001},
month = Jun,
year = {2001},
note = {www-gm3.univ-mrs.fr (suivre "\'equipe de Bordeaux")},
file = {LeRoux01.pdf:LeRoux01.pdf:PDF},
owner = {olivier},
timestamp = {2010.04.03}
}
@MISC{LeRoux05,
author = {Le{R}oux, A.-Y. and Le{R}oux, M.-N.},
title = {mathematical {M}odel for {R}ogue {W}aves, using {S}aint-{V}enant
{E}quations with {F}riction},
howpublished = {http://www.math.ntnu.no/conservation/2005/048.html},
month = Nov,
year = {2005},
note = {Preprint},
file = {LeRoux05.pdf:LeRoux05.pdf:PDF},
owner = {olivier},
timestamp = {2010.02.15}
}
@MISC{LeRoux04a,
author = {Le{R}oux, A.-Y. and Le{R}oux, M.-N.},
title = {Source {W}aves},
howpublished = {http://www.math.ntnu.no/conservation/2004/045.html},
year = {2004},
note = {Preprint},
file = {LeRoux04a.pdf:LeRoux04a.pdf:PDF},
owner = {olivier},
timestamp = {2010.02.15}
}
@MISC{LeRoux04b,
author = {Le{R}oux, A.-Y. and Le{R}oux, M.-N.},
title = {A {M}athematical {M}odel for {H}urricanes},
howpublished = {http://www.math.ntnu.no/conservation/2004/014.html},
month = Apr,
year = {2004},
note = {Preprint},
file = {LeRoux04b.pdf:LeRoux04b.pdf:PDF},
owner = {olivier},
timestamp = {2010.02.15}
}
@PHDTHESIS{Lhomme06,
author = {Lhomme, J.},
title = {Mod{\'e}lisation des inondations en milieu urbain : approches unidimensionnelle,
bidimensionnelle et macroscopique},
school = {Universit{\'e} Montpellier II},
year = {2006},
file = {Lhomme06.pdf:Lhomme06.pdf:PDF},
owner = {olivier},
timestamp = {2009.02.09}
}
@ARTICLE{Lhomme07,
author = {Lhomme, J. and Guinot, V.},
title = {A general approximate-state Riemann solver for hyperbolic systems
of conservation laws with source terms},
journal = {International Journal for Numerical Methods in Fluids},
year = {2007},
volume = {53},
pages = {1509--1540},
abstract = {An approximate-state Riemann solver for the solution of hyperbolic
systems of conservation laws with source terms is proposed. The formulation
is developed under the assumption that the solution is made of rarefaction
waves. The solution is determined using the Riemann invariants expressed
as functions of the components of the flux vector. This allows the
flux vector to be computed directly at the interfaces
between the computational cells. The contribution of the source term
is taken into account in the governing equations for the Riemann
invariants. An application to the water hammer equations and the
shallow water equations shows that an appropriate expression of the
pressure force at the interface allows the balance with the source
terms to be preserved, thus ensuring consistency with the equations
to be solved as well as a correct computation of steady-state flow
configurations. Owing to the particular structure of the variable
and flux vectors, the expressions of the fluxes are shown to coincide
partly with those given by the HLL/HLLC solver. Computational examples
show that the approximate-state solver yields more accurate solutions
than the HLL solver in the presence of discontinuous solutions and
arbitrary geometries.},
file = {Lhomme07.pdf:Lhomme07.pdf:PDF},
keywords = {Godunov-type schemes ; Riemann solvers ; source terms ; water hammer
equations ; shallow water equations},
owner = {olivier},
timestamp = {2009.02.09}
}
@ARTICLE{Li09,
author = {Li, Gary},
title = {Preliminary study of the interference of surface objects and rainfall
in overland flow resistance},
journal = {Catena},
year = {2009},
volume = {78},
pages = {154--158},
abstract = {Linear superposition approach, which states that composite resistance
of different types of roughness elements equals to the sum of individual
resistance, has been widely adopted in the study of overland ﬂow
hydraulics. The approach assumes that different roughness elements
act independently in the ﬂow. This seems to be implausible because
roughness elements in shallow overland ﬂow are often close to and
interfering with each other. The interference, such as that between
rainfall impact and stone generated vertex, may strengthen or restrain
ﬂow resistance on one another. To examine this possible interference
in ﬂow resistance, a set of ﬂume experiments using surface objects
and rainfall as roughness elements were conducted. Since the ﬂow
resistance due to each element cannot be measured directly, the linear
superposition equation had to be rewritten using friction factor
increment as variable. The experiments measured different friction
factor increments in ﬂows where Reynolds number was less than 2000
and Froude number less than 2. The result shows that the interference
between rainfall and surface roughness is signiﬁcant and the composite
resistance does not statistically equal to the sum of individual
resistance. The linear superposition approach is hence invalid in
the case of rainfall and surface roughness elements in overland ﬂow
resistance.},
file = {Li09.pdf:Li09.pdf:PDF},
keywords = {overland flow; flow resistance; surface objects; rainfall; interference;
friction},
owner = {olivier},
timestamp = {2010.06.28}
}
@ARTICLE{Li00,
author = {L. Li and D. A. Barry and C. Cunningham and F. Stagnitti and J. -Y.
Parlange},
title = {A two-dimensional analytical solution of groundwater responses to
tidal loading in an estuary and ocean},
journal = {Advances in Water Resources},
year = {2000},
volume = {23},
pages = {825 - 833},
number = {8},
abstract = {Previous studies on tidal dynamics of coastal aquifers have focussed
on the inland propagation of oceanic tides in the cross-shore direction,
a configuration that is essentially one-dimensional. Aquifers at
natural coasts can also be influenced by tidal waves in nearby estuaries,
resulting in a more complex behaviour of head fluctuations in the
aquifers. We present an analytical solution to the two-dimensional
depth-averaged groundwater flow equation for a semi-infinite aquifer
subject to oscillating head conditions at the boundaries. The solution
describes the tidal dynamics of a coastal aquifer that is adjacent
to a cross-shore estuary. Both the effects of oceanic and estuarine
tides on the aquifer are included in the solution. The analytical
prediction of the head fluctuations is verified by comparison with
numerical solutions computed using a standard finite-difference method.
An essential feature of the present analytical solution is the interaction
between the cross- and along-shore tidal waves in the aquifer area
near the estuary's entry. As the distance from the estuary or coastline
increases, the wave interaction is weakened and the aquifer response
is reduced, respectively, to the one-dimensional solution for oceanic
tides or the solution of Sun (Sun H. A two-dimensional analytical
solution of groundwater response to tidal loading in an estuary,
Water Resour Res 1997;33:1429-35) for two-dimensional non-interacting
tidal waves.},
doi = {DOI: 10.1016/S0309-1708(00)00016-6},
file = {Li00.pdf:Li00.pdf:PDF},
issn = {0309-1708},
keywords = {Tidal groundwater fluctuation; Estuarine tides; Oceanic tides; Two-dimensional
solution},
owner = {olivier},
timestamp = {2010.06.04},
url = {http://www.sciencedirect.com/science/article/B6VCF-40D617N-4/2/cd5a99c0b9972b66d17bdb1c6c0e6644}
}
@ARTICLE{Li05,
author = {Li, L. and Lockington, D.A. and Parlange, M.B. and Stagnitti, F.
and Jeng, D.-S. and Selker, J.S. and Telyakovskiy, A.S. and Barry,
D.A. and Parlange, J.-Y.},
title = {Similarity solution of axisymmetric flow in porous media},
journal = {Advances in Water Resources},
year = {2005},
volume = {28},
pages = {1076 - 1082},
number = {10},
note = {Flow Processes in Hydrology: Contributions of J.-Y. Parlange},
abstract = {Applications of the axisymmetric Boussinesq equation to groundwater
hydrology and reservoir engineering have long been recognised. An
archetypal example is invasion by drilling fluid into a permeable
bed where there is initially no such fluid present, a circumstance
of some importance in the oil industry. It is well known that the
governing Boussinesq model can be reduced to a nonlinear ordinary
differential equation using a similarity variable, a transformation
that is valid for a certain time-dependent flux at the origin. Here,
a new analytical approximation is obtained for this case. The new
solution,, which has a simple form, is demonstrated to be highly
accurate.},
doi = {DOI: 10.1016/j.advwatres.2005.04.004},
file = {Li05.pdf:Li05.pdf:PDF},
issn = {0309-1708},
keywords = {Drilling mud invasion; Density-dependent flow; Groundwater pumping;
Axisymmetric flow; Boussinesq equation; Sparging},
owner = {olivier},
timestamp = {2010.06.04},
url = {http://www.sciencedirect.com/science/article/B6VCF-4GCX1S5-1/2/e64c332b89bcbde600c12755e306751f}
}
@ARTICLE{Li08,
author = {Li, Q. and Unger, A.J.A. and Sudicky, E.A. and Kassenaar, D. and
Wexler, E.J. and Shikaze, S.},
title = {Simulating the multi-seasonal response of a large-scale watershed
with a 3D physically-based hydrologic model},
journal = {Journal of Hydrology},
year = {2008},
volume = {357},
pages = {317--336},
number = {3-4},
abstract = {Summary The physically-based surface-subsurface HydroGeoSphere model
is used to examine the hydrologic budget of the 286.6 km2 Duffins
Creek watershed, located 10 km northeast of metropolitan Toronto.
The primary objective of this study is to demonstrate the utility
of the model to simulate the three-dimensional hydrologic response
of the surface and subsurface flow systems in a large-scale watershed
driven by multi-season precipitation events. The hydrologic model
was calibrated to a consecutive sequence of hydrographs resulting
from all precipitation events between the months of April and December
1986, while hydrographs from 1987 were used to test the model's ability
for prediction. Results demonstrate that a physically-based modeling
approach which treats the surface and subsurface flow systems as
an integrated continuum can capture the dynamic response of a large
heterogeneous watershed as driven by transient precipitation events
over a multi-season period. It was also revealed that full coupling
of plant transpiration and surface-subsurface evaporation processes
into the governing flow equations was critical for the successful
calibration of the hydrographs. However, the ability of the model
to predict the shape of individual hydrographs in the following year,
during which the annual average precipitation rate decreased significantly,
was diminished even though the annual average stream flows were closely
replicated. We identify a number of data gaps that contribute to
the decline in the predictive capacity of the model, including difficulty
in establishing an appropriate initial condition, vertical mesh refinement
issues within the root zone, and the reliance on a largely empirical
relationship that distributes the net capacity for plant transpiration
among various factors that may change from one year to the next.},
doi = {DOI: 10.1016/j.jhydrol.2008.05.024},
file = {Li08.pdf:Li08.pdf:PDF},
issn = {0022-1694},
keywords = {Groundwater; Surface water; Watershed; Hydrologic model; Richards},
owner = {olivier},
timestamp = {2010.06.15},
url = {http://www.sciencedirect.com/science/article/B6V6C-4SMNY1G-1/2/022a67ba02f08989280ea472d969441b}
}
@ARTICLE{Liang09a,
author = {Liang, Qiuhua and Borthwick, Alistair~G.~L.},
title = {Adaptive quadtree simulation of shallow flows with wet-dry fronts
over complex topography},
journal = {Computers \& Fluids},
year = {2009},
volume = {38},
pages = {221-234},
file = {Liang09a.pdf:Liang09a.pdf:PDF},
owner = {olivier},
timestamp = {2009.07.27}
}
@ARTICLE{Liang04,
author = {Liang, Q. and Borthwick, A.~G.~L. and Stelling, G.},
title = {Simulation of dam- and dyke-break hydrodynamics on dynamically adaptative
grids},
journal = {International Journal for Numerical Methods in Fluids},
year = {2004},
volume = {46},
pages = {127-162},
abstract = {Flooding due to the failure of a dam or dyke has potentially disastrous
consequences. This paper presents a Godunov-type ÿnite volume solver
of the shallow water equations based on dynamically adaptive quadtree
grids. The Harten, Lax and van Leer approximate Riemann solver with
the Contact wave restored (HLLC) scheme is used to evaluate interface
uxes in both wet- and dry-bed applications. The numerical model is
validated against results from alternative numerical models for idealized
circular and rectangular dam breaks. Close agreement is achieved
with experimental measurements from the CADAM dam break test and
data from a laboratory dyke break undertaken at Delft University
of Technology. ?},
doi = {10.1002/ d.748},
file = {Liang04.pdf:Liang04.pdf:PDF},
keywords = {dam=dyke break; shallow water equations; Godunov-type scheme; HLLC
approximate Riemann solver; MUSCL-Hancock method; adaptive quadtree
grid},
owner = {olivier},
timestamp = {2009.07.27}
}
@ARTICLE{Liang09b,
author = {Liang, Qiuhua and Marche, Fabien},
title = {Numerical resolution of well-balanced shallow water equations with
complex source terms},
journal = {Advances in Water Resources},
year = {2009},
volume = {32},
pages = {873 - 884},
number = {6},
doi = {DOI: 10.1016/j.advwatres.2009.02.010},
file = {Liang09b.pdf:Liang09b.pdf:PDF},
issn = {0309-1708},
keywords = {Shallow water equations},
owner = {olivier},
timestamp = {2009.07.21},
url = {http://www.sciencedirect.com/science/article/B6VCF-4VR9FHT-3/2/5218868dcfded7d34380666f23000855}
}
@BOOK{Liggett75,
title = {Unsteady flow in open channels},
publisher = {Water Resources Publications, Fort Collins, Colorado},
year = {1975},
editor = {Mahmood, K. and Yevjevich, V. eds},
author = {Liggett, J.~J.},
file = {Liggett75.pdf:Liggett75.pdf:PDF},
owner = {olivier},
timestamp = {2010.04.21}
}
@BOOK{Lighthill78,
title = {Waves in Fluids},
year = {1978},
editor = {Cambridge University Press},
author = {Lighthill, James},
owner = {olivier},
timestamp = {2011.03.15}
}
@ARTICLE{Lighthill55,
author = {Lighthill, M.~J. and Whitham, G.~B.},
title = {On {K}inematic {W}aves. {I}. {F}lood {M}ovement in {L}ong {R}ivers},
journal = {Proceedings of the Royal Society of London. Series A, Mathematical
and Physical Sciences, Issue 1178},
year = {1955},
volume = {229},
pages = {281--316},
abstract = {In this paper and in part II, we give the theory of a distinctive
type of wave motion, which arises in any one-dimensional flow problem
when there is an approximate functional relation at each point between
the flow q (quantity passing a given point in unit time) and concentration
k (quantity per unit distance). The wave property then follows directly
from the equation of continuity satisfied by q and k. In view of
this, these waves are described as 'kinematic', as distinct from
the classical wave motions, which depend also on Newton's second
law of motion and are therefore called 'dynamic'. Kinematic waves
travel with the velocity partial q/partial k, and the flow q remains
constant on each kinematic wave. Since the velocity of propagation
of each wave depends upon the value of q carried by it, successive
waves may coalesce to form 'kinematic shock waves'. From the point
of view of kinematic wave theory, there is a discontinuous increase
in q at a shock, but in reality a shock wave is a relatively narrow
region in which (owing to the rapid increase of q) terms neglected
by the flow-concentration relation become important. The general
properties of kinematic waves and shock waves are discussed in detail
in section 1. One example included in section 1 is the interpretation
of the group-velocity phenomenon in a dispersive medium as a particular
case of the kinematic wave phenomenon. The remainder of part I is
devoted to a detailed treatment of flood movement in long rivers,
a problem in which kinematic waves play the leading role although
dynamic waves (in this case, the long gravity waves) also appear.
First (section 2), we consider the variety of factors which can influence
the approximate flow-concentration relation, and survey the various
formulae which have been used in attempts to describe it. Then follows
a more mathematical section (section 3) in which the role of the
dynamic waves is clarified. From the full equations of motion for
an idealized problem it is shown that at the 'Froude numbers' appropriate
to flood waves, the dynamic waves are rapidly attenuated and the
main disturbance is carried downstream by the kinematic waves; some
account is then given of the behaviour of the flow at higher Froude
numbers. Also in section 3, the full equations of motion are used
to investigate the structure of the kinematic shock; for this problem,
the shock is the 'monoclinal flood wave' which is well known in the
literature of this subject. The final sections (section section 4
and 5) contain the application of the theory of kinematic waves to
the determination of flood movement. In section 4 it is shown how
the waves (including shock waves) travelling downstream from an observation
point may be deduced from a knowledge of the variation with time
of the flow at the observation point; this section then concludes
with a brief account of the effect on the waves of tributaries and
run-off. In section 5, the modifications (similar to diffusion effects)
which arise due to the slight dependence of the flow-concentration
curve on the rate of change of flow or concentration, are described
and methods for their inclusion in the theory are given.},
file = {Lighthill55.pdf:Lighthill55.pdf:PDF},
owner = {olivier},
timestamp = {2010.04.28}
}
@ARTICLE{deLima03,
author = {de Lima, J.~L.~M.~P. and Singh, V.~P.},
title = {Laboratory experiments on the influence of storm movement on overland
flow},
journal = {Physics and Chemistry of the Earth},
year = {2003},
volume = {28},
pages = {277--282},
abstract = {This study presents the results of laboratory experiments, conducted
on an impermeable smooth plane surface with a movable sprinkling-type
rainfall simulator, simulating a moving storm. In order to assess
the eﬀect of storm movement while eliminating variations in other
factors that also inﬂuence the runoﬀ response, the only parameters
that were varied were storm velocity and direction. The results indicate
considerable diﬀerences in runoﬀ volumes and peaks and in overland
ﬂow hydrograph shapes, for storms moving upstream and downstream
at diﬀering velocities.},
file = {deLima03.pdf:deLima03.pdf:PDF},
keywords = {Overland ﬂow; Storm movement; Rainfall simulator; Laboratory experiments},
owner = {olivier},
timestamp = {2010.05.02}
}
@ARTICLE{deLima02,
author = {de Lima, J.~L.~M.~P. and Singh, V.~P.},
title = {influence of the pattern of moving rainstorms on overland flow},
journal = {Advances in Water Resources},
year = {2002},
volume = {25},
pages = {817--828},
abstract = {This study emphasizes the importance of spatial rainfall intensity
patterns of moving rainstorms on overland ﬂow. A simple numerical
model, based on the non-linear kinematic wave, was used for comparing
the results for hypothetical storms moving up and down an impervious
plane surface. Simulations were undertaken by varying the storm pattern,
length, speed and direction. No account was made for time varying
losses, such as inﬁltration, evaporation, etc. The results indicate
signiﬁcant diﬀerences in peak discharges and hydrograph shapes for
moving storms of various patterns. The sensitivity of runoﬀ to storm
patterns decreases as storm speed increases.},
file = {deLima02.pdf:deLima02.pdf:PDF},
keywords = {Rainfall pattern; Kinematic wave; Overland ﬂow; Storm movement},
owner = {olivier},
timestamp = {2010.05.02}
}
@ARTICLE{deLima03b,
author = {de Lima, J. L. M. P. and Singh, V.~P. and de Lima, M.~I.~P.},
title = {The influence of storm movement on water erosion: storm direction
and velocity effects},
journal = {Catena},
year = {2003},
volume = {52},
pages = {39--56},
abstract = {Although the problem of storm movement affecting flows (shape of the
hydrograph and peak discharges) has been recognised for a long time,
most overland flow and water erosion studies do not take into account
the effect on the runoff response caused by the movement of the storm
across the catchment. Ignoring of the storm movement can result in
considerable over- and underestimation of runoff volumes and peaks,
and associated soil loss by sheet erosion.
This work shows the results of laboratory experiments that were undertaken
to study the effect of moving storms on the water erosion process.
The experiments were carried out using a soil flume adjustable to
different slopes and a movable sprinkling-type rainfall simulator.
Both the effects of storm velocity and direction, and surface slope
were studied. To simulate moving rainstorms, the rainfall simulator
was moved upstream and downstream over the soil surface. The results
show that the storm direction and velocity strongly affect the water
erosion process. The soil loss caused by the downstream moving rainstorms
is higher than that caused by the identical upstream moving rainfall
storms.},
file = {deLima03b.pdf:deLima03b.pdf:PDF},
keywords = {Soil erosion; Storm movement; Rainfall simulation; Overland flow},
owner = {olivier},
timestamp = {2010.05.02}
}
@ARTICLE{DeLima88,
author = {de Lima, J.~L.~M.~P. and Van Der Molen, W.~H.},
title = {An analytical kinematic model for the rising limb of overland flow
on infiltrating parabolic shaped surfaces},
journal = {Journal of Hydrology},
year = {1988},
volume = {104},
pages = {363--370},
abstract = {Using the kinematic wave theory and Zarmi's hypothesis, an analytical
solution for overland flow over an infiltrating, parabolic shaped
surface (concave or convex surfaces, that may be represented by a
quadratic equation) is presented. The velocity of the water flow
is assumed to be independent of time. The analytical solution developed
is easier to utilize than numerical simulation and can be used to
calibrate numerical methods devised for more complicated cases. An
illustration is presented.},
file = {DeLima88.pdf:DeLima88.pdf:PDF},
keywords = {analyrical solution; kinematic; infiltration; parabolic shaped surface;
concave; convex; quadratic},
owner = {olivier},
timestamp = {2010.06.12}
}
@ARTICLE{Liu08,
author = {Liu, Jintao and Zhang, Jiabao and Feng, Jie},
title = {Green-Ampt {M}odel for {L}ayered {S}oils with {N}onuniform {I}nitial
{W}ater {C}ontent {U}nder {U}nsteady {I}nfiltration},
journal = {Soil Sci. Soc. Am. J.},
year = {2008},
volume = {72},
pages = {1041--1047},
number = {4},
abstract = {The Green–Ampt equation is often used to estimate inﬁltration in hydrologic
modeling. Only a few of the currently used simulation models, however,
can simulate inﬁltration into a heterogeneous soil with nonuniform
initial soil water content by the Green–Ampt equation during nonsteady
rainfall. In this study, we derived an inﬁltration model for layered
soils under nonsteady inﬁltration based on the Green–Ampt method
(Green–Ampt for Layered Soils, or GALS). In the GALS model, a formula
for estimating average suction (S) was derived to include initial
soil water effect, and the soil proﬁle was divided into several layers
to consider both soil texture and initial soil moisture effects on
inﬁltration. The new model can predict inﬁltration capacity, ponding
time, and cumulative inﬁltration. Three inﬁltration experiments,
steady-state inﬁltration into a layered soil with nonuniform initial
soil water content, nonsteady inﬁltration into a layered soil with
uniform soil water content; and nonsteady-state inﬁltration into
a layered soil with nonuniform soil water content, were conducted
for model testing. Comparison showed that the GALS model was in good
agreement with another Green–Ampt-based model and the measured data.},
doi = {10.2136/sssaj2007.0119},
file = {Liu08.pdf:Liu08.pdf:PDF},
keywords = {Green-Ampt; layered soils},
owner = {olivier},
timestamp = {2010.04.26}
}
@ARTICLE{Liu05,
author = {Liu, Q.~Q. and Chen, L. and Li, J.~C. and Singh, Vijay P.},
title = {Roll {W}aves in {O}verland {F}low},
journal = {Journal of Hydrologic Engineering},
year = {2005},
volume = {10},
pages = {110--117},
number = {2},
month = Mar,
abstract = {Abstract: Roll waves are frequently observed in overland ﬂow, especially
in rill ﬂow, which has an important effect on the development
of soil erosion. Using one-dimensional St. Venant equations, this
paper investigates the dynamics of periodic roll waves based on
Dressler’s and Brock’s work. Under the assumption that the average
ﬂow depth equals the uniform ﬂow depth, expressions of the
roll-wave speed and roll-wave proﬁle were obtained. Testing with the
results observed by Brock in 1970 for wave properties shows that
these expressions can approximately describe the characteristics of
periodic permanent roll waves. Numerical solutions of roll waves
under speciﬁc conditions are found. They show that when a roll wave
appears, the shear stress of ﬂow increases, and soil erosion
accelerates.},
file = {Liu05.pdf:Liu05.pdf:PDF},
keywords = {Overland flow; soil erosion; waves},
owner = {olivier},
timestamp = {2010.04.17}
}
@ARTICLE{Liu04,
author = {Liu, Q.~Q. and Chen, L. and Li, J.~C. and Singh, V.~P.},
title = {Two-dimensional kinematic wave model of overland-flow},
journal = {Journal of Hydrology},
year = {2004},
volume = {291},
pages = {28--41},
abstract = {A two-dimensional kinematic wave model was developed for simulating
runoff generation and flow concentration on an experimental infiltrating
hillslope receiving artificial rainfall. Experimental observations
on runoff generation and flow concentration on irregular hillslopes
showed that the topography of the slope surface controlled the direction
and flow lines of overland flow. The model-simulated results satisfactorily
compared with experimental observations. The erosive ability of the
concentrated flow was found to mainly depend on the ratio of the
width and depth of confluent grooves.},
file = {Liu04.pdf:Liu04.pdf:PDF},
keywords = {flow concentration route; infiltration; hillslope; kinematic wave
theory; numerical simulation; overland flow; runoff generation; 2D
flow model},
owner = {olivier},
timestamp = {2008.05.08}
}
@ARTICLE{Liu08b,
author = {Liu, X. and Landry, B.~J. and Garc\`ia, M.~H.},
title = {Two-dimensional scour simulations based on coupled model of shallow
water equations and sediment transport on unstructured meshes},
journal = {Coastal Engineering},
year = {2008},
volume = {55},
pages = {800--810},
abstract = {A two-dimensional scour model based on coupled system of shallow water
equations (SWEs) and sediment transport on unstructured mesh is developed.
The coupled system of hydrodynamic and morphodynamic equations is
solved by finite volume method using Godunov scheme. Roe's approximate
Riemann solver is used to calculate the inviscid fluxes. The use
of unstructured mesh makes the model applicable to complex domains.
However, it is difficult to evaluate the eigenvalues and eigenvectors
of the Jacobian matrix in the global coordinate. The method proposed
herein to deal with this difficulty is to transform the system into
the local coordinate with one of the axes in the same direction as
the interface outward normal vector. In the local coordinate system,
the Jacobian matrix is simplified and the eigenvalues are analyzed
using asymptotic method. Regular expansion breaks down when the flow
is near critical. Uniformity of the expansion is achieved by changing
the scales. Rotational invariance theorem is used to relate the interfacial
fluxes in the global and local coordinate systems. Special treatment
of the source term on unstructured grid makes the scheme stable and
physically balanced (both mass and momentum). The method proposed
in this paper for the eigen-system is very efficient comparing to
iterative numerical methods. Results from the test cases show good
agreement with the experiments.},
doi = {10.1016/j.coastaleng.2008.02.012},
file = {Liu08b.pdf:Liu08b.pdf:PDF},
keywords = {shallow water equations; sediment transpor; Godunov scheme; coupled
solver; unstructured mesh;},
owner = {olivier},
timestamp = {2010.11.24}
}
@ARTICLE{Liu03,
author = {Liu, Xu-Dong and Lax, Peter D.},
title = {Positive schemes for solving multi-dimensional hyperbolic systems
of conservation laws II},
journal = {Journal of Computational Physics},
year = {2003},
volume = {187},
pages = {428--440},
abstract = {Kurganov and Tadmor have developed a numerical scheme for solving
the initial value problem for hyperbolic systems of conservation
laws. They showed that in the scalar case their scheme satisﬁes a
local maximum–minimum principle i.e., the solution at future is bounded
above and below by the solution at current locally. In this paper
we show that this scheme is positive in the sense of Friedrichs for
systems as well. We present the scheme of Kurganov and Tadmor as
a convex combination of composites of positive schemes. Since each
component of a composite scheme is bounded in the l2 norm, so is
the convex combination of the composites. To achieve second order
accuracy in time, we use a Runge–Kutta type scheme due to Shu and
Osher. We present two numerical experiments to add to the ones carried
out by Kurganov and Tadmor.},
doi = {10.1016/S0021-9991(03)00100-1},
file = {Liu03.pdf:Liu03.pdf:PDF},
keywords = {positive scheme},
owner = {olivier},
timestamp = {2011.02.24}
}
@ARTICLE{Longo11,
author = {Longo, Sandro},
title = {Roll waves on a shallow layer of a dilatant fluid},
journal = {European Journal of Mechanics - B/Fluids},
year = {2011},
volume = {30},
pages = {57--67},
abstract = {This paper is about the free surface instabilities of granular flows,
usually called roll waves. A shallow layer of shear-thickening fluid
(τ = a(∂ u/∂ y)n with n = 2) is considered to study finite-amplitude
permanent roll waves down a slope, simplified by Karman’s momentum
integral approach. The existence of conditions of a periodic discontinuous
solution is derived, as smooth profiles with depth increasing monotonically
between periodic shocks. Energy dissipation in the body of the stream
and in the discontinuity is analysed and discussed. Two conditions
are derived. The first is related to the physically acceptable shape
of the smooth profiles, and the second is related to positive energy
loss across the shock. These conditions can be converted into a limiting
discharge, viewed in the fixed frame, and in a limiting flow thickness
(or limiting Froude number), for the permanent periodic roll wave
to exist without further conditions. A minimum-length roll wave (MLRW)
is defined as the periodic permanent roll waves with zero energy
dissipation in the shock. The MLRW also requires a limiting value
of the Froude number to exist.},
doi = {10.1016/j.euromechflu.2010.09.001},
file = {Longo11.pdf:Longo11.pdf:PDF},
keywords = {roll waves; free surface instabilities; granular flows; dilatant fluids;
shallow water},
owner = {olivier},
timestamp = {2011.02.23}
}
@PHDTHESIS{Lucas07,
author = {Lucas, C.},
title = {Effets de petites {\'e}chelles, du tenseur des contraintes, des conditions
au fond et {\`a} la surface sur les {\'e}quations de Saint-Venant},
school = {Universit{\'e} Joseph Fourier -- Grenoble I},
year = {2007},
month = nov,
abstract = {In a first part, we present some Shallow Water equations. About the
actual model, we firstly remark that, depending on the link between
the viscosity and the aspect ratio, keeping the complete Coriolis
force expression is essential : this gives a new model, with a so-called
{"}cosine effect{"}. We then show that the proofs of existence of
weak solutions can be adapted to this new system. Numerical simulations
of somme waves underline the fact that this term is of importance.
Next we study the influence of the limit conditions (surface, bottom)
and of the stress tensor on Shallow-Water type models. We also present
some models obtained using multiple scales in space and time. Finally
we analyze a new model of sedimentation from a theorical and numerical
point of view and then we give some results for visco-plastic fluids.
In a second part, we are interested in the limit equation, namely
the Quasi-Geostrophic (QG) equations and the lake equations. The
numerical study of the 2d QG equations enables us to emphasize the
role of the cosine effect from the Coriolis force. Depending on the
topography we consider, we show that this effect can turn out to
be not negligible. Still about the QG equations, we give a numerical
scheme, based on asymptotic developments, which capture the boundary
layer well and also give the opportunity to add a topography term
to the solution for a flat bottom, without re-computing everything.
Lastly we explain how to get the lake equations with cosine effect
and we prove that the properties of existence of soltuions to such
equations are still valid.},
file = {Lucas07.pdf:Lucas07.pdf:PDF},
keywords = {differential partial equations; Shallow-Water equations; models of
rotating fluids; asymptotic developments; multi-scale analysis; a
priori estimates; stability of approximated solutions; numerical
studies},
owner = {olivier},
timestamp = {2008.04.30}
}
@ARTICLE{Luce92,
author = {Luce, Charles H. and Cundy, Terrance W.},
title = {Modification of the {K}inematic {W}ave-{P}hilip {I}nfiltration {O}verland
{F}low {M}odel},
journal = {Water Resources Research},
year = {1992},
volume = {28},
pages = {1179-1186},
number = {4},
month = Apr,
file = {Luce92.pdf:Luce92.pdf:PDF},
owner = {olivier},
timestamp = {2010.02.06}
}
@ARTICLE{LukacovaMedvidova07,
author = {Luk\'acov\'a-Medvid'ov\'a, M. and Noelle, S. and Kraft, M.},
title = {Well-balanced finite volume evolution {G}alerkin methods for the
shallow water equations},
journal = {Journal of Computational Physics},
year = {2007},
volume = {221},
pages = {122 - 147},
number = {1},
abstract = {We present a new well-balanced finite volume method within the framework
of the finite volume evolution Galerkin (FVEG) schemes. The methodology
will be illustrated for the shallow water equations with source terms
modelling the bottom topography and Coriolis forces. Results can
be generalized to more complex systems of balance laws. The FVEG
methods couple a finite volume formulation with approximate evolution
operators. The latter are constructed using the bicharacteristics
of multidimensional hyperbolic systems, such that all of the infinitely
many directions of wave propagation are taken into account explicitly.
We derive a well-balanced approximation of the integral equations
and prove that the FVEG scheme is well-balanced for the stationary
steady states as well as for the steady jets in the rotational frame.
Several numerical experiments for stationary and quasi-stationary
states as well as for steady jets confirm the reliability of the
well-balanced FVEG scheme.},
doi = {DOI: 10.1016/j.jcp.2006.06.015},
file = {LukacovaMedvidova07.pdf:LukacovaMedvidova07.pdf:PDF},
issn = {0021-9991},
keywords = {Well-balanced schemes},
owner = {olivier},
timestamp = {2009.08.26},
url = {http://www.sciencedirect.com/science/article/B6WHY-4KJV3D4-1/2/194c7d1a6f9c1a68518e00de0b5626b9}
}
@ARTICLE{LukacovaMedvidova06,
author = {Luk\'acov\'a-Medvid'ov\'a, M. and Teschke, U.},
title = {Comparison study of some finite volume and finite element methods
for the shallow water equations with bottom topography and friction
terms},
journal = {J. Appl. Mech. Math. (ZAMM)},
year = {2006},
volume = {86},
pages = {874-891},
number = {11},
abstract = {We present a comparison of two discretization methods for the shallow
water equations, namely the ﬁnite volume method and the ﬁnite element
scheme. A reliable model for practical interests includes terms modelling
the bottom topography as well as the friction effects. The resulting
equations belong to the class of systems of hyperbolic partial differential
equations of ﬁrst order with zero order source terms, the so-called
balance laws. In order to approximate correctly steady equilibrium
states we need to derive a well-balanced approximation of the source
term in the ﬁnite volume framework. As a result our ﬁnite volume
method, a genuinely multidimensional ﬁnite volume evolution Galerkin
(FVEG) scheme, approximates correctly steady states as well as their
small perturbations (quasi-steady states). The second discretization
scheme, which has been used for practical river ﬂow simulations,
is the ﬁnite element method (FEM). In contrary to the FVEG scheme,
which is a time explicit scheme, the FEM uses an implicit time discretization
and the Newton-Raphson iterative scheme for inner iterations. We
show that both discretization techniques approximate correctly steady
and quasi-steady states with bottom topography and friction and compare
their accuracy and performance.},
doi = {10.1002/zamm.200510280},
file = {LukacovaMedvidova06.pdf:LukacovaMedvidova06.pdf:PDF},
keywords = {well-balanced schemes; steady states; systems of hyperbolic balance
laws; shallow water equations; evolution Galerkin schemes; ﬁnite
element schemes; Darcy-Weisbach friction law; Newton-Raphson method},
owner = {olivier},
timestamp = {2010.02.07}
}
@ARTICLE{LukacovaMedvidova05b,
author = {Luk\'acov\'a-Medvid'ov\'a, M. and Vlk, Z.},
title = {Well-balanced finite volume evolution {G}alerkin methods for the
shallow water equations with source terms},
journal = {International Journal for Numerical Methods in Fluids},
year = {2005},
volume = {47},
pages = {1165-1171},
number = {10-11},
abstract = {The goal of this paper is to present a new well-balanced genuinely
multidimensional high-resolution ﬁnite volume evolution Galerkin
method for systems of balance laws. The derivation of the method
will be illustrated for the shallow water equation with geometrical
source term modelling the bottom topography. The results can be generalized
to more complex systems of balance laws.},
file = {LukacovaMedvidova05b.pdf:LukacovaMedvidova05b.pdf:PDF},
keywords = {well-balanced methods; ﬁnite volume evolution Galerkin schemes; shallow
water equations; trully multidimensional ﬁnite volume methods},
owner = {olivier},
timestamp = {2010.02.07}
}
@INPROCEEDINGS{LukacovaMedvidova05a,
author = {Luk\'acov\'a-Medvidov\'a, M\'aria},
title = {Numerical {M}odeling of {S}hallow {F}lows {I}ncluding {B}ottom {T}opography
and {F}riction {E}ffects},
booktitle = {Proceedings of {A}lgoritmy 2005, Slovakia},
year = {2005},
editor = {Handlovicova, Angela and Kriva, Zuzana and Mikula, Karol and Sevcovic,
Daniel},
pages = {73-82},
file = {LukacovaMedvidova05a.pdf:LukacovaMedvidova05a.pdf:PDF},
owner = {olivier},
timestamp = {2010.02.06}
}
@ARTICLE{Lynett02,
author = {Lynett, Patrick~J. and Wu, T.-R. and Liu, Philip L.-F.},
title = {Modeling wave runup with depth-integrated equations},
journal = {Coastal Engineering},
year = {2002},
volume = {46},
pages = {89-107},
abstract = {In this paper, a moving boundary technique is developed to investigate
wave runup and rundown with depth-integrated equations. Highly nonlinear
and weakly dispersive equations are solved using a high-order finite
difference scheme. An eddy viscosity model is adopted for wave breaking
so as to investigate breaking wave runup. The moving boundary technique
utilizes linear extrapolation through the wet – dry boundary and
into the dry region. Nonbreaking and breaking solitary wave runup
is accurately predicted by the proposed model, yielding a validation
of both the wave breaking parameterization and the moving boundary
technique. Two-dimensional wave runup in a parabolic basin and around
a conical island is investigated, and agreement with published data
is excellent. Finally, the propagation and runup of a solitary wave
in a trapezoidal channel is examined.},
file = {Lynett02.pdf:Lynett02.pdf:PDF},
keywords = {Wave runup; Breaking waves; Boussinesq equations},
owner = {olivier},
timestamp = {2010.01.26}
}
@ARTICLE{vanLeer79,
author = {van {L}eer, Bram},
title = {{T}owards the ultimate conservative difference scheme. {V}. {A} second-order
sequel to {G}odunov's method},
journal = {Journal of Computational Physics},
year = {1979},
volume = {32},
pages = {101 - 136},
number = {1},
abstract = {A method of second-order accuracy is described for integrating the
equations of ideal compressible flow. The method is based on the
integral conservation laws and is dissipative, so that it can be
used across shocks. The heart of the method is a one-dimensional
Lagrangean scheme that may be regarded as a second-order sequel to
Godunov's method. The second-order accuracy is achieved by taking
the distributions of the state quantities inside a gas slab to be
linear, rather than uniform as in Godunov's method. The Lagrangean
results are remapped with least-squares accuracy onto the desired
Euler grid in a separate step. Several monotonicity algorithms are
applied to ensure positivity, monotonicity and nonlinear stability.
Higher dimensions are covered through time splitting. Numerical results
for one-dimensional and two-dimensional flows are presented, demonstrating
the efficiency of the method. The paper concludes with a summary
of the results of the whole series #Towards##the##Ultimate##Conservative##Difference##Scheme.#},
doi = {DOI: 10.1016/0021-9991(79)90145-1},
issn = {0021-9991},
owner = {olivier},
timestamp = {2009.11.10},
url = {http://www.sciencedirect.com/science/article/B6WHY-4DD1N8T-C5/2/9b051d1cfcff715a3d0f4b7b7b0397cc}
}
@ARTICLE{Ma10,
author = {Ma, Ying and Feng, Shaoyuan and Su, Dongyuan and Gao, Guangyao and
Huo, Zailin},
title = {Modeling water infiltration in a large layered soil column with a
modified Green-Ampt model and HYDRUS-1D},
journal = {Computers and Electronics in Agriculture},
year = {2010},
volume = {71},
pages = {S40 - S47},
number = {Supplement 1},
note = {Special issue on computer and computing technologies in agriculture},
abstract = {A modified Green-Ampt model was developed in this study to describe
water infiltration through a 300-cm long and five-layered soil column.
In the modified Green-Ampt model, a saturation coefficient was introduced
to determine the water content and hydraulic conductivity of the
wetted zone. The saturation coefficient was determined by the ratio
between measured moisture volume and total saturated moisture volume
of the wetted zone, and it should be less than 1. In this experiment,
the calculated saturation coefficient was 0.8. The wetting front
suction head was determined by Bouwer and Neuman methods. For comparison,
the infiltration process was also simulated by traditional Green-Ampt
model and HYDRUS-1D code which was based on the Richards equation.
It was found that the traditional Green-Ampt model was unable to
describe the infiltration process adequately. The HYDRUS-1D provided
good simulation results of infiltration rate and accumulative infiltration.
However, it was difficult to track the movement of wetting front
along the soil profile and the corresponding root mean square error
(RMSE) value was up to 57.17 cm. For the modified Green-Ampt model
with Bouwer method, the RMSE values of simulated infiltration rate,
accumulative infiltration and wetting front depth were 2.01E-3 cm/min,
1.28 and 8.29 cm, respectively, which were much smaller than those
of traditional Green-Ampt model and HYDRUS-1D. Moreover, the modified
Green-Ampt model with Bouwer method could adequately capture the
infiltration rate, the accumulative infiltration and the movement
process of wetting front in the large layered soil column. Therefore,
it appears that the modified Green-Ampt model presented in this study
is a highly effective approach to simulate water infiltration in
layered soils.},
doi = {DOI: 10.1016/j.compag.2009.07.006},
file = {Ma10.pdf:Ma10.pdf:PDF},
issn = {0168-1699},
keywords = {Water infiltration; Layered soils; Modified Green-Ampt model; HYDRUS-1D},
owner = {olivier},
timestamp = {2010.06.06},
url = {http://www.sciencedirect.com/science/article/B6T5M-4WXRDG0-1/2/2a504bd5333ccda6b8199cd884eb39a8}
}
@PHDTHESIS{MacDonald96,
author = {Mac{D}onald, I.},
title = {Analysis and computation of steady open channel flow},
school = {University of Reading--Department of mathematics},
year = {1996},
month = sep,
file = {MacDonald96.pdf:MacDonald96.pdf:PDF},
owner = {olivier},
timestamp = {2008.05.05}
}
@TECHREPORT{MacDonald94a,
author = {Mac{D}onald, I.},
title = {Test problems with analytic solutions for steady open channel flow},
institution = {Department of Mathematics--University of Reading},
year = {1994},
file = {MacDonald94a.pdf:MacDonald94a.pdf:PDF},
owner = {olivier},
timestamp = {2008.05.05}
}
@TECHREPORT{MacDonald94b,
author = {Mac{D}onald, I. and Baines, M.~J. and Nichols, N.~K.},
title = {Analysis and computation of steady open channel flow using a singular
perturbation problem},
institution = {Department of Mathematics--University of Reading},
year = {1994},
number = {7},
file = {MacDonald94b.pdf:MacDonald94b.pdf:PDF},
owner = {olivier},
timestamp = {2008.05.05}
}
@ARTICLE{MacDonald97,
author = {Mac{D}onald, I. and Baines, M.~J. and Nichols, N.~K. and Samuels,
P.~G.},
title = {Analytic benchmark solutions for open-channel flows},
journal = {Journal of Hydraulic Engineering},
year = {1997},
volume = {123},
pages = {1041-1045},
number = {11},
month = nov,
abstract = {An important test of the quality of a computational model is its ablllty
to reproduce standard test cases or benchmarks. For steady open-channel
flow based on the Saint Venant equations some benchmarks exist for
simple geometries from the work of Bresse, Bakhmeteff rnd Chow but
these are tabulated in the form of standard- integrals. This paper
provides benchmark solutions for a wider range of cases, which may
have a nonprismatic cross section, nonunifom bed slope, and transitions
between subcritical and supercritical flow.
This makes it possible to assess the underlylng quality of computational
algorithms in more difficult cases, including those with hydraulic
jumps. Several new test cases are given in detail and the performarce
of a commercial steady flow package is evaluated agalnst two of them.
The test cÂses may also be used as benchmarks for both steady flow
models and unsteady flow models in the steady limit.},
file = {MacDonald97.pdf:MacDonald97.pdf:PDF},
owner = {olivier},
timestamp = {2008.08.20}
}
@TECHREPORT{MacDonald95,
author = {Mac{D}onald, I. and Baines, M.~J. and Nichols, N.~K. and Samuels,
P.~G.},
title = {Steady open channel test problems with analytic solutions},
institution = {Department of Mathematics--University of Reading},
year = {1995},
number = {3},
abstract = {In many areas of computational fluid dynamics there are benchmark
test problems which have known analytic solutions. For the case of
steady flow in an open channel there is a need for such test problems,
so as to give a measure of the performance of numerical methods.
This is especially true for problems where the flow changes between
subcritical and supercritical. In this report a method is described
that allows the construction of a wide range of such test problems,
where in each case the exact solution to the full steady Saint Venant
equation is known. In particular the report discusses how to construct
problems with solutions having a hydraulic jump. Example test problems
are given along with their analytic solution. These can be readily
used by modellers to test their own particular software. For some
of the example test problems, results from a commercial software
package are compared with the exact solutions, thus demonstrating
how the method is a valuable tool for validating both steady and
unsteady flow solvers.},
file = {MacDonald95.pdf:MacDonald95.pdf:PDF},
owner = {olivier},
timestamp = {2008.05.05}
}
@PHDTHESIS{Maison00,
author = {Maison, P.},
title = {Un mod{\'e}le hydrologique de suivi de la pollution diffuse en bassin
versant : Approche m{\'e}caniste simplifi{\'e}e de la zone non satur{\'e}e},
school = {Institut National Polytechnique de Toulouse},
year = {2000},
file = {Maison00.pdf:Maison00.pdf:PDF},
owner = {olivier},
timestamp = {2008.05.04}
}
@ARTICLE{Mandal08,
author = {Mandal, J.C. and Subramanian, J.},
title = {On the link between weighted least-squares and limiters used in higher-order
reconstructions for finite volume computations of hyperbolic equations},
journal = {Applied Numerical Mathematics},
year = {2008},
volume = {58},
pages = {705 - 725},
number = {5},
abstract = {In this paper, a novel technique of obtaining high resolution, second
order accurate, oscillation free, solution dependent weighted least-squares
(SDWLS) reconstruction in finite volume method is explored. A link
between the weights of the weighted least-squares based gradient
estimation and various existing limiter functions used in variable
reconstruction is established for one-dimensional problems for the
first time. In this process, a class of solution dependent weights
are derived from the link which is capable of producing oscillation
free second order accurate solutions for hyperbolic systems of equations
without the use of limiter function. The link also helps in unifying
various independently proposed limiter functions available in the
literature. The way to generate numerous new limiter functions from
the link is demonstrated in the paper. An approach to verify TVD
criterion of the SDWLS formulation for different choice of weights
is explained. The present high resolution scheme is then extended
to solve multi-dimensional problems with the interpretation of weights
in SDWLS as influence coefficients. A few numerical test examples
involving one- and two-dimensional problems are solved using three
different new limiter functions in order to demonstrate the utility
of the present approach.},
doi = {DOI: 10.1016/j.apnum.2007.02.003},
file = {Mandal08.pdf:Mandal08.pdf:PDF},
issn = {0168-9274},
keywords = {Higher-order reconstruction; limiters; TVD; solution dependent weighted
least-squares; SDWLS; finite volume method; hyperbolic conservation
laws},
owner = {olivier},
timestamp = {2010.06.03},
url = {http://www.sciencedirect.com/science/article/B6TYD-4N43RHY-1/2/bf692674b812e1149d36807a54a64c85}
}
@ARTICLE{Mangeney07,
author = {Mangeney, A. and Bouchut, F. and Thomas, N. and Vilotte, J.~P. and
Bristeau, M.-O.},
title = {Numerical modeling of self-channeling granular flow and of their
levee-channel deposits},
journal = {Journal of Geophysical Research},
year = {2007},
volume = {112},
pages = {F02017},
number = {F2},
month = may,
abstract = {When not laterally confined in valleys, pyroclastic flows create their
own channel along the slope by selecting a given flowing width. Furthermore,
the lobe-shaped deposits display a very specific morphology with
high parallel lateral levees. A numerical model based on Saint Venant
equations and the empirical variable friction coefficient proposed
by Pouliquen and Forterre (2002) is used to simulate unconfined granular
flow over an inclined plane with a constant supply. Numerical simulations
successfully reproduce the self-channeling of the granular lobe and
the levee-channel morphology in the deposits without having to take
into account mixture concepts or polydispersity. Numerical simulations
suggest that the quasi-static shoulders bordering the flow are created
behind the front of the granular material by the rotation of the
velocity field due to the balance between gravity, the two-dimensional
pressure gradient, and friction. For a simplified hydrostatic model,
competition between the decreasing friction coefficient and increasing
surface gradient as the thickness decreases seems to play a key role
in the dynamics of unconfined flows. The description of the other
disregarded components of the stress tensor would be expected to
change the balance of forces. The front's shape appears to be constant
during propagation. The width of the flowing channel and the velocity
of the material within it are almost steady and uniform. Numerical
results suggest that measurement of the width and thickness of the
central channel morphology in deposits in the field provides an estimate
of the velocity and thickness during emplacement.},
doi = {10.1029/2006JF000469},
file = {Mangeney07.pdf:Mangeney07.pdf:PDF},
keywords = {SAINT VENANT EQUATIONS; VOLCAN-DE-COLIMA; 3-DIMENSIONAL TERRAIN; PYROCLASTIC
FLOWS; LABORATORY EXPERIMENTS; UNZEN VOLCANO; SURFACE FLOW; AVALANCHES;
MOTION; MASS},
owner = {olivier},
timestamp = {2008.05.06}
}
@ARTICLE{MangeneyCastelnau05,
author = {Mangeney-Castelnau, A. and Bouchut, F. and Vilotte, J. P. and Lajeunesse,
E. and Aubertin, A. and Pirulli, M.},
title = {On the use of Saint-Venant equations to simulate the spreading of
a granular mass},
journal = {Journal of Geophysical Research},
year = {2005},
volume = {110},
pages = {B09103},
abstract = {[1] Cliff collapse is an active geomorphological process acting at
the surface of the Earth and telluric planets. Recent laboratory
studies have investigated the collapse of an initially cylindrical
granular mass along a rough horizontal plane for different initial
aspect ratios a = Hi/Ri, where Hi and Ri are the initial height and
radius, respectively. A numerical simulation of these experiments
is performed using a minimal depth-integrated model based on a long-wave
approximation. A dimensional analysis of the equations shows that
such a model exhibits the scaling laws observed experimentally. Generic
solutions are independent of gravity and depend only on the initial
aspect ratio a and an effective friction angle. In terms of dynamics,
the numerical simulations are consistent with the experiments for
a 1. The experimentally observed saturation of the final height of
the deposit, when normalized with respect to the initial radius of
the cylinder, is accurately reproduced numerically. Analysis of the
results sheds light on the correlation between the area overrun by
the granular mass and its initial potential energy. The extent of
the deposit, the final height, and the arrest time of the front can
be directly estimated from the ‘‘generic solution’’ of the model
for terrestrial and extraterrestrial avalanches. The effective friction,
a parameter classically used to describe the mobility of gravitational
flows, is shown to depend on the initial aspect ratio a. This dependence
should be taken into account when interpreting the high mobility
of large volume events.},
file = {MangenayCastelnau05.pdf:MangenayCastelnau05.pdf:PDF},
owner = {olivier},
timestamp = {2010.05.02}
}
@ARTICLE{Manzini04,
author = {Manzini, Gianmarco and Ferraris, Stefano},
title = {Mass-conservative finite volume methods on 2-D unstructured grids
for the Richards' equation},
journal = {Advances in water resources},
year = {2004},
volume = {27},
pages = {1199--1215},
abstract = {The solution to the 2-D time-dependent unsaturated ﬂow equation is
numerically approximated by a second-order accurate cell-centered
ﬁnite-volume discretization on unstructured grids. The approximation
method is based on a vertex-centered Least Squares linear reconstruction
of the solution gradients at mesh edges. A Taylor series development
in time of the water content dependent variable in a ﬁnite-diﬀerence
framework guarantees that the proposed ﬁnite volume method is mass
conservative. A Picard iterative scheme solves at each time step
the resulting non-linear algebraic problem. The performance of the
method is assessed on ﬁve diﬀerent test cases and implementing four
distinct soil constitutive relationships. The ﬁrst test case deals
with a column inﬁltration problem. It shows the capability of providing
a mass-conservative behavior. The second test case veriﬁes the numerical
approximation by comparison with an analytical mixed saturated–unsaturated
solution. In this case, the water drains from a fully saturated portion
of a 1-D column. The third and fourth test cases illustrate the performance
of the approximation scheme on sharp soil heterogeneities on 1-D
and 2-D multi-layered inﬁltration problems. The 2-D case shows the
passage of an abrupt inﬁltration front across a curved interface
between two layers. Finally, the ﬁfth test case compares the numerical
results with an analytical solution that is developed for a 2-D heterogeneous
soil with a source term representing plant roots. This last test
case illustrates the formal second-order accuracy of the method in
the numerical approximation of the pressure head.},
file = {Manzini04.pdf:Manzini04.pdf:PDF},
keywords = {Richards' equation; unsaturated flow; piecewise polynomial reconstructions;
cell-centered finite volume methods; unstructured meshes},
owner = {olivier},
timestamp = {2010.06.13}
}
@ARTICLE{Marchandise08,
author = {Marchandise, Emilie and Chevaugeon, Nicolas and Remacle, Jean-Fran\c{c}ois},
title = {Spatial and spectral superconvergence of discontinuous Galerkin method
for hyperbolic problems},
journal = {Journal of Computational and Applied Mathematics},
year = {2008},
volume = {215},
pages = {484--494},
number = {2},
note = {Proceedings of the Third International Conference on Advanced Computational
Methods in Engineering (ACOMEN 2005)., Proceedings of the Third International
Conference on Advanced Computational Methods in Engineering (ACOMEN
2005).},
abstract = {In this paper, we analyze the spatial and spectral superconvergence
properties of one-dimensional hyperbolic conservation law by a discontinuous
Galerkin (DG) method. The analyses combine classical mathematical
arguments with MATLAB experiments. Some properties of the DG schemes
are discovered using discrete Fourier analyses: superconvergence
of the numerical wave numbers, Radau structure of the X spatial error.},
doi = {DOI: 10.1016/j.cam.2006.03.061},
file = {Marchandise08.pdf:Marchandise08.pdf:PDF},
issn = {0377-0427},
keywords = {Discontinuous Galerkin method; Superconvergence; Hyperbolic systems},
owner = {olivier},
timestamp = {2011.03.10},
url = {http://www.sciencedirect.com/science/article/B6TYH-4MN3V8R-3/2/0bb0cd0d831f13f6105135c1f6c77587}
}
@ARTICLE{Marche07a,
author = {Marche, F.},
title = {Derivation of a new two-dimensional viscous shallow water model with
varying topography, bottom friction and capillary effects},
journal = {European Journal of Mechanics B/Fluids},
year = {2007},
volume = {26},
pages = {49--63},
abstract = {Considering the three-dimensional Navier-Stokes equations with a free
moving surface boundary condition and hydrostatic approximation,
we study the derivation, with asymptotic analysis, of a new two-dimensional
viscous shallow water model in rotating framework, with irregular
topography, linear and quadratic bottom friction terms and capillary
effects. A new formulation of the viscous effects, consistent with
a previous one-dimensional analysis, is obtained. Finally, we propose
some simple numerical experiments in order to validate the proposed
model.},
doi = {10.1016/j.euromechflu.2006.04.007},
file = {Marche07a.pdf:Marche07a.pdf:PDF},
keywords = {asymptotic analysis; shallow water equations; viscosity; friction;
capillary effects},
owner = {olivier},
timestamp = {2008.04.29}
}
@PHDTHESIS{Marche05,
author = {Marche, F.},
title = {Theoretical and numerical study of shallow water models. Applications
to nearshore hydrodynamics},
school = {Laboratoire de math{\'e}matiques appliqu{\'e}es -- universit{\'e}
de Bordeaux 1},
year = {2005},
month = dec,
abstract = {In this study we focus on theoretical and numerical questions around
the shallow water equations. The first part is devoted to the formal
derivation of a new viscous shallow water model with friction and
surface tension extra terms. We perform then a mathematical analysis
of the obtained model in order to obtain existence results for global
weak solutions. In The second part we develop a new numerical well-balanced
model which appears to be particularly well-suited for problems involving
a moving shoreline and strong topography variations, in a two dimensional
framework. The third part is devoted to the applications of our numerical
model to several problems concerning nearshore hydrodynamcs. More
precisely, the propagationin coastal domains of long waves regarded
as tsunamis are first investigated. Then we perform a study of nonlinear
wave/currents interactions in the Inner Surf Zone.},
file = {Marche05.pdf:Marche05.pdf:PDF},
keywords = {viscous shallow water model; asymptotic analysis; weak solution; finite
volume method; well-balanced scheme; moving shoreline; source term;
run-up of solitary waves; inner surf zone hydrodynamics},
owner = {olivier},
timestamp = {2008.04.28}
}
@ARTICLE{Marche08,
author = {Marche, Fabien and Berthon, Christophe},
title = {A Positive Preserving High Order VFRoe Scheme for Shallow Water Equations:
A Class of Relaxation Schemes},
journal = {{SIAM} {J}ournal on {S}cientific {C}omputing },
year = {2008},
volume = {30 },
pages = {pp. 2587-2612 },
number = {5},
month = aug,
note = {75{M}12, 35{L}65, 65{M}12 },
abstract = {{T}he {VFR}oe scheme has been recently introduced by {B}uffard, {G}allou{\"e}t,
and {H}{\'e}rard [{C}omput. {F}luids, 29 (2000), pp. 813-847] to
approximate the solutions of the shallow water equations. {O}ne of
the main interests of this method is to be easily implemented. {A}s
a consequence, such a scheme appears as an interesting alternative
to other more sophisticated schemes. {T}he {VFR}oe methods perform
approximate solutions in good agreement with the expected ones. {H}owever,
the robustness of this numerical procedure has not been proposed.
{F}ollowing the ideas introduced by {J}in and {X}in [{C}omm. {P}ure
{A}ppl. {M}ath., 45 (1995), pp. 235-276], a relevant relaxation method
is derived. {T}he interest of this relaxation scheme is twofold.
{I}n the first hand, the relaxation scheme is shown to coincide with
the considered {VFR}oe scheme. {I}n the second hand, the robustness
of the relaxation scheme is established, and thus the nonnegativity
of the water height obtained involving the {VFR}oe approach is ensured.
{F}ollowing the same idea, a family of relaxation schemes is exhibited.
{N}ext, robust high order slope limiter methods, known as {MUSCL}
reconstructions, are proposed. {T}he final scheme is obtained when
considering the hydrostatic reconstruction to approximate the topography
source terms. {N}umerical experiments are performed to attest the
interest of the procedure},
affiliation = {{I}nstitut de {M}ath{\'e}matiques et de {M}od{\'e}lisation de {M}ontpellier
- {I}3{M} - {CNRS} : {UMR}5149 - {U}niversit{\'e} {M}ontpellier {II}
- {S}ciences et {T}echniques du {L}anguedoc - {L}aboratoire de {M}ath{\'e}matiques
{J}ean {L}eray - {LMJL} - {CNRS} : {UMR}6629 - {U}niversit{\'e} de
{N}antes - {\'E}cole {C}entrale de {N}antes },
audience = {internationale },
day = {01},
file = {Marche08.pdf:Marche08.pdf:PDF},
keywords = {positivity preserving, shallow water equations, {VFR}oe schemes, relaxation
schemes, high order {MUSCL} extensions},
language = {{A}nglais},
owner = {olivier},
timestamp = {2009.08.26},
url = {http://hal.archives-ouvertes.fr/hal-00370486/en/}
}
@ARTICLE{Marche07b,
author = {Marche, F. and Bonneton, P. and Fabrie, P. and Seguin, N.},
title = {Evaluation of well-balanced bore-capturing schemes for 2{D} wetting
and drying processes},
journal = {International Journal for Numerical Methods in Fluids},
year = {2007},
volume = {53},
pages = {867--894},
abstract = {We consider numerical solutions of the two-dimensional non-linear
shallow water equations with a bed slope source term. These equations
are well-suited for the study of many geophysical phenomena, including
coastal engineering where wetting and drying processes are commonly
observed. To accurately describe the evolution of moving shorelines
over strongly varying topography, we first investigate two well-balanced
methods of Godunov-type, relying on the resolution of non-homogeneous
Riemann problems. But even if these schemes were previously proved
to be efficient in many simulations involving occurences of dry zones,
they fail to compute accurately moving shorelines. From this, we
investigate a new model, called SURF_WB, especially designed for
the simulation of wave transformations over strongly varying topography.
This model relies on a recent reconstruction method for the treatment
of the bed-slope source term and is able to handle strong variations
of topography and to preserve the steady states at rest. In adition,
the use of the recent VFRoe-ncv Riemann solver leads to a robust
treatment of wetting and drying phenomena. An adapted 'second order'
reconstruction generates accurate bore-capturing abilities. This
scheme is validated against several analytical solutions, involving
varying topography, time dependent moving shorelines and convergences
toward steady states. This model should have an impact in the prediction
of 2D moving shorelines over strongly irregular topography.},
doi = {10.1002/fld.1311},
file = {Marche07b.pdf:Marche07b.pdf:PDF},
keywords = {non-linear shallow water; well-balanced; finite volumes; moving shoreline;
topography},
owner = {olivier},
timestamp = {2008.04.29}
}
@INPROCEEDINGS{Martin05,
author = {Martin, Vincent and Cl\'ement, Fran\c{c}ois and Decoene, Astrid and
Gerbeau, Jean-Fr\'ed\'eric},
title = {Parameter identification for a one-dimensional blood flow model},
booktitle = {ESAIM: PROCEEDINGS},
year = {2005},
editor = {Eric Canc\`es \& Jean-Fr\'ed\'eric Gerbeau},
volume = {14},
pages = {174--200},
month = Sep,
abstract = {Abstract. The purpose of this work is to use a variational method
to identify some of the parameters of one-dimensional models for
blood ﬂow in arteries. These parameters can be ﬁt to approach as
much as possible some data coming from experimental measurements
or from numerical simulations performed using more complex models.
A nonlinear least squares approach to parameter estimation was taken,
based on the optimization of a cost function. The resolution of such
an optimization problem generally requires the eﬃcient and accurate
computation of the gradient of the cost function with respect to
the parameters. This gradient is computed analytically when the one-dimensional
hyperbolic model is discretized with a second order Taylor-Galerkin
scheme. An adjoint approach was used. Some preliminary numerical
tests are shown. In these simulations, we mainly focused on determining
a parameter that is linked to the mechanical properties of the arterial
walls, the compliance. The synthetic data we used to estimate the
parameter were obtained from a numerical computation performed with
a more accurate model: a three-dimensional ﬂuid-structure interaction
model. The ﬁrst results seem to be promising. In particular, it is
worth noticing that the estimated compliance which gives the best
ﬁt is quite diﬀerent from the values that are commonly used in practice.
R\´esum\´e. Le but de ce travail est d’identiﬁer certains des param\`etres
existant dans des mod\`eles 1-d d’\´ecoulement sanguin dans des art\`eres.
Ces param\`etres peuvent permettre d’approcher autant que possible
des conﬁgurations g\´eom\´etriques r\´ealistes ou des donn\´ees exp\´erimentales.
Une approche de l’estimation de param\`etres par moindres carr\´es
non-lin\´eaires a \´et\´e adopt\´ee, bas\´ee sur l’optimisation d’une
certaine fonction cout. La r\´esolution d’un tel probl\`eme de minimisation
requiert le calcul eﬃcace et pr\´ecis du gradient de la fonction
cout par rapport aux param\`etres. Le gradient est discr\´etis\´e
analytiquement dans le cas d’une discr\´etisation du mod\`ele hyperbolique
1-d par le sch\'ema de Taylor-Galerkin. Une approche par l’\´etat
adjoint a \´et\´e employ\´ee. Des premiers r\´esultats num\´eriques
sont fournis. Pour ces simulations, nous nous sommes concentr\´es
sur la d\´etermination d’un param\`etre li\´e aux propri\´et\´es
m\´ecaniques de la paroi art\´erielle. Les donn\´ees synth\´etiques
utilis\´ees pour l’estimation de ce param\`etre ont \´et\´e obtenues
a partir d’un mod\`ele beaucoup plus raﬃn\´e : un mod\`ele 3-d d’interaction
ﬂuide-structure. Les r\´esultats semblent int\´eressants car le param\`etre
estim\´e est assez diﬀ\´erent de ce \`e quoi on s’attendrait a priori.},
doi = {10.1051/proc:2005014},
file = {Martin05.pdf:Martin05.pdf:PDF},
keywords = {blood flow; Taylor-Galerkin; boundary condition; optimization; adjoint
state; 1D model; 3D model},
owner = {olivier},
timestamp = {2011.02.24}
}
@MASTERSTHESIS{McGrogan07,
author = {McGrogan, Sean},
title = {Modeling and simulation of oil transport for studying piston deposit
formation inIC engines},
school = {Massachusetts Institute of Technology},
year = {2007},
month = {june},
file = {McGrogan07.pdf:McGrogan07.pdf:PDF},
owner = {olivier},
timestamp = {2009.07.28}
}
@ARTICLE{McLaren00,
author = {McLaren, Robert G. and Forsyth, Peter A. and Sudicky, Edward A. and
VanderKwaak, Joel E. and Schwartz, Franklin W. and Kessler, John
H.},
title = {Flow and transport in fractured tuff at Yucca Mountain: numerical
experiments on fast preferential flow mechanisms},
journal = {Journal of Contaminant Hydrology},
year = {2000},
volume = {43},
pages = {211--238},
number = {3-4},
abstract = {Recent discovery of bomb-related 36Cl at depth in fractured tuff in
the unsaturated zone at the Yucca Mountain candidate high-level waste
(HLW) repository site has called into question the usual modeling
assumptions based on the equivalent continuum model (ECM). A dual
continuum model (DCM) for simulating transient flow and transport
at Yucca Mountain is developed. In order to ensure properly converged
flow solutions, which are used in the transport simulation, a new
flow solution convergence criteria is derived. An extensive series
of simulation studies is presented which indicates that rapid movement
of solute through the fractures will not occur unless there are intense
episodic infiltration events. Movement of solute in the environs
of the repository is enhanced if the properties of the tuff layer
at the repository horizon are modified from current best-estimate
values. Due to a large advective-dispersive coupling between the
matrix and fractures, the matrix acts as a major buffer which inhibits
rapid transport along the fractures. Consequently, fast movement
of solutes through the fractures to the repository depth can only
be explained if the matrix-fracture coupling term is significantly
reduced from a value that would be calculated on the basis of data
currently available.},
doi = {DOI: 10.1016/S0169-7722(00)00085-1},
file = {McLaren00.pdf:McLaren00.pdf:PDF},
issn = {0169-7722},
keywords = {Unsaturated zone; Fracture-matrix interaction; Numerical modeling;
Dual permeability; Fast preferential flow; Yucca Mountain; Darcy;
transport},
owner = {olivier},
timestamp = {2010.06.15},
url = {http://www.sciencedirect.com/science/article/B6V94-40379HH-2/2/c460e94d72785191f0fb86ef1964e90b}
}
@ARTICLE{Mein74,
author = {Mein, Russell G. and Farrell, D.~A.},
title = {Determination of {W}etting {F}ront {S}uction in the {G}reen-{A}mpt
{E}quation},
journal = {Soil Sci. Soc. Amer. Proc.},
year = {1974},
volume = {38},
pages = {872--876},
abstract = {Interest in the Green-Ampt equation to predict infiltration rates
into uniform and layered soils has increased in recent years. The
work reported here is a study of the theorical justification of determining
the suction (at the wetting front) parameter in the equation from
the hydraulic conductivity versus capillary suction relationship
for the soil. It is shown that the wetting front suction so determined
and used in a form of the Green-Ampt equation which allows for the
surface boundary condition initially being one of constant flux gives
predictions of infiltration volumes comparable to those determined
by numerical solution of the complex partial-differential equation
of moisture flow.},
file = {Mein74.pdf:Mein74.pdf:PDF},
keywords = {infiltration; Green-Ampt},
owner = {olivier},
timestamp = {2010.05.03}
}
@ARTICLE{Mein73,
author = {Mein, Russell G. and Larson, Curtis L.},
title = {Modeling {I}nfiltration during a {S}teady {R}ain},
journal = {Water Resources Research},
year = {1973},
volume = {9},
pages = {384--394},
number = {2},
month = Apr,
abstract = {Few of the infiltration models in current use are suitable for the
situation in which the rainfall intensity is initially less than
the infiltration capacity of the soil. In this paper a simple two-stage
model is developed for infiltration under a constant intensity rainfall
into a homogeneous soil with uniform initial moisture content. The
first stage predicts the volume of infiltration to the moment at
which surface ponding begins. The second stage, which is the Green-Ampt
model modified for the infiltration prior to surface saturation,
describes the subsequent infiltration behavior. A method for estimating
the mean suction of the wetting front is given. Comparison of the
model predictions with experimental data and numerical solutions
of the Richards equation for several soil types shows excellent agreement.},
file = {Mein73.pdf:Mein73.pdf:PDF},
keywords = {infiltration model; Green-Ampt},
owner = {olivier},
timestamp = {2010.04.22}
}
@ARTICLE{Meng08,
author = {Meng, H. and Green, T.~R. and Salas, J.~D. and Ahuja, L.~R.},
title = {Development and testing of a terrain-based hydrologic model for spatial
Hortonian infiltration and runoff/on},
journal = {Environmental Modelling \& Software},
year = {2008},
volume = {23},
pages = {794--812},
abstract = {Efficient numerical simulation of process interactions between infiltration
and Hortonian runoff is needed to evaluate patterns of internal state
variables and fluxes within a watershed. A fully distributed rainfall-runoff
model was developed for event-based studies of space-time watershed
processes. A routing hierarchy was defined over the watershed using
the D-infinity contributing area algorithm. Computation of ponding
time was included to handle variable run-on and rainfall intensity.
The Green-Ampt model was adopted to calculate surface infiltration,
and the kinematic wave model was used to route Hortonian runoff and
channel flow. The model can handle input rainfall, soil parameters,
and other properties that vary in space and time. The model was tested
first against analytical solutions for idealized overland planes.
After a sensitivity analysis to identify the most significant parameters,
it was then calibrated and verified using rainfall and streamflow
data from the USDA-ARS Walmut Gulch experimental watershed in Arizona,
USA. The coefficients of efficiency for runoff volume, peak flow,
and time to peak flow with respect to calibration/validation are
0.95/0.65, 0.85/0.09 and 0.69/0.88, respectively. Example applications
of the model show its potential for simulating internal states and
fluxes. The open-source model is provided for space-time simulation
and scaling of event-based Hortonian runoff and infiltration.},
doi = {10.1016/j.envsoft.2007.09.014},
file = {Meng08.pdf:Meng08.pdf:PDF},
keywords = {infiltration; hortonian runoff; mpdel development; calibration; model
testing},
owner = {olivier},
timestamp = {2008.05.03}
}
@ARTICLE{Meng06,
author = {Meng, H. and Salas, J.~D. and Green, T.~R. and Ahuja, L.~R.},
title = {Scaling analysis of space-time infiltration based on the universal
multifractal model},
journal = {Journal of Hydrology},
year = {2006},
volume = {322},
pages = {220-235},
abstract = {There is broad interest in the space–time scaling behavior of inﬁltration
over a watershed, but ﬁeld data is lacking to identify such scaling
and the controlling factors. Here, theoretical effects of rainfall
and saturated hydraulic conductivity (Ks) on space–time inﬁltration
are simulated using process-based numerical experiments in the framework
of a universal multifractal (UM) model. A series of rainfall and
Ks ﬁelds are generated including both random, non-scaling ﬁelds and
multifractal ﬁelds produced using the UM model. By varying the UM
model parameters based on physical considerations, rain and Ks ﬁelds
with various scaling characteristics are obtained. These rain and
Ks data are then fed into a distributed rainfall-runoff model developed
for this study to produce space–time inﬁltration, including the effects
of overland ﬂow from upslope areas. The scaling properties of the
inﬁltration are then analyzed to ﬁnd the impact from the rain and
Ks ﬁelds mainly in terms of the connections among the UM model parameters
between the input and the output ﬁelds. Some of the major ﬁndings
from this research are: (1) rainfall spatial characteristics determine
the scaling of inﬁltration only at very early times; (2) Ks, rather
than rain, determines if the resulting inﬁltration ﬁeld displays
scaling behavior after an adjusting period; (3) generally, the heterogeneity
of a rain ﬁeld and the singularity and sparseness of a Ks ﬁeld have
strong impacts on inﬁltration; (4) usually, inﬁltration ﬁelds are
statistically non-homogeneous; and (5) if an inﬁltration ﬁeld subject
to space–time rain becomes less singular (localized large inﬁltration
rates) in time, it tends to become less sparse and more heterogeneous,
and vice versa. The relationships and sensitivities identiﬁed
above help us understand some key factors controlling the potential
scaling behavior of inﬁltration.},
file = {Meng06.pdf:Meng06.pdf:PDF},
keywords = {Inﬁltration; Rainfall-runoff; Soil water; Process simulation; Scaling;
Multifractal},
owner = {olivier},
timestamp = {2010.01.27}
}
@ARTICLE{Menziani07,
author = {Menziani, Marilena and Pugnaghi, Sergio and Vincenzi, Sergio},
title = {Analytical solutions of the linearized Richards equation for discrete
arbitrary initial and boundary conditions},
journal = {Journal of Hydrology},
year = {2007},
volume = {332},
pages = {214--225},
abstract = {Summary Solutions of the linearized one-dimensional Richards equation
for discrete arbitrary initial and boundary conditions are presented.
The result is the soil water content at any required time and depth
in a semi-inﬁnite unsaturated porous medium domain. The initial condition
can be any discrete soil water content proﬁle (e.g., experimentally
measured) and the boundary condition can be any discrete water ﬂux
applied at the surface (e.g., experimentally derived). The procedure
described in the paper is valid for any series of successive atmosphere-controlled
and soil-controlled phases of inﬁltration or evaporation as required
by the given boundary condition. The procedure provides the ponding
time, the desiccation time and the surface water ﬂux during the soil-controlled
phases. The comparison among the proposed solutions and some exact
analytical solutions is presented as well as the cumulative ﬂuxes.
As expected, the agreement between the proposed solutions and the
exact analytical solutions depend on the time step chosen for the
boundary condition and on the space step chosen for the initial condition.},
file = {Menziani07.pdf:Menziani07.pdf:PDF},
keywords = {Richards equation; unsatured zone flow; infiltration; evaporation},
owner = {olivier},
timestamp = {2010.06.07}
}
@ARTICLE{Merz02,
author = {Merz, Bruno and B\'ardossy, Andr\'as and Schiffler, Gerd R.},
title = {Different methods for modelling the areal infiltration of a grass
field under heavy precipitation},
journal = {Hydrological Processes},
year = {2002},
volume = {16},
pages = {1383--1402},
abstract = {The areal inﬁltration behaviour of a grass ﬁeld is studied using a
data set of 78 sprinkler inﬁltration experiments. The analysis of
the experimental data shows a distinct event dependency: once runoff
begins, the ﬁnal inﬁltration rate increases with increasing rainfall
intensity. This behaviour is attributed to the effects of small-scale
variability. Increasing rainfall intensity increases the ponded area
and therefore the portion of the plot which inﬁltrates at maximum
rate. To describe the areal inﬁltration behaviour of the grass ﬁeld
the study uses two different model structures and investigates different
approaches for consideration of subgrid variability. It is found
that the effective parameter approach is not suited for this purpose.
A good representation of the observed behaviour is obtained by using
a
distribution function approach or a parameterization approach. However,
it is not clear how the parameters can be derived for these two approaches
without a large measurement campaign. The data analysis and the simulations
show the great importance of considering the effects of spatial variability
for the inﬁltration process. This may be signiﬁcant even at a small
scale for a comparatively homogeneous area. The consideration of
heterogeneity seems to be more important than the choice of the model
type. Furthermore, similar results may be obtained with different
modelling approaches. Even the relatively detailed data set does
not seem to permit a clear model choice. In view of these results
it is questionable to use very complex and detailed simulation models
given the approximate nature of the problem. Although the principle
processes may be well understood there is a lack of models that represent
these processes and, more importantly, there is a lack of techniques
to measure and parameterize them.},
doi = {10.1002/hyp.347},
file = {Merz02.pdf:Merz02.pdf:PDF},
keywords = {infiltration; infiltration experiments; physically-based modelling;
spatial variability; Richards; Manning's equation},
owner = {olivier},
timestamp = {2010.04.25}
}
@ARTICLE{Miglio03,
author = {Miglio, Edie and Quarteroni, Alfio and Saleri, Fausto},
title = {Coupling of free surface and groundwater flow},
journal = {Computers \& Fluids},
year = {2003},
volume = {32},
pages = {73--83},
abstract = {In this paper we present some preliminary results about the coupling
of shallow water equations for free surface ﬂows and Darcy equation
for groundwater ﬂows. A suitable set of interface conditions is discussed:
the Beavers and Joseph formula for the bottom stress is used. An
iterative algorithm to solve the coupled problem is proposed and
some numerical results are presented.},
file = {Miglio03.pdf:Miglio03.pdf:PDF},
keywords = {free surface flows; shallow water equations; groundwater flows; Darcy's
law; porous media; interface conditions; Stokes},
owner = {olivier},
timestamp = {2010.06.13}
}
@ARTICLE{Mishra03,
author = {Mishra, Surendra Kumar and Tyagi, J.~V. and Singh, Vijay P.},
title = {Comparison of infiltration models},
journal = {Hydrological Processes},
year = {2003},
volume = {17},
pages = {2629--2652},
abstract = {Fourteen popular, representative inﬁltration models, some physically
based, some semi-empirical and some empirical, were selected for
a comparative evaluation. Using the Nash and Sutcliffe efﬁciency
criterion, the models were evaluated and compared for 243 sets of
inﬁltration data collected from ﬁeld and laboratory tests conducted
in India and the USA on soils ranging from coarse sand to ﬁne clay.
Based on a relative grading scale, the semi-empirical Singh–Yu general
model, Holtan model and Horton model were graded respectively as
6.52, 5.57 and 5.48 out of 10. The empirical Huggins and Monke model,
modiﬁed Kostiakov and Kostiakov model were graded as 5.57, 5.30 and
5.22, respectively. The physically based non-linear and linear models
of Smith–Parlange were graded as 5.48 and 5.22,
respectively. Other models were ranked lower than these models. All
the models generally performed poorly in ﬁeld tests on Georgia’s
sandy soils, except the Robertsdale loamy sand.},
file = {Mishra03.pdf:Mishra03.pdf:PDF},
keywords = {infiltration dynamics; conceptual models; empirical models; Nash-Sutcliffe
efficiency criterion; physically based models; soil hydrology; Philip;
Green-Ampt; Smith-Parlange; Singh-Yu; Mishra-Singh; Smith; Horton;
Holtan; Overton; Kostiakov; Huggins-Monke; Collis-George},
owner = {olivier},
timestamp = {2010.04.24}
}
@ARTICLE{Misra98,
author = {Misra, Rajeev},
title = {Recursive algorithm for steady flow in a canal network},
journal = {Advances in Engineering Software},
year = {1998},
volume = {29},
pages = {77 - 86},
number = {1},
abstract = {A recursive-iterative algorithm to solve the equation for one-dimensional
gradually varied steady flow in a canal network is developed. The
recursion is used to sweep up and down the network, whereas iterations
are used to obtain convergence for the discharge distribution at
canal junctions. The convergence characteristics of different discharge
updating techniques are discussed. The application of the algorithm
is demonstrated through eight test problems on two networks, by starting
the computations from different initial guesses of discharge distribution
in the network.},
doi = {DOI: 10.1016/S0965-9978(97)00027-6},
file = {Misra98.pdf:Misra98.pdf:PDF},
issn = {0965-9978},
owner = {olivier},
timestamp = {2009.11.29},
url = {http://www.sciencedirect.com/science/article/B6V1P-3SYVFS2-8/2/11c0e9e3c47c63d662a39fb4ef124a4b}
}
@ARTICLE{Misra96,
author = {Misra, Rajeev},
title = {Spatially varied steady flow in irrigation canals},
journal = {Agricultural Water Management},
year = {1996},
volume = {30},
pages = {217 - 235},
number = {2},
abstract = {A mathematical model is developed for the analysis of spatially varied
steady flow in an irrigation canal. The spatially varied steady flow
equations are solved using the finite difference method. The model
results are verified with the observed water surface profiles available
in literature. The effect of canal seepage, canal condition, turnout
flows, backwater and drawdown conditions are studied in terms of
discharge in the canals, performance of turnouts and spatial variability
of flow. It is observed that even for design roughness and seepage
parameters, the actual depth and discharge in the canal is significantly
different from the designed ones.},
doi = {DOI: 10.1016/0378-3774(95)01224-9},
file = {Misra96.pdf:Misra96.pdf:PDF},
issn = {0378-3774},
owner = {olivier},
timestamp = {2009.11.29},
url = {http://www.sciencedirect.com/science/article/B6T3X-3W494JX-F/2/bef83d41c9b6f3ad57e047d230fef8ea}
}
@ARTICLE{Miyoshi05,
author = {Miyoshi, Takahiro and Kusano, Kanya},
title = {A multi-state HLL approximate Riemann solver for ideal magnetohydrodynamics},
journal = {Journal of Computational Physics},
year = {2005},
volume = {208},
pages = {315 - 344},
number = {1},
abstract = {A new multi-state Harten-Lax-van Leer (HLL) approximate Riemann solver
for the ideal magnetohydrodynamic (MHD) equations is developed based
on the assumption that the normal velocity is constant over the Riemann
fan. This assumption is same as that used in the HLLC (#C# denotes
Contact) approximate Riemann solver for the Euler equations. From
the assumption, it is naturally derived that the Riemann fan should
consist of four intermediate states for Bx [not equal to] 0, whereas
the number of the intermediate states is reduced to two when Bx = 0.
Since the intermediate states satisfied with all jump conditions
in this approximate Riemann system are analytically obtained, the
multi-state HLL Riemann solver can be constructed straightforwardly.
It is shown that this solver can exactly resolve isolated discontinuities
formed in the MHD system, and hence named as HLLD Riemann solver.
(Here, #D# stands for Discontinuities.) It is also analytically proved
that the HLLD Riemann solver is positively conservative like the
HLLC Riemann solver. Indeed, the HLLD Riemann solver corresponds
to the HLLC Riemann solver when the magnetic field vanishes. Numerical
tests demonstrate that the HLLD Riemann solver is more robust and
efficient than the linearized Riemann solver, and its resolution
is equally good. It indicates that the HLLD solver must be useful
in practical applications for the ideal MHD equations.},
doi = {DOI: 10.1016/j.jcp.2005.02.017},
file = {Miyoshi05.pdf:Miyoshi05.pdf:PDF},
issn = {0021-9991},
keywords = {Magnetohydrodynamics; approximate Riemann solver; HLL; HLLC; HLLD;
positivity},
owner = {olivier},
timestamp = {2010.06.03},
url = {http://www.sciencedirect.com/science/article/B6WHY-4FY3P80-7/2/426234268c96dcca8a828d098b75fe4e}
}
@ARTICLE{Mohamadian05,
author = {Mohamadian, A. and {Le Roux}, D.~Y. and Tajrishi, M. and Mazaheri,
K.},
title = {A mass conservative scheme for simulating shallow flows over variable
topographies using unstructured grid},
journal = {Advances in Water Resources},
year = {2005},
volume = {28},
pages = {523--539},
abstract = {Most available numerical methods face problems, in the presence of
variable topographies, due to the imbalance between the source and
flux terms. Treatments for this problem generally work well for structured
grids, but most of them are not directly applicable for unstructured
grids. On the other hand, despite of their good performance for discontinuous
flows, most available numerical schemes (such as HLL flux and ENO
schemes) induce a high level of numerical diffusion in simulating
recirculating flows. A numerical method for simulating shallow recirculating
flows over a variable topography on unstructured grids is presented.
This mass conservative approach can simulate different flow conditions
including recirculating, transcritical and discontinuous flows over
variable topographies without upwinding of source terms and with
a low level of numerical diffusion. Different numerical tests cases
are presented to show the performance of the scheme for some challenging
problems.},
doi = {10.1016/j.advwatres.2004.10.006},
file = {Mohamadian05.pdf:Mohamadian05.pdf:PDF},
keywords = {shallow water; variable topography; unstructured grid; recirculating
flow; finite volume method; mass conservative approach},
owner = {olivier},
timestamp = {2008.05.04}
}
@TECHREPORT{Mohammadi94,
author = {Mohammadi, Bijan},
title = {Fluid {D}ynamics {C}omputation with {NSC2KE} {A}n {U}ser-{G}uide
{R}elease 1.0},
institution = {INRIA},
year = {1994},
number = {RT-0164},
month = may,
abstract = {NSC2KE is a Finite-Volume Galerkin program computing 2D and axisymmetric
flows on unstructured meshes. To solve the Euler part of the equations,
a Roe, an Osher and a Kinetic solvers are available. To compute turbulent
ows a k -\epsilon model is available. Near-wall turbulence is computed
either by wall-laws or by a two-layer approach. Time dependant problems
can also be considered as a fourth order Runge-Kutta solver has been
used.},
file = {Mohammadi94.pdf:Mohammadi94.pdf:PDF},
keywords = {CFD; Compressible Navier-Stokes Equations; Turbulence; k-\epsilon
Two-equation Model; Two-layer Approach; Wall-Laws},
owner = {olivier},
timestamp = {2009.12.11}
}
@PHDTHESIS{Mohammadian06,
author = {Mohammadian, Abdolmajid},
title = {Conservative characteristic-based schemes for shallow flows},
school = {Facult\'e des \'etudes sup\'erieures de l'universit\'e de Laval},
year = {2006},
abstract = {Les équations en eaux peu profondes, encore appelées équations de
Saint-Venant, sont utilisées dans de nombreux cas importants comme
les fleuves, les lacs, les estuaires et les océans. La conservation
de certaines quantités est une propriété importante qui est habituellement
désirée pour assurer la précision des simulations à long terme et
également pour le cas des écoulements complexes avec présence d'ondes
de choc.
Cette thèse examine tout d'abord la formulation de schémas semi-Lagrangiens,
qui sont bien connus pour demeurer stables pour des nombres très
élevés de CFL. Cependant, ces schémas perdent leur propriété de stabilité
lorsque la conservation totale des quantités, qui est cruciale pour
une simulation correcte les ondes de chocs, est imposée. Un schéma
semi-Lagrangien entièrement conservatif est développé ici et ce dernier
demeure stable pour des nombres élevés de CFL. L'approche proposée
est ensuite étendue à la méthode des caractéristiques (MOC) et une
version conservative du schéma MOC est développée.
Contrairement au schéma MOC original, qui ne peut pas simuler correctement
les ondes de choc à cause du manque de conservation, le schéma proposé
les simule avec succès. De plus, le nouveau schéma présente des avantages
sur le plan numérique, tant pour la diffusion et la dispersion que
pour la stabilité. Le cas 2D est ensuite considéré, et la méthode
de volume finie est utilisée à cause de son conservation inhérente.
Le cas 2D est ensuite considéré, et la méthode de volumes finis est
utilisée à cause de ses qualités inhérentes de conservation. La plupart
des méthodes numériques disponibles sont sensibles au problème du
déséquilibre entre les termes source et de flux, particulièrement
en présence d'un maillage non structuré. D'autre part, la plupart
des schémas numériques disponibles (par exemple les schémas HLL et
ENO) induisent un niveau élevé de diffusion numérique en simulant
des écoulements tourbillonnaires. Trois approches différentes, applicables
sur des maillages non structurés sont développées ici. Elles peuvent
simuler des conditions complexes d'écoulement comprenant les topographies
variables, les écoulements tourbillonnaires, trans-critiques et discontinus.
Finalement plusieurs méthodes de volumes finis upwind sont utilisées,
via une analyse de type Fourier, pour évaluer le niveau d`amortissement
des modes de Rossby. Contrairement aux bons résultats habituellement
obtenus par les méthodes de volumes finis upwind dans le cas d'écoulements
dominés par la convection, on remarque ici que les ondes de Rossby
sont amorties de manière excessive.},
file = {Mohammadian06.pdf:Mohammadian06.pdf:PDF},
owner = {olivier},
timestamp = {2009.07.28}
}
@ARTICLE{Monthe99,
author = {Monthe, L. A. and Benkhaldoun, F. and Elmahi, I.},
title = {Positivity preserving finite volume Roe: schemes for transport-diffusion
equations},
journal = {Computer Methods in Applied Mechanics and Engineering},
year = {1999},
volume = {178},
pages = {215--232},
number = {3-4},
abstract = {The motion of flood waves resulting from dam break are investigated
numerically. The Roe approximate Riemann solver is applied to the
system of shallow water equations. This system is combined with pollutant
transport diffusion equation and solved on structured and non-structured
grids. An entropy fix for the numerical scheme enables to handle
initial dry area flows even in complicated geometry cases, without
loss of mass positivity. To discretize the diffusion term, a nine
point spatial discretization is used on a structured grid and a four
point finite volume scheme is used on unstructured meshes. In order
to have flexibility upon the complex configurations domain, non-structured
grid meshing is utilized. A semi-implicit discretization of the source
terms, as well as the use of second order schemes, makes it possible
to succesfully investigate problems with friction and non-horizontal
ground.},
doi = {DOI: 10.1016/S0045-7825(99)00015-8},
file = {Monthe99.pdf:Monthe99.pdf:PDF},
issn = {0045-7825},
keywords = {Saint Venant equations; Riemann solver; Entropy modification; Nine
point finite volume scheme; Four point finite volume scheme; Diffusion;
Source terms; positive preserving; transport; friction; semi-implicit},
owner = {olivier},
timestamp = {2010.06.18},
url = {http://www.sciencedirect.com/science/article/B6V29-3X9RXXF-1/2/a48b03ce2cb3ef3b14b4a8fb88c52faa}
}
@INCOLLECTION{Montuori61,
author = {Montuori, Carlo},
title = {La formazione spontanea dei treni d'onde su canali a pendenza molto
forte},
booktitle = {Estratto dal fascicolo n. 2 Vol. XXXVIII della Rivista mensile "L'Energia
Elettrica"},
year = {1961},
file = {Montuori61.pdf:Montuori61.pdf:PDF},
keywords = {roll waves; Vedernikov},
owner = {olivier},
timestamp = {2010.05.02}
}
@ARTICLE{Moodie86,
author = {Moodie, T.~B. and Barclay, D.~W. and Greenwald, S.~E.},
title = {Impulse Propagation in Liquid Filled Distensible Tubes: Theory and
Experiment for Intermediate to Long Wavelengths},
journal = {Acta Mechanica},
year = {1986},
volume = {59},
pages = {47--58},
abstract = {A theory of wave propagation in liquid filled distensible tubes, which
extends the region of validity of the linear long wavelength theory
commonly employed in haemodynamics, is presented and tested against
experiments on water filled latex tubes. he theory which is linear
and involves but a single free parameter provides excellent agreement
with the impulse experiments.},
file = {Moodie86.pdf:Moodie86.pdf:PDF},
keywords = {blood flow; wave; experiment; Korteweg-Moens},
owner = {olivier},
timestamp = {2010.11.26}
}
@ARTICLE{Moodie84,
author = {Moodie, T.~B. and Barelay, D.~W. and Greenwald, S.~E. and Newman,
D.~L.},
title = {Waves in Fluid Filled Tubes: Theory and Experiment},
journal = {Acta Mechanica},
year = {1984},
volume = {54},
pages = {107--119},
abstract = {A viscoelastic shell theory model for transient pressure perturbations
in fluid filled tubes is presented and tested against experiments
involving water filled latex tubes. The agreement between theory
and experiment is good.},
file = {Moodie84.pdf:Moodie84.pdf:PDF},
keywords = {blood flow; input pressure; experiment},
owner = {olivier},
timestamp = {2010.11.26}
}
@ARTICLE{Moore81,
author = {I.D. Moore and C.L. Larson and D.C. Slack and B.N. Wilson and F.
Idike and M.C. Hirschi},
title = {Modelling infiltration: A measurable parameter approach},
journal = {Journal of Agricultural Engineering Research},
year = {1981},
volume = {26},
pages = {21 - 32},
number = {1},
abstract = {Development of a 2-stage, measured parameter, infiltration model is
reviewed. The model has been verified against finite difference solutions
of the unsaturated flow equation, by laboratory tests and has been
evaluated under field conditions. Progress of recent research utilizing
this model is discussed. Results of recent research indicate that
the effects of air entrapment on hydraulic conductivity must be taken
into account. A reasonable approach to this problem is to evaluate
relative conductivity as a function of relative moisture content
and use this relationship to evaluate hydraulic conductivity at field
saturation. Additional factors which have been investigated include
air viscous effects and the effects of tillage and surface sealing.
While significant progress has been made toward including these effects
in the model, additional research is required. An attractive attribute
of the model is that all parameters utilized in the model are measurable
and thus no parameter fitting is required. The paper discusses how
parameters may be evaluated and how the model operates, and presents
some examples of model predictions under different conditions of
soil composition and rainfall pattern.},
doi = {DOI: 10.1016/0021-8634(81)90124-4},
file = {Moore81.pdf:Moore81.pdf:PDF},
issn = {0021-8634},
owner = {olivier},
timestamp = {2010.05.12},
url = {http://www.sciencedirect.com/science/article/B6WH1-495VBF5-1F/2/eeb6978c6da10101b97ba1311990b16f}
}
@PHDTHESIS{Morales07,
author = {Morales De Luna,T.},
title = {Sch{\'e}mas entropiques pour la r{\'e}solution de syst{\`e}mes de
type Saint Venant},
school = {universit{\'e} Paris VI},
year = {2007},
file = {Morales07.pdf:Morales07.pdf:PDF},
owner = {olivier},
timestamp = {2008.04.28}
}
@ARTICLE{Morris80,
author = {Morris, E.~M.},
title = {The propagation of waves in shallow water flow with lateral inflow},
journal = {Hydrological Sciences Bulletin},
year = {1980},
volume = {25},
pages = {25--32},
number = {1},
abstract = {The propagation characteristics of small amplitude waves in shallow
water flow with lateral inflow are determined using a linear perturbation
method. Expressions relating the celerity, attenuation and wave number
of the waves are given and used to establish two critical values
of the Froude number.},
file = {Morris80.pdf:Morris80.pdf:PDF},
owner = {olivier},
timestamp = {2008.05.04}
}
@ARTICLE{Morris79,
author = {Morris, E. M.},
title = {The effect of the small-slope approximation and lower boundary conditions
on solutions of the Saint-Venant equations},
journal = {Journal of Hydrology},
year = {1979},
volume = {40},
pages = {31--47},
abstract = {A new implicit finite difference scheme is used to investigate the
effect of the small slope approximation and the choice of lower boundary
conditions on solutions of the Saint-Venant equations. It is found
that for a range of values of the Froude and kinematic wave numbers
which covers most cases of hydrological interest these factors have
no significant effect on the depth and velocity profiles for surface
flow.},
file = {Morris79.pdf:Morris79.pdf:PDF},
owner = {olivier},
timestamp = {2010.05.03}
}
@TECHREPORT{Morris00,
author = {Morris, M.~W.},
title = {CADAM Concerted Action on Dambreak Modelling, Final Report February
1998 - January 2000},
institution = {EC Contract number ENV4-CT97-0555},
year = {2000},
number = {Report SR 571},
month = Jan,
file = {Morris00.pdf:Morris00.pdf:PDF},
owner = {olivier},
timestamp = {2010.05.09}
}
@ARTICLE{Mortensen08,
author = {Mortensen, J. and Telyakovskiy, A.S. and Li, L. and Lockington, D.A.
and Parlange, M.B. and Stagnitti, F. and Jeng, D.-S. and Selker,
J.S. and Barry, D.A. and Parlange, J.-Y.},
title = {Erratum to } # Similarity # solution # of # axisymmetric # flow #
in # porous # media # { [Adv. Water Resour. 28 (2005) 1076-1082]},
journal = {Advances in Water Resources},
year = {2008},
volume = {31},
pages = {1764 - 1764},
number = {12},
doi = {DOI: 10.1016/j.advwatres.2008.05.008},
file = {Mortensen08.pdf:Mortensen08.pdf:PDF},
issn = {0309-1708},
owner = {olivier},
timestamp = {2010.06.04},
url = {http://www.sciencedirect.com/science/article/B6VCF-4T1944G-1/2/52e7c6edcd1ec29263fbd3ee8c4a501a}
}
@INPROCEEDINGS{MouraCarmona06,
author = {Moura Carmona, M. and Moura Neto, F.D. and Ferreira, F.F. and Van
Hombeeck, M.},
title = {A semi-implicit semi-lagrangian finite difference method for the
simulation of the hydrodynamics of a pollutant in a shallow water
regimen},
booktitle = {Journal of Coastal Research, SI 39 (Proceedings of the 8th International
Coastal Symposium), 1606-1609, Itaja\'i, SC, Brazil},
year = {2006},
abstract = {This paper deals with the simulation of the transport of a scalar
non-interacting and non-dissipative pollutant in a shallow water
environment. We present a semi-implicit semi-Lagrangian method for
the discretization of the time variable involving the convective
and advective terms coupled with a centered finite difference scheme
for the space discretization of the shallow water equations together
with an equation for a non-reacting and non-diffusive pollutant field.
The linear terms, in the coupled equations for the pertubation of
the water column, are responsible for the gravitational effects,
and give rise to fast waves which can be handled by an implicit method
resulting in a precise numerical scheme. This method allows the use
of fine space resolution without incurring in severe time step restrictions
(no CFL restriction). In this way reliable monitoring of pollutant
fields is accomplished with low computational costs when compared
with Eulerian methods.},
file = {MouraCarmona06.pdf:MouraCarmona06.pdf:PDF},
keywords = {shallow water equations; semi-lagrangian method; finite difference;
transport of pollutants; numerical solutions},
owner = {olivier},
timestamp = {2010.04.25}
}
@ARTICLE{Moussa00,
author = {Moussa, R. and Bocquillon, C.},
title = {Approximation zones of the Saint-Venant equations for flood routing
with overbank flow},
journal = {Hydrology and Earth System Sciences},
year = {2000},
volume = {4},
pages = {251--261},
number = {2},
abstract = {The classification of river waves as gravity, diffusion or kinematic
waves, corresponds to different forms of the momentum equation in
the Saint-Venant system. This paper aims to define approximation
zones of the Saint-Venant equations for flood routing in natural
channels with overbank flow in the flooded area. Using linear perturbation
theory, the different terms in the Saint-Venant equations were analysed
as a function of the balance between friction and inertia. Then,
using non-dimensionalised variables, flood waves were expressed as
a function of three parameters: the Froude number of the steady uniform
flow, a dimensionless wave number of the unsteady component of the
motion and the ratio between the flooded area zone width and the
main channel width. Finally, different theoretical cases, corresponding
to different flooded area zone widths were analysed and compared.
Results show that, when the width of the flooded area increases,
the domain of application of the diffusive wave and the kinematic
wave models is restricted.},
file = {Moussa00.pdf:Moussa00.pdf:PDF},
keywords = {Saint-Venant equations; river waves; overbank flow},
owner = {olivier},
timestamp = {2008.05.04}
}
@ARTICLE{Munz88,
author = {Munz, Claus-Dieter},
title = {On the Numerical Dissipation of High Resolution Schemes for Hyperbolic
Conservation Laws},
journal = {Journal of Computational Physics},
year = {1988},
volume = {77},
pages = {18--39},
abstract = {In recent years, a number of new shock-capturing finite difference
schemes, often called high resolution schemes, have been constructed.
This paper presents a comparison of these schemes in terms of their
numerical dissipation, which becomes very obvious from numerical
results obtained for two initial value problems of a two-dimensional
advection equation. We consider TVD schemes, which are constructed
to prevent the total variation of the numerical approximations from
increasing, as well as UN0 schemes which only guarantee that the
number of local extrema does not increase.},
file = {Munz88.pdf:Munz88.pdf:PDF},
keywords = {TVD schemes; UNO schemes; minmod; van Leer; monotonized central difference;
van Albada; uperbee; slope limiter},
owner = {olivier},
timestamp = {2011.02.24}
}
@INPROCEEDINGS{Mura10,
author = {Mura, Joaqu\'in and Fern\'andez, Miguel A. and Gerbeau, Jean-Fr\'ed\'eric},
title = {Numerical simulation of the fluid-structure interaction in stented
aneurysms},
booktitle = {V European Conference on Computational Fluid Dynamics, ECCOMAS CFD
2010, J. C. F. Pereira and A. Sequeira (Eds), Lisbon, Portugal, 14-17
June 2010},
year = {2010},
abstract = {Abstract. An aneurysm is a pathological condition whereby a weakened
artery wall may dilates up to dangerous proportions. One of the most
common treatments consists of the insertion of a stent graft, which
is a medical device introduced into the artery lumen in order to
diminish the pressure on the aneurysm wall and so avoiding its rupture.
In this article we perform the simulation of the fluid-structure
interaction between the blood, the artery wall and the stent. We
consider the blood modeled by incompressible Navier-Stokes equations
in ALE formulation, while the solid parts are modeled using non-linear
shells in a Lagrangian framework. We suppose the stent being perfectly
matched with the artery, i.e., with no filtrations or endoleaks,
such that we obtain two disconnected regions of fluid by the stent
wall.
The main difficulty in this problem is the numerical solution for
the isolated portion of fluid, where the explicit coupling with standard
Dirichlet-Neumann boundary conditions may lead to non uniqueness
for the intra-aneurysm pressure and also to violate the divergence
free condition. To address this issue we use Robin-Neumann conditions
for the coupling, which allow us not only to obtain successful numerical
simulations but also a less sensitive scheme to the added-mass effect
and a more stable and robust iterative technique than the Dirichlet-Neumann
procedure. We present numerical evidence of the well-posedeness of
this technique and examples showing the effect of the stent on the
aneurysm wall.},
file = {Mura10.pdf:Mura10.pdf:PDF},
keywords = {Fluid-structure interaction; Robin-Neumann boundary conditions; Hemodynamics;
Enclosed fluid problems; blood flow},
owner = {olivier},
timestamp = {2011.03.17}
}
@ARTICLE{Murillo10,
author = {Murillo, J. and Garc\'ia-Navarro, P.},
title = {An Exner-based coupled model for two-dimensional transient flow over
erodible bed},
journal = {Journal of Computational Physics},
year = {2010},
volume = {229},
pages = {8704--8732},
abstract = {Transient ﬂow over erodible bed is solved in this work assuming that
the dynamics of the bed load problem is described by two mathematical
models: the hydrodynamic model, assumed to be well formulated by
means of the depth averaged shallow water equations, and the Exner
equation. The Exner equation is written assuming that bed load transport
is governed by a power law of the ﬂow velocity and by a ﬂow/sediment
interaction parameter variable in time and space. The complete system
is formed by four coupled partial differential equations and a genuinely
Roe-type ﬁrst order scheme has been used to solve it on triangular
unstructured meshes. Exact solutions have been derived for the particular
case of initial value Riemann problems with variable bed level and
depending on particular forms of the solid discharge formula. The
model, supplied with the corresponding solid transport formulae,
is tested by comparing with the exact solutions. The model is validated
against laboratory experimental data of different unsteady problems
over erodible bed.},
doi = {10.1016/j.jcp.2010.08.006},
file = {Murillo10.pdf:Murillo10.pdf:PDF},
keywords = {finite volume method; shallow water; bedload sediment transport; Exner
equation; 2D weak solutions; Roe method; bank equilibrium},
owner = {olivier},
timestamp = {2011.02.24}
}
@ARTICLE{Murillo09,
author = {Murillo, J. and Garc\'ia-Navarro, P. and Burguete, J.},
title = {Conservative numerical simulation of multi-component transport in
two-dimensional unsteady shallow water flow},
journal = {Journal of Computational Physics},
year = {2009},
volume = {228},
pages = {5539 - 5573},
number = {15},
doi = {DOI: 10.1016/j.jcp.2009.04.039},
file = {Murillo09.pdf:Murillo09.pdf:PDF},
issn = {0021-9991},
keywords = {Multi-component transport},
owner = {olivier},
timestamp = {2009.07.21},
url = {http://www.sciencedirect.com/science/article/B6WHY-4W7J15Y-3/2/e6a7c08d077c793b2d64659d3fd367bd}
}
@ARTICLE{Murillo08,
author = {Murillo, J. and Garc\'ia-Navarro, P. and Burguete, J.},
title = {Time step restrictions for well-balanced shallow water solutions
in non-zero velocity steady states},
journal = {International Journal for Numerical Methods in Fluids},
year = {2008},
doi = {10.1002/fld},
file = {Murillo08.pdf:Murillo08.pdf:PDF},
keywords = {finite volumes;unstructured grids;friction term;explicit discretization;implicit
discretization;numerical stability;well-balanced solution;},
owner = {olivier},
timestamp = {2009.07.24}
}
@ARTICLE{Muzik74,
author = {Muzik, I.},
title = {State variable model of overland flow},
journal = {Journal of Hydrology},
year = {1974},
volume = {22},
pages = {347--364},
abstract = {The state variable approach to systems analysis and synthesis is used
to develop a lumped mathematical model of overland flow. The model
describes the unsteady non-uniform flow in terms of a set of first
order ordinary differential equations and a set of arithmetic equations.
Conceptually the model consists of a series of interacting reaches
with unsteady uniform flow subjected to impulse inputs. The change
in hydraulic roughness due to rainfall impact effect is accounted
for. The regeneration performance of the model is tested by comparison
with experimental hydrographs of overland flow from a laboratory
catchment. Close agreement between experimental and calculated hydrographs
is obtained for both uniformly distributed as well as temporally
and spatially varied rainfall inputs. The state variable approach
is not limited to overland flow; it provides a comprehensive mathematical
framework for a general hydrologic model.},
file = {Muzik74.pdf:Muzik74.pdf:PDF},
keywords = {rain; friction; hydrograph},
owner = {olivier},
timestamp = {2010.05.03}
}
@ARTICLE{Myers03,
author = {Myers, T.~G.},
title = {Unsteady laminar flow over a rough surface},
journal = {Journal of Engineering Mathematics},
year = {2003},
volume = {46},
pages = {111--126},
abstract = {A model is developed for the unsteady laminar flow of a thin fluid
film over a substrate with roughness of the same order as the film
height. The limits of large and small surface resistance and small
surface-roughness are investigated and it is shown that at leading
order the classical parabolic form for the velocity profile is retrieved
in all cases. Empirical expressions for the depth-avaraged velocity
and the ratio of the average to maximum velocities are investigated
and shown to agree with the present theory under certain conditions.
The method is verified by comparison with experiments for steady
uni-directional flow over a surface of known roughness.},
file = {Myers03.pdf:Myers03.pdf:PDF},
keywords = {laminar flow; rough surface; thin film},
owner = {olivier},
timestamp = {2008.05.01}
}
@ARTICLE{Nash70,
author = {Nash, J.~E. and Sutcliffe, J.~V.},
title = {River flow forecasting through conceptual models Part I - A discussion
of principles},
journal = {Journal of Hydrology},
year = {1970},
volume = {10},
pages = {282--290},
abstract = {The principles governing the application of the conceptual model technique
to river flow forecasting are discussed. The necessity for a systematic
approach to the development and testing of the model is explainde
and some preliminary ideas suggested.},
file = {Nash70.pdf:Nash70.pdf:PDF},
keywords = {residual variance; initial variance; efficiency of a model; Nash-Sutcliffe},
owner = {olivier},
timestamp = {2010.05.02}
}
@ARTICLE{Needham84,
author = {Needham, D. J. and Merkin, J. H.},
title = {On Roll Waves down an Open Inclined Channel},
journal = {Proceedings of the Royal Society of London. Series A, Mathematical
and Physical},
year = {1984},
volume = {394},
pages = {259--278},
abstract = {Flow down an open inclined channel is considered. Dressler (Communs
(I949),) using the equations of the shallow water theory augmented
by the Chezy formula for drag, has shown that the uniform flow becomes
unstable when the Froude number F exceeds 4, and in this case he
was able to construct a one-parameter family of discontinuous periodic
solutions by piecing together continuous sections of wave profile
and a series of hydraulic jumps. Here the work of Dressler is extended
by the inclusion of a further term that accounts for energy dissipation
by shearing normal to the flow. It is shown that the inclusion of
such a term does not alter the condition for stability of the uniform
flow, and that when the uniform flow is unstable, a one-parameter
family of quasi-steady periodic solutions exists (parametrized by
the propagation speed U), appearing as a Hopf bifurcation out of
the uniform flow at the critical value U, = 1 + F-i. After the existence
of these periodic solutions has been shown, uniformly valid expansions
for the periodic solutions are obtained by using the Krylov-Bogoliubov-Mitropolski
averaging method, and the results are also extended to larger amplitudes
by numerical integration.},
file = {Needham84.pdf:Needham84.pdf:PDF},
keywords = {roll waves; diffusion; Chezy; stability},
owner = {olivier},
timestamp = {2010.06.30}
}
@ARTICLE{Neuman77,
author = {Neuman, S.P.},
title = {Theorical Derivation of Darcy's law},
journal = {Acta Mechanica},
year = {1977},
volume = {25},
pages = {153--170},
abstract = {Theoretical Derivation of Darcy's Law. Darcy's law for anisotropic
porous media is derived from the Navier-Stokes equation by using
a formal averaging procedure. Particular emphasis is placed upon
the proof that the permeability tensor is symmetric. In addition,
it is shown that there is a one-to-one relationship between the local
and macroscopic velocity fields. This leads to the interesting phenomenological
observation that the local velocity vector at any given point must
always lie either on a fixed line or in a fixed plane. All of this
holds true for an incompressible homogeneous Newtonian fluid moving
slowly through a rigid porous medium with uniform porosity under
isothermal and steady state conditions. The question whether Darcy's
law is applicable under nonsteady or compressible flow conditions,
or when the medium has nonuniform porosity, is also discussed. Finally,
it is shown that the Hagen-Poiseuille equation, as well as the expression
describing Couette flow between parallel plates, can be derived from
the equations presented in this work and may thus be viewed as special
cases of Darcy's law.},
file = {Neuman77.pdf:Neuman77.pdf:PDF},
keywords = {Darcy},
owner = {olivier},
timestamp = {2010.06.13}
}
@ARTICLE{Niemczynowicz91,
author = {Niemczynowicz, Janusz},
title = {On storm movement and its applications},
journal = {Atmospheric Research},
year = {1991},
volume = {27},
pages = {109--127},
abstract = {Rainfall-runoff models applicable for design and analysis of sewage
systems in urban areas are further developed in order to represent
better different physical processes going on an urban catchment.
However, one important part of the modelling procedure, the generation
of the rainfall input is still a weak point. The main problem is
lack of adequate rainfall data which represent temporal and spatial
variations of the natural rainfall process. Storm movement is a natural
phenomenon which influences urban runoff. However, the rainfall movement
and its influence on runoff generation process is not represented
in presently available urban runoff simulation models. Physical description
of the rainfall movement and its parameters is given based on detailed
measurements performed on twelve gauges in Lund, Sweden. The paper
discusses the significance of the rainfall movement on the runoff
generation process and gives suggestions how the rainfall movement
parameters may be used in runoff modelling},
file = {Niemczynowicz91.pdf:Niemczynowicz91.pdf:PDF},
owner = {olivier},
timestamp = {2010.05.03}
}
@ARTICLE{Noble06,
author = {Noble, Pascal},
title = {On the {S}pectral {S}tability of {R}oll-waves},
journal = {Indiana University Mathematics Journal},
year = {2006},
volume = {55},
pages = {795-848},
number = {2},
file = {Noble06.pdf:Noble06.pdf:PDF},
owner = {olivier},
timestamp = {2010.02.21}
}
@ARTICLE{Noble04,
author = {Noble, Pascal},
title = {Existence et stabilit\'e de roll-waves pour les \'equations de Saint-Venant},
journal = {C. R. Acad. Sci. Paris, Ser. I},
year = {2004},
volume = {338},
pages = {819-824},
abstract = {Existance and stability of roll-waves for the Saint Venant equations.
Roll-waves are entropic travelling waves of the Saint Venant system
with a source term. In this Note, we study two connected problems:
on the one hand the existence of roll-waves in a channel with a periodic
bottom, on the other hand the linear stability of roll-waves over
a ﬂat bottom. The main issue is due to the presence of an inﬁnite
number of shocks. With the help of a suitable change of variables,
we can restrict our attention to C 1 functions on R \ {iL, i ∈ Z}.
Then we prove the existence of small amplitude roll-waves with wavespeeds
oscillating around an average velocity in a channel with a periodic
bottom. For channels with a ﬂat bottom, we show the linear stability
of roll-waves when the slope is small enough.},
file = {Noble04.pdf:Noble04.pdf:PDF},
owner = {olivier},
timestamp = {2010.01.26}
}
@ARTICLE{Noelle06,
author = {Noelle, Sebastian and Pankratz, Normann and Puppo, Gabriella and
Natvig, Jostein~R.},
title = {Well-balanced finite volume schemes of arbitrary order of accuracy
for shallow water flows},
journal = {Journal of Computational Physics},
year = {2006},
volume = {213},
pages = {474 - 499},
number = {2},
abstract = {Many geophysical flows are merely perturbations of some fundamental
equilibrium state. If a numerical scheme shall capture such flows
efficiently, it should be able to preserve the unperturbed equilibrium
state at the discrete level. Here, we present a class of schemes
of any desired order of accuracy which preserve the lake at rest
perfectly. These schemes should have an impact for studying important
classes of lake and ocean flows.},
doi = {DOI: 10.1016/j.jcp.2005.08.019},
file = {Noelle06.pdf:Noelle06.pdf:PDF},
issn = {0021-9991},
keywords = {Hyperbolic conservation laws},
owner = {olivier},
timestamp = {2009.08.26},
url = {http://www.sciencedirect.com/science/article/B6WHY-4HB4DN4-1/2/15c5962d035c22b4fee10302b2606fa6}
}
@ARTICLE{Noelle07,
author = {Noelle, Sebastian and Xing, Yulong and Shu, Chi~-Wang},
title = {High-order well-balanced finite volume WENO schemes for shallow water
equation with moving water},
journal = {Journal of Computational Physics},
year = {2007},
volume = {226},
pages = {29 - 58},
number = {1},
abstract = {A characteristic feature of hyperbolic systems of balance laws is
the existence of non-trivial equilibrium solutions, where the effects
of convective fluxes and source terms cancel each other. Recently
a number of so-called well-balanced schemes were developed which
satisfy a discrete analogue of this balance and are therefore able
to maintain an equilibrium state. In most cases, applications treated
equilibria at rest, where the flow velocity vanishes. Here we present
a new very high-order accurate, exactly well-balanced finite volume
scheme for moving flow equilibria. Numerical experiments show excellent
resolution of unperturbed as well as slightly perturbed equilibria.},
doi = {DOI: 10.1016/j.jcp.2007.03.031},
file = {Noelle07.pdf:Noelle07.pdf:PDF},
issn = {0021-9991},
keywords = {Shallow water equation},
owner = {olivier},
timestamp = {2009.08.26},
url = {http://www.sciencedirect.com/science/article/B6WHY-4NG3TH4-3/2/546ff3d247ae9db8ed41e3de935ee892}
}
@ARTICLE{Norbiato08,
author = {Norbiato, Daniele and Borga, Marco},
title = {Analysis of hysteretic behaviour of a hillslope-storage kinematic
wave model for subsurface flow},
journal = {Advances in Water Resources},
year = {2008},
volume = {31},
pages = {118--131},
number = {1},
abstract = {The objective of this work is to analyse the storage-flux hysteretic
behaviour of a simplified model for subsurface flow processes. The
subsurface flow dynamics is analysed by means of a model based on
the kinematic wave assumptions and by using a width weighting/depth
averaging scheme which allows to map the three-dimensional soil mantle
into a one-dimensional profile. Continuity and a kinematic form of
Darcy's law lead to a hillslope-storage kinematic wave equation for
subsurface flow, solvable with the method of characteristics. Adopting
a second order polynomial function to describe the bedrock slope
and an exponential function to describe the variation of the width
of the hillslope with hillslope distance, we derive general solutions
to the hillslope-storage kinematic wave equations, applicable to
a wide range of hillslopes. These solutions provide a physical basis
for deriving two geometric parameters [alpha] and [psi] which define
the hydrological similarity between hillslopes with respect to their
characteristic response and hysteresis. The hysteresis [eta], quantified
by the area of the hysteretic dimensionless loop, has been therefore
computed for a range of values of parameters [alpha] and [psi]. Slopes
exhibit generally clockwise hysteretic loop in the flux-storage plot,
with higher groundwater mean volume for given discharge on rising
limb than at same discharge on falling limb. It has been found that
hysteresis increases with decreasing [alpha] and [psi], i.e. with
increasing convergence (for the shape) and concavity (for the profile),
and vice versa. For relatively large values of [alpha] and [psi]
the hysteresis may take a complex pattern, with combination of clockwise
to anticlockwise loop cycles. Application of the theory to three
hillslopes in the Eastern Italian Alps provides an opportunity to
examine how natural topographies are represented by the two hillslope
hydrological similarity parameters.},
doi = {DOI: 10.1016/j.advwatres.2007.07.001},
file = {Norbiato08.pdf:Norbiato08.pdf:PDF},
issn = {0309-1708},
keywords = {analytical solutions; Darcy},
owner = {olivier},
timestamp = {2010.06.15},
url = {http://www.sciencedirect.com/science/article/B6VCF-4PC3SMG-2/2/f4ca4fcc7effb9451ce266d8dfdb4fdd}
}
@PHDTHESIS{Nord06,
author = {Nord, Guillaume},
title = {Mod{\'e}lisation {\`a} base physique des processus de l'{\'e}rosion
hydrique {\`a} l'{\'e}chelle de la parcelle},
school = {Universit{\'e} Joseph Fourier -- Grenoble 1},
year = {2006},
month = {14 } # sep,
note = {326~pages},
abstract = {This study comes within the development of physically based models
of water erosion at the field scale. The objective is to build a
numerical model (PSEM_2D, Plot Soil Erosion Model) coupling the mechanisms
of infiltration, overland flow and erosion. The selected parameterizations
are first implemented in the model. A preliminary evaluation using
data of the literature gives acceptable results and highlights the
usefulness of such a tool for studying the transfer of water and
sediment. The study then focuses on the processes of rill erosion.
Data from an American database on particle-size distribution of exported
sediment, hydraulics and erosion regimes in rills are analysed. The
results reveal that different behaviours may be distinguished depending
on the soil texture. A comparison between the observed data and the
results of PSEM_2D is carried out. The transport capacity formulae
of Low (1989) and Govers (1992) give the best results. The detachment
model allows reproducing the erosion regimes but reaches its limits
when deep rills are forming. An experimental study in a 3 m long
flume is undertaken to improve the parameterization of the transport
of particles. Suspension and bed load transport are distinguished
based on the size and density of the particles. Finally, PSEM_2D
is used for a case study on water erosion. 192 simulations are run
over a 100 m2 plot for different conditions of rain, run-on, topography
and soil properties. The results are examined at the outlet of the
plot and within the plot divided in 5 zones along the slope length.},
file = {Nord06.pdf:Nord06.pdf:PDF},
keywords = {water erosion ; physically-based modelling ; plot scale ; rill erosion
; overland flow; particle-size distribution ; sediment transport
; laboratory experiment},
owner = {Fred. DARBOUX},
review = {Mod{\`e}le Saint-Venant avec infiltration et {\'e}rosion con{\c{c}}u
pour prendre en compte explicitement la micro-topographie},
timestamp = {2007.09.28}
}
@ARTICLE{Nord05,
author = {Nord, G. and Esteves, M.},
title = {{PSEM\_2D}: {A} physically based model of erosion processes at the
plot scale},
journal = wrr,
year = {2005},
volume = {41},
pages = {W08407},
number = {8},
month = aug,
abstract = {This paper presents the development and first applications of the
Plot Soil Erosion Model 2D (PSEM_2D). Infiltration is computed using
a Green and Ampt model, overland flow is computed using the depth-averaged
two-dimensional unsteady flow equations (Saint Venant equations),
and soil erosion is computed by combining the equation of mass conservation
of sediment and a detachment-transport coupling model for erosion
by runoff. A shear stress approach is used to determine the transport
capacity. The formation of a covering cohesionless layer as a result
of depositing sediment and action of rainfall impact before runoff
is considered. The erosion processes involved are rainfall and runoff
detachment of original soil, rainfall redetachment, and overland
flow entrainment of sediment from the deposited layer, and deposition.
The model uses a single representative particle size. Complex rainfall
events on natural slopes can be simulated. The accuracy of the predictions
for erosion of planar surfaces is tested by comparison with observed
data obtained from experiments and with an analytical solution. Good
agreement between the calculated results and measured data was found.
A sensitivity analysis was also performed. Limitations related to
the description of overland flow on plane soil surface are pointed
out. Finally, an application to a nonplanar natural surface of 75
m2 illustrated the distribution of erosion and sedimentation over
the plot.},
doi = {10.1029/2004WR003690},
file = {Nord05.pdf:Nord05.pdf:PDF},
keywords = {erosion; sedimentation; sediment transport; two-dimensional modeling;
physically based model; plot scale; mapmo},
owner = {Fred. DARBOUX},
review = {Modele d'�coulement avec topographie explicite},
timestamp = {2007.09.28}
}
@ARTICLE{Noussair00,
author = {Noussair, Ahmed},
title = {Analysis of nonlinear resonance in conservation laws with point sources
and well-balanced scheme},
journal = {Nonlinear Analysis},
year = {2000},
volume = {42},
pages = {1431--1464},
file = {Noussair00.pdf:Noussair00.pdf:PDF},
keywords = {conservation laws; resonance; Riemann problem; steady solutions},
owner = {olivier},
timestamp = {2011.02.24}
}
@ARTICLE{Novak00,
author = {Nov\'ak, V. and Simunek, J. and van Genuchten, M. Th.},
title = {Infiltration of {W}ater into {S}oil with {C}racks},
journal = {Journal of Irrigation and Drainage Engineering},
year = {2000},
volume = {126},
pages = {41--47},
number = {1},
abstract = {ABSTRACT: This paper presents the physical basis of the FRACTURE submodel
for simulating inﬁltration of precipitation/irrigation water into
relatively dry, cracked, ﬁne-textured soils. The FRACTURE submodel
forms part of the HYDRUS-ET variably saturated ﬂow/transport model.
Inﬁltration into the soil matrix is formally divided into two components:
(1) Vertical inﬁltration through the soil surface; and (2) lateral
inﬁltration via soil cracks. The ﬁrst component is described and
solved using the 1D Richards’ equation. Excess water that does not
inﬁltrate through the soil surface is either considered to be runoff,
if no soil cracks are present, or routed into soil cracks from where
it may laterally inﬁltrate into the soil matrix. Horizontal inﬁltration
from soil cracks into the soil matrix is calculated using the Green-Ampt
approach and incorporated as a positive source/sink term S f in the
Richards’ equation describing ﬂow in the matrix. In addition to the
hydraulic properties of the soil matrix, the FRACTURE submodel requires
parameters characterizing the soil cracks, notably the speciﬁc crack
length per surface area lc and the relationship between crack porosity
Pc and the gravimetric soil water content w. An example problem shows
that inﬁltration from soil cracks can be an important process affecting
the soil water regime of cracked soils. A comparison with the more
traditional approach, involving surface inﬁltration only, indicates
important differences in the soil water content distribution during
a rainfall/irrigation event. This extension of the classical approach
to include crack inﬁltration signiﬁcantly improves the identiﬁcation
and
prediction of the soil water regime.},
file = {Novak00.pdf:Novak00.pdf:PDF},
keywords = {infiltration; cracks; Richards; Green-Ampt},
owner = {olivier},
timestamp = {2010.04.24}
}
@ARTICLE{Novikov87,
author = {Novikov, E. A.},
title = {An analytical solution of the shallow water equations},
journal = {Physics Letters A},
year = {1987},
volume = {123},
pages = {287--288},
number = {6},
month = Aug,
abstract = {The general analytical solution of one-dimensional shallow water equations
is presented. The solution corresponds to the propagation of spherical
waves in four-dimensional space. The problem of two-dimensional rotating
shallow water is discussed.},
file = {Novikov87.pdf:Novikov87.pdf:PDF},
keywords = {analyrical solution},
owner = {olivier},
timestamp = {2011.02.24}
}
@ARTICLE{Nsom00,
author = {Nsom, Blaise and Debiane, Khaled and Piau, J.-M.},
title = {Bed slope effect on the dam break problem},
journal = {Journal of Hydraulic Research},
year = {2000},
volume = {38},
pages = {459--464},
number = {6},
abstract = {We consider the dam break problem upon an inclined plane. The flow
of a series of Newtonian fluids is generated by the collapse of a
dam in a completely transparent channel with variable slope. The
stage at given abscissa and the front wave evolution are accurately
investigated using ultrasonic and image analysis facilities, respectively.
While the Navier Stokes and the continuity equations are properly
rendered non dimensional in the viscous regime and solved with the
1D shallow water approximation. A successful comparison is shown
between the experimental and the theoretical results.},
file = {Nsom00.pdf:Nsom00.pdf:PDF},
keywords = {dam-break;},
owner = {Fred. DARBOUX},
timestamp = {2008.07.24}
}
@BOOK{Ockendon83,
title = {Inviscid Fluid Flows},
year = {1983},
editor = {Springer-Verlag, New York-Berlin-Heidelberg-Tokyo (Applied Mathematical
Sciences)},
author = {Ockendon, Hilary and Tayler, Alan B.},
owner = {olivier},
timestamp = {2011.03.15}
}
@ARTICLE{Ogawa92,
author = {Ogawa, Shigeru and Kishi, Yosuke and Yamada, Ayumi},
title = {Studies on the infiltration-discharge of rain water and translation
phenomena in soil},
journal = {Journal of Hydrology},
year = {1992},
volume = {132},
pages = {1--23},
abstract = {Infiltration and discharge of rain water and water movement in soil
were investigated by a numerical analysis based on a one-dimensional
infiltration model. A simple approximate formula for the piezometric
head and water content distribution in soil in a steady state was
obtained. Computational results in unsteady state indicated that
the vertical downward speed of the wetting front is generally much
larger than that of a tracer, which is assumed to be injected together
with the rain water at the soil surface. Theoretical considerations
were then developed to relate the movement ~)f the wetting front
and that of the tracer front to water movement in soil. Finally,
numerical analyses were performed for various precipitation intensities,
under various initial soil moisture conditions and with various soil
properties. The speed of the wetting front approaches that of the
tracer as the precipitation intensity increases, as the initial soil
moisture decreases, and the grain size increases.},
file = {Ogawa92.pdf:Ogawa92.pdf:PDF},
keywords = {infiltration; tracer; Richards},
owner = {olivier},
timestamp = {2010.06.13}
}
@ARTICLE{Olufsen99,
author = {Olufsen, Mette~S.},
title = {Structured tree outflow condition for blood flow in larger systemic
arteries},
journal = {American Journal of Physiology -- Heart and Circulatory Physiology},
year = {1999},
volume = {276},
pages = {257--268},
abstract = {Structured tree outflow condition for blood flow in larger systemic
arteries. Am. J. Physiol. 276 (Heart Circ. Physiol 45): 257–268,
1999.—A central problem in modeling blood flow and pressure in the
larger systemic arteries is determining a physiologically based boundary
condition so that the arterial tree can be truncated after a few
generations. We have used a structured tree attached to the terminal
branches of the truncated arterial tree in which the root impedance
is estimated using a semianalytical approach based on a linearization
of the viscous axisymmetric Navier-Stokes equations. This provides
a dynamic boundary condition that maintains the phase lag between
blood flow and pressure as well as the high-frequency oscillations
present in the impedance spectra. Furthermore, it accommodates the
wave propagation effects for the entire systemic arterial tree. The
result is a model that is physiologically adequate as well as computationally
feasible. For validation, we have compared the structured tree model
with a pure resistance and a windkessel model as well as with measured
data.},
file = {Olufsen99.pdf:Olufsen99.pdf:PDF},
keywords = {arterial modeling; mathematical modeling; arterial outflow boundary
condition; blood flow},
owner = {olivier},
timestamp = {2010.11.26}
}
@ARTICLE{Olufsen00,
author = {Olufsen, Mette~S. and Peskin, Charles~S. and Kim, Won~Yong and Pedersen,
Erik~M. and Nadim, Ali and Larsen, Jesper},
title = {Numerical Simulation and Experimental Validation of Blood Flow in
Arteries with Structured-Tree Outflow Conditions},
journal = {Annals of Biomedical Engineering},
year = {2000},
volume = {28},
pages = {1281--1299},
abstract = {Blood flow in the large systemic arteries is modeled using one-dimensional
equations derived from the axisymmetric Navier–Stokes equations for
flow in compliant and tapering vessels. The arterial tree is truncated
after the first few generations of large arteries with the remaining
small arteries and arterioles providing outflow boundary conditions
for the large arteries. By modeling the small arteries and arterioles
as a structured tree, a semi-analytical approach based on a linearized
version of the governing equations can be used to derive an expression
for the root impedance of the structured tree in the frequency domain.
In the time domain, this provides the proper outflow boundary condition.
The structured tree is a binary asymmetric tree in which the radii
of the daughter vessels are scaled linearly with the radius of the
parent vessel. Blood flow and pressure in the large vessels are computed
as functions of time and axial distance within each of the arteries.
Comparison between the simulations and magnetic resonance measurements
in the ascending aorta and nine peripheral locations in one individual
shows excellent agreement between the two.},
file = {Olufsen00.pdf:Olufsen00.pdf:PDF},
keywords = {arterial blood flow; arterial modeling; blood flow modeling; arterial
outflow conditions; biofluid dynamics; mathematical modeling},
owner = {olivier},
timestamp = {2010.11.26}
}
@ARTICLE{Paglieri97,
author = {Paglieri, L. and Ambrosi, D. and Formaggia, L. and Quarteroni, A.
and Scheinine, A.~L.},
title = {Parallel computation for shallow water flow: A domain decomposition
approach},
journal = {Parallel Computing},
year = {1997},
volume = {23},
pages = {1261--1277},
abstract = {This paper describes a strategy for the parallelization of a finite
element code for the numerical simulation of shallow water flow.
The numerical scheme adopted for the discretization of the equations
in the scalar algorithm is briefly described, with emphasis on the
aspects concerning its porting to a parallel architecture. The parallelization
strategy is of the domain decomposition type: the implicit computational
kernel of the scheme, a Poisson problem, is solved by an additive
Schwarz preconditioning technique within conjugate gradient iterations.
Both the theoretical and the implementation aspects of the domain
decomposition method are described as applied in the present context.
Finally, some computational examples are shown and discussed.},
file = {Paglieri97.pdf:Paglieri97.pdf:PDF},
keywords = {shallow water; finite elements; parallelization; domain decomposition;
additive Schwarz preconditioning; Manning},
owner = {olivier},
timestamp = {2010.11.24}
}
@ARTICLE{Palla09,
author = {Palla, A. and Gnecco, I. and Lanza, L.G.},
title = {Unsaturated 2D modelling of subsurface water flow in the coarse-grained
porous matrix of a green roof},
journal = {Journal of Hydrology},
year = {2009},
volume = {379},
pages = {193--204},
number = {1-2},
abstract = {Summary The analysis of the interactions between hydrologic processes
and green roof installations in the urban environment requires to
improve the understanding of the unsaturated water flow in the coarse-grained
porous media usually employed in such technological solutions. In
order to base our research on experimental evidences, a monitoring
program was carried out at the green roof experimental site of the
University of Genoa (Italy). A continuous acquisition system is available
at the experimental site for rainfall intensity and subsurface water
flow measurements at 1 min resolution. Soil water content is also
measured at the same resolution in time by four TDR probes located
along a vertical profile. The SWMS_2D model, based on Richards' law
and the Van Genuchten-Mualem functions, is here applied to simulate
the variably saturated flow within the green roof system. The model
was calibrated and validated using rainfall-runoff events observed
at the experimental site. The calibration and validation strategy
involved comparing predicted and measured outflow hydrographs. The
model adequately reproduces the hydrographs, as demonstrated by the
limited relative percentage deviations obtained for the total discharged
volume, the peak flow and the hydrograph centroid. Furthermore the
predicted water content closely matches the observed one at various
depths along the vertical profile where measurements are available,
thus confirming that the model correctly describes the variably saturated
flow field within the green roof. The mechanistic model, based on
a single porosity approach, here employed to describe the variably
saturated flow within the thin stratigraphy, is demonstrated to suitably
describe the hydrologic performance of a green roof, which is typically
realized with high hydraulic conductivity and coarse-grained porous
media.},
doi = {DOI: 10.1016/j.jhydrol.2009.10.008},
file = {Palla09.pdf:Palla09.pdf:PDF},
issn = {0022-1694},
keywords = {Infiltration; Variably saturated flow; Hydrologic restoration; Coarse
porous media; Green roof; Storm water; Richards; Van Genuchten},
owner = {olivier},
timestamp = {2010.06.18},
url = {http://www.sciencedirect.com/science/article/B6V6C-4XF8413-5/2/ab10caa05bfcc448ca40607c54cd0d8f}
}
@ARTICLE{Pan06,
author = {Pan, C. and Shangguan, Z.},
title = {Runoff hydraulic characteristics and sediment generation in sloped
grassplots under simulated rainfall conditions},
journal = {Journal of Hydrology},
year = {2006},
volume = {331},
pages = {178--185},
abstract = {Summary Evaluation of grass influence on soil erosion process can
provide important information in soil and water conservation. The
laboratory experiment was conducted to study runoff and sediment
producing processes and runoff hydraulics in the grassplots with
different covers (35%, 45%, 65% and 90%) and bare soil plot (control)
at a slope of 15 degrees. The results showed that grass significantly
reduced runoff and sediment. Compared with bare soil plot, the grassplots
had a 14-25% less runoff and an 81-95% less sediment, and played
a more important role in reducing sediment at the final stage of
rainfall. There was a significantly negative logarithmic relationship
between sediment yield rate (SDR) and cover (C): SDR = 1.077-2.911
ln(C) (R2 = 0.999**). Sediment yield rate of grassplots decreased
with rainfall duration, and decreased linearly as runoff rate increased.
Overland flow velocities deceased with increase in grass cover, and
the cover had greater effect on lower slope velocity than upper one.
Froude numbers decreased with increase in cover, and flow regimes
of all treatments were laminar and tranquil. Darcy-Weisbach and Manning
friction coefficients of grassplots increased as ground cover increased.
Therefore, increase in grass coverage can efficiently reduce soil
loss and improve ecological environments.},
doi = {10.1016/j.jhydrol.2006.05.011},
file = {Pan06.pdf:Pan06.pdf:PDF},
keywords = {grass cover; runoff; sediment; hydraulic characteristics; simulated
rainfall},
owner = {olivier},
timestamp = {2008.05.04}
}
@ARTICLE{Panday04,
author = {Panday, Sorab and Huyakorn, Peter S.},
title = {fully coupled physically-based spatially-distributed model for evaluating
surface/subsurface flow},
journal = {Advances in Water Resources},
year = {2004},
volume = {27},
pages = {361--382},
abstract = {A physically-based, spatially-distributed model is presented for simulation
of surface/subsurface ﬂow and the interactions between these domains.
The model is designed for practical application to a wide variety
of hydrologic evaluations, at various scales of simulation. The system
is represented by the three-dimensional saturated–unsaturated ﬂow
equation for the subsurface, coupled with the diﬀusion wave equation
for areal overland ﬂow, both of which are coupled with the diﬀusion
wave equation for ﬂow through a network of streams and channels,
including hydraulic structures. Ground surface unevenness at the
grid scale is incorporated via the concept of detention storage,
and thick vegetation or urban features are included via an obstruction
storage exclusion term. Evapotranspiration from the surface and subsurface
are modeled using land cover and climatic factors to deﬁne the complete
water budget using a physically-based formulation. The system of
equations is discretized using a fully implicit procedure, with the
Newton–Raphson method to handle non-linearities eﬃciently. Robustness,
stability and accuracy of solution are obtained for a wide variety
of cases including dry systems and large surface/subsurface interaction
ﬂuxes. Adaptive time-stepping schemes and under-relaxation formulas
further alleviate the computational burden. Veriﬁcation and application
examples demonstrate the need for a rigorous, fully-coupled solution
to the set of equations, for complete hydrologic-cycle analysis.},
file = {Panday04.pdf:Panday04.pdf:PDF},
keywords = {Richards; diffusion wave; friction; rain; interception; evapotranspiration},
owner = {olivier},
timestamp = {2010.06.14}
}
@ARTICLE{Panday93,
author = {Panday, Sorab and Huyakorn, Peter S. and Therrien, Ren\'e and Nichols,
Ralph L.},
title = {Improved three-dimensional finite-element techniques for field simulation
of variably saturated flow and transport},
journal = {Journal of Contaminant Hydrology},
year = {1993},
volume = {12},
pages = {3--33},
abstract = {Accurate three-dimensional simulations of saturated-unsaturated groundwater
flow and contaminant transport in highly heterogeneous subsurface
media require extreme agility in the numerical techniques of solution.
The primary limitations of simulating large-scale complex field problems
are the available computing power, and the considerable data management
effort required to calibrate, validate and perform sensitivity analyses
to these systems. An efficient finite-element model is presented
which overcomes many of the challenges encountered in solving complex
problems. The Galerkin and upstream weighted residual procedures
are employed for solving the flow and transport equations. Options
for using chord-slope Newton-Raphson linearization and upstream weighting
of the relative permeabilities are necessary for highly nonlinear
flow problems. Computational savings are otherwise achieved using
the less robust Picard scheme. Underrelaxation formulas further alleviate
convergence difficulties in the solution of the nonlinear equations.
Hexahedral orthogonai curvilinear elements are used to accurately
and efficiently discretize domains with irregular formation geometry,
and transition elements are employed to grade the finite-element
mesh for finer discretization only in regions of high gradients.
Element matrices are generated using influence coefficient formulas,
thus avoiding costly numerical integration. The 7-, 11- and 27-point
lattice connectivity structures are provided as options that increase
the accuracy of solution, or enhance computational speed and storage
requirements. Galerkin and upstream weighting schemes alleviate stability
problems in solving the transport equations without excessive smearing
of concentrations. Preconditioned conjugate gradient (PCG) and ORTHOMIN
techniques are used to solve the large symmetric and asymmetric matrix
equations arising from the assembly of the elemental flow and transport
equations, respectively, and repeated matrix assembly and decomposition
are eliminated from the calculations, if the situation permits. Assembly
of the entire model is discussed, with reference to previously published
works for details of schemes already tested and implemented. Only
further developments of the schemes are detailed herein. Application
of the model is demonstrated by selected simulation examples involving
assessment of moisture movement and contaminant migration from a
shallow waste disposal design above a multilayer unconfined aquifer
system.},
file = {Panday93.pdf:Panday93.pdf:PDF},
keywords = {Richards; solute transport},
owner = {olivier},
timestamp = {2010.06.14}
}
@PHDTHESIS{Pankratz07,
author = {Pankratz, Normann},
title = {High-order well-balanced finite-volume schemes for geophysical flows.
Development and numerical comparisons.},
year = {2007},
abstract = {In this thesis we have developed a general class of high resolution
shock capturing and stable well-balanced schemes for shallow water
ﬂows. Moreover, we showed that the schemes are also applicable to
complex oceanographic ﬂows,as a prototype example.
The ﬁnite-volume scheme is much more expensive with respect to computer
time than the traditional ﬁnite-diﬀerence scheme, but one beneﬁts
from a lot higher accuracy. To obtain a similar accuracy for smooth
ﬂows with the ﬁnite-diﬀerence scheme one would have to reﬁne the
grid several times. For non-smooth ﬂows, the ﬁnite volume scheme
is accurate and robust, while the ﬁnite diﬀerence scheme develops
dispersive oscillations which need to be damped by artiﬁcial viscosity.
This may, for example, make the ﬁnite-volume scheme attractive for
studies of high frequency oscillations associated with strong current
shears or small scale bathymetric features on the shelf edge. The
high accuracy and robustness of the developed ﬁnite volume schemes
as well as the growing international interest in oceanographic and
other geophysical ﬂows strongly motivates to continue the development
of the schemes and deepen the collaboration with geophysicists.
Key items for future research are
• reducing the computational cost signiﬁcantly, while maintaining
a com-
parable accuracy
• analysing the stability of the new inﬂow boundary condition
• extending the scheme to more complex applications, including bottom
friction, turbulence modeling, wet/dry fronts and multi-layer shallow
water},
file = {Pankratz07.pdf:Pankratz07.pdf:PDF},
owner = {olivier},
timestamp = {2009.07.19}
}
@ARTICLE{Pappenberger04,
author = {Pappenberger, Florian and Beven, Keith J.},
title = {Functional classification and evaluation of hydrographs based on
{M}ulticomponent {M}apping (M^x)},
journal = {Int. J. River Basin Management},
year = {2004},
volume = {2},
pages = {89-100},
number = {2},
abstract = {The literature offers a wealth of different performance measures to
evaluate model results. However, visual graphical evaluation based
on the simple plotting of two curves is still the most intuitive
and favoured approach by many modellers. This paper introduces a
performance measure, which is based on this method (the Multicomponent
Mapping (M^x )). The hydrograph is subdivided into box areas to which
membership values according to the distance to the hydrograph are
assigned. The box size is inﬂuenced by the expected effective observation
error structure. It is demonstrated that this method can be used
not only to calculate a quantitative performance measure but also
to classify hydrograph outputs of Monte Carlo runs into functional
classes in order to enable, for example, the cascading of uncertainties
in large modelling systems. A comparison to traditional measures
like the Nash-Sutcliffe and the Cumulative Absolute Error is performed.},
file = {Pappenberger04.pdf:Pappenberger04.pdf:PDF},
keywords = {uncertainty; model calibration; hydrograph evaluation; Nash-Sutcliffe;
cluster analysis},
owner = {olivier},
timestamp = {2010.02.06}
}
@PHDTHESIS{Paquier95,
author = {Paquier, Andr\'e},
title = {Mod\'elisation et simulation de la propagation de l'onde de rupture
de barrage},
school = {Universit\'e Jean Monnet},
year = {1995},
file = {Paquier95.pdf:Paquier95.pdf:PDF},
owner = {olivier},
timestamp = {2009.07.21}
}
@ARTICLE{Parker09,
author = {Parker, Kim H.},
title = {A brief history of arterial wave mechanics},
journal = {Med Biol Eng Comput},
year = {2009},
volume = {47},
pages = {111--118},
month = feb,
abstract = {The history of arterial wave mechanics is long and distinguished.
The arterial pulse was familiar to Chinese, Indian, Greek and Roman
physicians who exploited it regularly in the diagnosis of disease.
For more than 3,000 years, palpation of the radial pulse has been
a central observation in traditional Chinese medicine. One of the
ﬁrst and best known books devoted to analysis of the arterial pulse
is the Mai Jing or Pulse Classic which was written by Wang Shu-he
in the late Han dynasty (circa 220 AD) [49]. Pulse diagnosis in India
probably has a similar span although it is difﬁcult to know because
much of the teaching has been oral, directly from master to student,
rather than written. The traditional texts show a detailed knowledge
of the arterial pulse, but provide little insight into the mechanics
of the pulse, which is hardly surprising since they were developed
millennia before the discipline of mechanics was invented.
Galen (129–210 AD) wrote a book On Prognosis from the Pulse [16] in
which he describes 27 varieties of pulses and their meaning. He reports
experiments from which he concludes correctly that the arteries are
ﬁlled with blood, not air or spirits as others had asserted. He also
carried out experiments that convinced him that the pulsative property
of the heart extends from the heart by the walls of the arteries
and concluded wrongly that they are ﬁlled by ‘that pulsiﬁc force,
because they expand like bellows, and do not dilate because they
are ﬁlled like skins’. In other words, he felt that the arteries
expanded pulling blood into them rather than being expanded by the
blood entering from the heart.},
file = {Parker09.pdf:Parker09.pdf:PDF},
keywords = {blood flow},
owner = {olivier},
timestamp = {2011.03.15}
}
@ARTICLE{Parlange99,
author = {Parlange, J. -Y. and Hogarth, W. L. and Barry, D. A. and Parlange,
M. B. and Haverkamp, R. and Ross, P. J. and Steenhuis, T. S. and
DiCarlo, D. A. and Katul, G.},
title = {Analytical approximation to the solutions of Richards' equation with
applications to infiltration, ponding, and time compression approximation},
journal = {Advances in Water Resources},
year = {1999},
volume = {23},
pages = {189 - 194},
number = {2},
abstract = {A recent approach to solve Richards' equation is further improved.
This approach brings understanding into the physical processes of
infiltration and ponding. In particular we apply it to analyze the
standard hydrologic tool of Time Compression Approximation (TCA).
We also suggest that the new approach provides a more reliable alternative
to TCA, e.g. for predicting ponding time.},
doi = {DOI: 10.1016/S0309-1708(99)00022-6},
file = {Parlange99.pdf:Parlange99.pdf:PDF},
issn = {0309-1708},
keywords = {Infiltration; Ponding; Time compression approximation; Richards' equation},
owner = {olivier},
timestamp = {2010.06.04},
url = {http://www.sciencedirect.com/science/article/B6VCF-3XJKG52-9/2/fcb4d2ebaa0ee74a8b0a114d2584d4b2}
}
@ARTICLE{Parlange02,
author = {Parlange, J.-Y. and Barry, D.A. and Haverkamp, R.},
title = {Explicit infiltration equations and the Lambert W-function},
journal = {Advances in Water Resources},
year = {2002},
volume = {25},
pages = {1119 - 1124},
number = {8-12},
abstract = {The Green and Ampt infiltration formula, as well as the Talsma and
Parlange formula, are two-parameter equations that are both expressible
in terms of Lambert W-functions. These representations are used to
derive explicit, simple and accurate approximations for each case.
The two infiltration formulas are limiting cases that can be deduced
from an existing three-parameter infiltration equation, the third
parameter allowing for interpolation between the limiting cases.
Besides the limiting cases, there is another case for which the three-parameter
infiltration equation yields an exact solution. The three-parameter
equation can be solved by fixed-point iteration, a scheme which can
be exploited to obtain a sequence of increasingly complex explicit
infiltration equations. For routine use, a simple, explicit approximation
to the three-parameter infiltration equation is derived. This approximation
eliminates the need to iterate for most practical circumstances.},
doi = {DOI: 10.1016/S0309-1708(02)00051-9},
file = {Parlange02.pdf:Parlange02.pdf:PDF},
issn = {0309-1708},
keywords = {Lambert W, Green-Ampt},
owner = {olivier},
timestamp = {2010.06.04},
url = {http://www.sciencedirect.com/science/article/B6VCF-478RM4X-C/2/74dd25017c69e6d5e9a889bd11af5456}
}
@ARTICLE{Parlange97,
author = {Parlange, J.-Y. and Barry, D.A. and Parlange, M.B. and Hogarth, W.L.
and Haverkamp, R. and Ross, P. J. and Ling, L. and Steenhuis, T.
S.},
title = {New approximate analytical technique to solve Richards equation for
arbitrary surface boundary conditions},
journal = {Water Resources Research},
year = {1997},
volume = {33},
pages = {903--906},
number = {4},
abstract = {A general approximation for the solution to the one-dimensional Richards
equation is presented. It applies to arbitrary soil properties and
boundary conditions but only uniform initial conditions at current
stage. The result is very accurate (within 2%) when the diffusivity
is constant, suggesting that the present general formulation is reliable,
since the approximation becomes increasingly accurate as the soil-water
diffusivity approaches a delta function.},
file = {Parlange97.pdf:Parlange97.pdf:PDF},
keywords = {Richards; infiltration},
owner = {olivier},
timestamp = {2010.06.14}
}
@ARTICLE{Parlange90,
author = {Parlange, J.-Y. and Hogarth, W. and Sander, G. and Rose, C. and Haverkamp,
R. and Surin, A. and Brutsaert, W.},
title = {Asymptotic expansion for steady state overland flow},
journal = {Water Resources Research},
year = {1990},
volume = {26},
pages = {579--583},
number = {4},
month = apr,
abstract = {The full Saint Venant equations of overland flow on a plane are often
replaced by simpler models. The errors in the kinematic and the diffusion
models are estimated by comparing their predictions with the exact
numerical solution of the Saint Venant equations under steady state
conditions. It is shown that the two approximate models can have
significant errors even for critical flow and fairly large kinematic
wave numbers. When the kinematic approximation is inaccurate, the
improvement of the diffusion approximation seems modest. For the
same level of mathematical complexity as the diffusion approximation,
a far more accurate approximation is proposed when the kinematic
wave number is large. It is then possible to split the solution of
the Saint Venant equation in two regions, one near the downstream
end of the plane and the other covering most of the plane.},
file = {Parlange90.pdf:Parlange90.pdf:PDF},
owner = {olivier},
timestamp = {2008.04.30}
}
@ARTICLE{Paz11,
author = {Paz, Rodrigo R. and Storti, Mario A. and Garelli, Luciano},
title = {Local absorbent boundary condition for non-linear hyperbolic problems
with unknown Riemann invariants},
journal = {Computers \& Fluids},
year = {2011},
volume = {40},
pages = {52--67},
abstract = {Generally, in problems where the Riemann invariants (RI) are known
(e.g. the ﬂow in a shallow rectangular channel, the isentropic gas
ﬂow equations), the imposition of non-reﬂective boundary conditions
is straightforward. In problems where Riemann invariants are unknown
(e.g. the ﬂow in non-rectangular channels, the stratiﬁed 2D shallow
water ﬂows) it is possible to impose that kind of conditions analyzing
the projection of the Jacobians of advective ﬂux functions onto normal
directions of ﬁctitious surfaces or boundaries. In this paper a general
methodology for developing absorbing boundary conditions for non-linear
hyperbolic advective–diffusive equations with unknown Riemann invariants
is presented. The advantage of the method is that it is very easy
to implement in a ﬁnite element code and is based on computing the
advective ﬂux functions (and their Jacobian projections), and then,
imposing non-linear constraints via Lagrange multipliers. The application
of the dynamic absorbing boundary conditions to typical wave propagation
problems with unknown Riemann invariants, like non-linear Saint-Venant
system of conservation laws for non-rectangular and non-prismatic
1D channels and stratiﬁed 1D/2D shallow water equations, is presented.
Also, the new absorbent/dynamic condition can handle automatically
the change of Jacobians structure when the ﬂow regime changes from
subcritical to supercritical and viceversa, or when recirculating
zones are present in regions near ﬁctitious walls.},
doi = {10.1016/j.compfluid.2010.08.001},
file = {Paz11.pdf:Paz11.pdf:PDF},
keywords = {local absorbent boundary condition; Riemann invariants; hyperbolic
PDE's; shallow water},
owner = {olivier},
timestamp = {2011.02.24}
}
@ARTICLE{Pearson89,
author = {Pearson, C.~P.},
title = {One-dimensional flow over a plane: Criteria for kinematic wave modelling},
journal = {Journal of Hydrology and Earth System Sciences},
year = {1989},
volume = {111},
pages = {39--48},
abstract = {Criteria for using kinematic wave approximation to the Saint Venant
equatons for the shallow water flow are examined. Attention is focused
on the steady-state upstream depth, which, for the condition of zero
flow at the upstream boundary, is generally non-zero (proven mathematically)
but in the kinematic approximation is implicitly assumed to be zero.
Contours of dimensionless steady-state upstream depth over a two-parameter
plane are used to obtain a further criterion for kinematic wave modelling.
The new criterion is consistent with, and improves upon, the existing
criteria. Application of the criteria to catchment modelling is demonstrated
and discussed.},
file = {Pearson89.pdf:Pearson89.pdf:PDF},
keywords = {Saint-Venant; kinematic},
owner = {olivier},
timestamp = {2010.05.03}
}
@BOOK{Pedley80,
title = {The Fluid Mechanics of Large Blood Vessel},
year = {1980},
editor = {Cambridge University press},
author = {Pedley, T. J.},
owner = {olivier},
timestamp = {2011.03.15}
}
@ARTICLE{Pel02,
author = {Pel, L. and Landman, K.A. and Kaasschieter, E.F.},
title = {Analytic solution for the non-linear drying problem},
journal = {International Journal of Heat and Mass Transfer},
year = {2002},
volume = {45},
pages = {3173--3180},
abstract = {Recently, Landman, Pel and Kaasschieter proposed an analytic solution
for a non-linear drying problem using a quasi-steady state solution.
This analytic model for drying is explained here. An important consequence
of this model is that the drying front has a constant speed when
it is entering the material. This is also observed in experiments.
On the basis of this constant drying front speed comparisons are
made between the analytic model and numerical simulations. Finally
comparisons are made between measured moisture proﬁles during drying
and the analytic model.},
file = {Pel02.pdf:Pel02.pdf:PDF},
keywords = {Drying; Modelling; Porous media},
owner = {olivier},
timestamp = {2010.04.23}
}
@ARTICLE{Pelanti11,
author = {Pelanti, Marica and Bouchut, Fran\c{c}ois and Mangeney, Anne},
title = {A Riemann solver for single-phase and two-phase shallow flow models
based on relaxation. Relations with Roe and VRoe solvers},
journal = {Journal of Computational Physics},
year = {2011},
volume = {230},
pages = {515--550},
abstract = {We present a Riemann solver derived by a relaxation technique for
classical single-phase shallow ﬂow equations and for a two-phase
shallow ﬂow model describing a mixture of solid granular material
and ﬂuid. Our primary interest is the numerical approximation of
this two-phase solid/ﬂuid model, whose complexity poses numerical
difﬁculties that cannot be efﬁciently addressed by existing solvers.
In particular, we are concerned with ensuring a robust treatment
of dry bed states. The relaxation system used by the proposed solver
is formulated by introducing auxiliary variables that replace the
momenta in the spatial gradients of the original model systems. The
resulting relaxation solver is related to Roe solver in that its
Riemann solution for the ﬂow height and relaxation variables is formally
computed as Roe’s Riemann solution. The relaxation solver has the
advantage of a certain degree of freedom in the speciﬁcation of the
wave structure through the choice of the relaxation parameters. This
ﬂexibility can be exploited to handle robustly vacuum states, which
is a well known difﬁculty of standard Roe’s method, while maintaining
Roe’s low diffusivity. For the single-phase model positivity of ﬂow
height is rigorously preserved. For the two-phase model positivity
of volume fractions in general is not ensured, and a suitable restriction
on the CFL number might be needed. Nonetheless, numerical experiments
suggest that the proposed two-phase ﬂow solver efﬁciently models
wet/dry fronts and vacuum formation for a large range of ﬂow conditions.
As a corollary of our study, we show that for single-phase shallow
ﬂow equations the relaxation solver is formally equivalent to the
VFRoe solver with conservative variables of Gallouët and Masella
[T. Gallouët, J.-M. Masella, Un schéma de Godunov approché C.R. Acad.
Sci. Paris, Série I, 323 (1996) 77–84]. The relaxation interpretation
allows establishing positivity conditions for this VFRoe method.},
doi = {10.1016/j.jcp.2010.10.001},
file = {Pelanti11.pdf:Pelanti11.pdf:PDF},
keywords = {shallow flow models; two-phase granular flows; Riemann solvers; relaxation;
positivity; wet/dry fronts},
owner = {olivier},
timestamp = {2011.02.24}
}
@ARTICLE{Perrier02,
author = {Perrier, Edith and Garnier, Patricia and Leclerc, Christian},
title = {ECOUL: an interactive computer tool to study hydraulic behavior of
swelling and rigid soils},
journal = {Computers \& Geosciences},
year = {2002},
volume = {28},
pages = {1107 - 1118},
number = {9},
abstract = {ECOUL is an interactive, didactic software package which simulates
vertical water flow in unsaturated soils. End-users are given an
easily-used tool to predict the evolution of the soil water profile,
with a large range of possible boundary conditions, through a classical
numerical solution scheme for the Richards equation. Soils must be
characterized by water retention curves and hydraulic conductivity
curves, the form of which can be chosen among different analytical
expressions from the literature. When the parameters are unknown,
an inverse method is provided to estimate them from available experimental
flow data. A significant original feature of the software is to include
recent algorithms extending the water flow model to deal with deforming
porous media: widespread swelling soils, the volume of which varies
as a function of water content, must be described by a third hydraulic
characteristic property, the deformation curve. Again, estimation
of the parameters by means of inverse procedures and visualization
facilities enable exploration, understanding and then prediction
of soil hydraulic behavior under various experimental conditions.},
doi = {DOI: 10.1016/S0098-3004(02)00027-4},
file = {Perrier02.pdf:Perrier02.pdf:PDF},
issn = {0098-3004},
keywords = {Water flow modeling; Richards equation; deforming soils; unsatured
hydraulic properties; inverse method},
owner = {olivier},
timestamp = {2010.06.04},
url = {http://www.sciencedirect.com/science/article/B6V7D-46P9KN1-7/2/392b00caf5893e8ccffff24e6af0063b}
}
@ARTICLE{Perthame01,
author = {Perthame, B. and Simeoni, C.},
title = {A kinetic scheme for the Saint-Venant system with a source term},
journal = {Calcolo},
year = {2001},
volume = {38},
pages = {201--231},
note = {10.1007/s10092-001-8181-3},
abstract = {The aim of this paper is to present a numerical scheme to compute
Saint-Venant equations with a source term, due to the bottom topography,
in a one-dimensional framework, which satisfies the following theoretical
properties: it preserves the steady state of still water, satisfies
an entropy inequality, preserves the non-negativity of the height
of water and remains stable with a discontinuous bottom. This is
achieved by means of a kinetic approach to the system, which is the
departing point of the method developed here. In this context, we
use a natural description of the microscopic behavior of the system
to define numerical fluxes at the interfaces of an unstructured mesh.
We also use the concept of cell-centered conservative quantities
(as usual in the finite volume method) and upwind interfacial sources
as advocated by several authors. We show, analytically and also by
means of numerical results, that the above properties are satisfied.},
affiliation = {Département de Mathématiques et Applications, École Normale Supérieure,
45, rue d'Ulm, 75230 Paris Cedex 05, France¶e-mail: Benoit.Perthame@ens.fr;
Chiara.Simeoni@ens.fr FR},
file = {Perthame01.pdf:Perthame01.pdf:PDF},
issn = {0008-0624},
issue = {4},
keyword = {Mathematics and Statistics},
keywords = {Saint-Venant; shallow water; well-balanced; kinetic},
owner = {olivier},
publisher = {Springer Milan},
timestamp = {2011.03.10},
url = {http://dx.doi.org/10.1007/s10092-001-8181-3}
}
@ARTICLE{Peugeot97,
author = {Peugeot, C. and Esteves, M. and Galle, S. and Rajot, J.L. and Vandervaere,
J.P.},
title = {Runoff generation processes: results and analysis of field data collected
at the East Central Supersite of the HAPEX-Sahel experiment},
journal = {Journal of Hydrology},
year = {1997},
volume = {188--189},
pages = {179--202},
file = {Peugeot97.pdf:Peugeot97.pdf:PDF},
owner = {olivier},
timestamp = {2010.05.17}
}
@MISC{Peugeot07,
author = {Peugeot, J\'e\'emie},
title = {Mod{\'e}lisation de ruissellement le long d'une parcelle},
howpublished = {Rapport de stage de licence de Math{\'e}matiques Appliqu{\'e}es et
Industrielles. Universit{\'e} Joseph Fourier},
month = {@sep},
year = {2007},
note = {Encadrants : Michel Esteves et C{\'e}dric Legout},
file = {Peugeot07.pdf:Peugeot07.pdf:PDF},
keywords = {shallow flow equation; Saint-Venant; model; PSEM_2D; ridges and furrows;
oriented roughness; overland flow; model limits; ANR METHODE},
owner = {Fred. DARBOUX},
timestamp = {2008.08.11}
}
@ARTICLE{Philip57a,
author = {Philip, J. R.},
title = {The theory of infiltration: 1. The infiltration equation and its
solution},
journal = {Soil Science},
year = {1957},
volume = {83},
pages = {345--357},
file = {Philip57a.pdf:Philip57a.pdf:PDF},
keywords = {infiltration},
owner = {olivier},
timestamp = {2010.06.02}
}
@ARTICLE{Philip57b,
author = {Philip, J. R.},
title = {The theory of infiltration: 2. The profile of infinity},
journal = {Soil Science},
year = {1957},
volume = {83},
pages = {435--448},
file = {Philip57b.pdf:Philip57b.pdf:PDF},
keywords = {infiltration},
owner = {olivier},
timestamp = {2010.06.02}
}
@ARTICLE{Philip57c,
author = {Philip, J. R.},
title = {The theory of infiltration: 3. Moisture profiles and relation to
experiment},
journal = {Soil Science},
year = {1957},
volume = {84},
pages = {163--178},
file = {Philip57c.pdf:Philip57c.pdf:PDF},
keywords = {infiltration},
owner = {olivier},
timestamp = {2010.06.02}
}
@ARTICLE{Philip57d,
author = {Philip, J. R.},
title = {The theory of infiltration: 4. Sorptivity and algebraic infiltration
equation},
journal = {Soil Science},
year = {1957},
volume = {84},
pages = {257--264},
file = {Philip57d.pdf:Philip57d.pdf:PDF},
keywords = {infiltration},
owner = {olivier},
timestamp = {2010.06.02}
}
@ARTICLE{Philip57e,
author = {Philip, J. R.},
title = {The theory of infiltration: 5. The influence of the initial moisture
content},
journal = {Soil Science},
year = {1957},
volume = {84},
pages = {329--339},
file = {Philip57e.pdf:Philip57e.pdf:PDF},
owner = {olivier},
timestamp = {2010.06.02}
}
@ARTICLE{Philip57f,
author = {Philip, J. R.},
title = {The theory of infiltration: 6. Effect of water depth over soil},
journal = {Soil Science},
year = {1957},
volume = {85},
pages = {278--286},
file = {Philip57f.pdf:Philip57f.pdf:PDF},
keywords = {infiltration},
owner = {olivier},
timestamp = {2010.06.02}
}
@ARTICLE{Philip57g,
author = {Philip, J. R.},
title = {The theory of infiltration: 7.},
journal = {Soil Science},
year = {1957},
volume = {85},
pages = {333--337},
file = {Philip57g.pdf:Philip57g.pdf:PDF},
keywords = {infiltration},
owner = {olivier},
timestamp = {2010.06.02}
}
@ARTICLE{Pindera09,
author = {Pindera, Maciej Z. and Ding, Hui and Athavale, Mahesh M. and Chen,
Zhijian},
title = {Accuracy of 1D microvascular flow models in the limit of low Reynolds
numbers},
journal = {Microvascular Research},
year = {2009},
volume = {77},
pages = {273--280},
number = {3},
abstract = {We describe results of numerical simulations of steady flows in tubes
with branch bifurcations using fully 3D and reduced 1D geometries.
The intent is to delineate the range of validity of reduced models
used for simulations of flows in microcapillary networks, as a function
of the flow Reynolds number Re. Results from model problems indicate
that for Re less than 1 and possibly as high as 10, vasculatures
may be represented by strictly 1D Poiseuille flow geometries with
flow variation in the axial dimensions only. In that range flow rate
predictions in the different branches generated by 1D and 3D models
differ by a constant factor, independent of Re. When the cross-sectional
areas of the branches are constant these differences are generally
small and appear to stem from an uncertainty of how the individual
branch lengths are defined. This uncertainty can be accounted for
by a simple geometrical correction. For non-constant cross-sections
the differences can be much more significant. If additional corrections
for the presence of branch junctions and flow area variations are
not taken into account in 1D models of complex vasculatures, the
resultant flow predictions should be interpreted with caution.},
doi = {DOI: 10.1016/j.mvr.2008.11.006},
file = {Pindera09.pdf:Pindera09.pdf:PDF},
issn = {0026-2862},
keywords = {Vascular networks; Numerical modeling; Simulations; Reynolds number},
owner = {olivier},
timestamp = {2011.03.16},
url = {http://www.sciencedirect.com/science/article/B6WN8-4V59W3D-1/2/34024497531a550ed28ec3a5aeefc401}
}
@ARTICLE{Piperno98,
author = {Piperno, Serge and Depeyre, Sophie},
title = {Criteria for the design of limiters yielding efficient high resolution
TVD schemes},
journal = {Computers \& Fluids},
year = {1998},
volume = {27},
pages = {183--197},
number = {2},
abstract = {High resolution, finite-volume, conservative schemes, based on the
classical MUSCL (Monotonic Upwind Schemes for Conservation Laws)
construction and non-linear interpolation limiters are considered.
Possible criteria are established for the construction of the limiters,
yielding monotonic and efficient schemes. For scalar hyperbolic conservation
laws, new limiters for both upwind and centred numerical flux functions
are proposed and compared with existing limiters. These limiters
are also compared in the case of the computation of the two-dimensional
inviscid flow around a NACA0012 airfoil with particular attention
to the issues of iterative convergence to steady state and monotonicity
preservation of the computed solution. We actually show that the
proposed criteria do control these issues.},
file = {Piperno98.pdf:Piperno98.pdf:PDF},
keywords = {MUSCL; TVD; upwind schemes; Van Leer; Van Albada; Spekreijse; Koren},
owner = {olivier},
timestamp = {2010.06.13}
}
@ARTICLE{Planchon00,
author = {Planchon, Olivier and Esteves, Michel and Silvera, Norbert and Lapetite,
Jean-Marc},
title = {Raindrop erosion of tillage induced microrelief: possible use of
the diffusion equation},
journal = {Soil \& Tillage Research},
year = {2000},
volume = {56},
pages = {131--144},
abstract = {The purpose of this paper is to evaluate the possibility of using
the diffusion equation for raindrop erosion modelling. We wanted
in particular to know if such a model could provide accurate interpolations
of microrelief between two known dates. In a theoretical section,
we show that the assumption that soil particles follow parabolic
trajectories when splashed by raindrop impacts leads to a diffusion
equation. This equation suggests a linear relation between Dz, the
variation of height between two dates, and the Laplacian. This relation
is confirmed by data from a simulated rainfall experiment carried
out in the sandy soils of the Senegalese groundnut belt. Four square
plots of side 4 m each were used. They were hoed with a traditional
horse-drawn three-tined hoe. Three rains of 70 mm h-1 lasting 30
min each were applied. An automated relief meter designed and constructed
by the authors was used to measure the distribution of heights for
every 5 cm before the first rain, and after the first and the third
rains. The mean correlation coefficient of the model was 62% for
the first rain and 46% for the next two rains. Besides raindrop erosion,
compaction occurred during the first rain. Adding a crude description
of compaction enhanced the mean of the correlation coefficients of
the model up to 70% for the first rain. Furthermore, the coefficient
of variation of the four adjusted total diffusion lessens from 10
to 6%. The simulated surfaces were smoother than the real ones, which
was an expected result, but the surface storage capacity was overestimated.
The latter result illustrates the role of runoff in shaping the ¯ow
paths it follows and, consequently, in lessening the surface storage
capacity. The main conclusion is that the diffusion equation provides
a promising frame for further development of models simulating microrelief
evolution during rainfall. Another conclusion is that these models
should integrate existing routines for runoff erosion at small scale
in order to simulate surfaces with realistic hydraulic properties.},
file = {Planchon00.pdf:Planchon00.pdf:PDF},
keywords = {Rainfall simulation; microrelief; raindrop erosion; Senegal; RIDES;
splash},
owner = {olivier},
timestamp = {2010.06.11}
}
@ARTICLE{Planchon99,
author = {Planchon, Olivier and Esteves, Michel and Silvera, Norbert and Lapetite,
Jean-Marc and Cadet, Patrice},
title = {Les microreliefs g\'en\'er\'es par la culture attel\'ee dans le bassin
arachidier s\'en\'egalais : des formes utiles mais \'eph\'em\`eres},
journal = {Bulletin - R\'eseau Erosion},
year = {1999},
pages = {405--416},
number = {19},
abstract = {{L}'article met en {\'e}vidence et analyse les relations entre le
microrelief g{\'e}n{\'e}r{\'e} par le travail du sol et l'infiltration.
{L}es sols {\'e}tudi{\'e}s se trouvent au {S}ud du bassin arachidier
s{\'e}n{\'e}galais. {E}n surface, ils sont sableux {\`a} sables fins
et coh{\'e}sifs. {L}a culture, attel{\'e}e, g{\'e}n{\`e}re des microreliefs
d'une dizaine de centim{\`e}tres d'amplitude qui permettent (a) de
retenir {\`a} la surface du sol une lame d'eau de 7 mm en moyenne
et (b) un surcro{\^i}t d'infiltration de 6.7 mm en moyenne par rapport
{\`a} une surface lisse non travaill{\'e}e. {O}n montre pourtant
que ces microreliefs s'{\'e}rodent rapidement. {U}n mod{\`e}le simple
sugg{\`e}re que l'impact des gouttes de pluie est la principale cause
de cette {\'e}rosion. {L}es propri{\'e}t{\'e}s favorables pour l'infiltration
disparaissent aussi rapidement. {O}n montre {\'e}galement que, dans
les conditions les plus probables de pluie dans la r{\'e}gion, la
quasi-totalit{\'e} de l'infiltration se produit avant le d{\'e}but
du ruissellement. {M}aintenir les propri{\'e}t{\'e}s de r{\'e}tention
de la surface du sol repr{\'e}sente ainsi un enjeu tr{\`e}s important
et largement sous-estim{\'e} dans un contexte de pluies irr{\'e}guli{\`e}rement
espac{\'e}es dans le temps. {I}l est regrettable que, malgr{\'e}
leur grande simplicit{\'e} de mise en oeuvre, les techniques de sarclage
am{\'e}lior{\'e} n'aient pas re{\c{c}}u la diffusion qu'elles m{\'e}ritent.
({R}{\'e}sum{\'e} d'auteur)},
booktitle = {{L}'influence de l'homme sur l'{\'e}rosion : 1. {A} l'{\'e}chelle
du versant},
file = {Planchon99.pdf:Planchon99.pdf:PDF},
keywords = {Degradation du sol; erosion; pratique culturale; arachide; travail
du sol; microrelief; surface du sol; surface d'erosion; infiltration;
ruissellement; simulation de pluie; etude regionale; Senegal; RIDES},
language = {{FRE}},
numero = {19},
owner = {olivier},
timestamp = {2010.06.12},
url = {http://www.documentation.ird.fr/hor/fdi:010023899}
}
@ARTICLE{Planchon05,
author = {Planchon, Olivier and Silvera, Norbert and Gimenez, Raphael and Favis-Mortlock,
David and Wainwright, John and {Le Bissonnais}, Yves and Govers,
Gerard},
title = {An automated salt-tracing gauge for flow-velocity measurement},
journal = espl,
year = {2005},
volume = {30},
pages = {833--844},
number = {7},
abstract = {This article introduces the SVG (salt-velocity gauge), a novel automated
technique for measuring flow velocity by means of salt tracing. SVG
allows a high measuring rate (up to one every 2 seconds), short control
section length (down to 10 cm), high accuracy (+/-1.5 cm s-1), and
unbiased calculation of the mean velocity in experimental conditions
with turbulent, supercritical flow. A few cubic centimetres of saturated
salt solution (NaCl) are injected into the flow at regular time intervals
using a programmable solenoid valve. The tracer successively passes
two conductivity probes placed a short distance downstream. The transformation
of the signal between the two probes is modelled as a one-dimensional
diffusion wave equation. Model calibration gives an estimation of
the mean velocity and the diffusion for each salt plume. Two implementations
of the SVG technique are described. The first was an outdoors simulated
rainfall experiment in Senegal (conductivity probes at 40 cm apart,
8 Hz measurement rate, salt injections at 10 second intervals). Mean
velocity was estimated to range between 0.1 and 0.3 m s-1. The second
was a laboratory-based flume experiment (conductivity probes at 10
cm apart, 32 Hz, salt injections at 2 second intervals). Another
SVG with probes at 34 cm apart was used for comparison. An acoustic
Doppler velocimeter (ADV) was also used to give an independent assessment
of velocity. Using the 10 cm salt gauge, estimated mean velocity
ranged from 0.6 to 0.9 m s-1 with a standard deviation of 1.5 cm
s-1. Comparisons between ADV, 10 cm SVG and 34 cm SVG were consistent
and demonstrated that the salt-tracing results were unbiased and
independent of distance between probes. Most peaks were modelled
with r2 > 90 per cent. The SVG technology offers an alternative to
the dye-tracing technique, which has been severely criticized in
the literature because of the wide interval of recommended values
for the correction factor to be applied to the timings. This article
demonstrates that a fixed value of is inappropriate, since the correction
factor varies with velocity, diffusion and the length of the control
section.},
doi = {10.1002/esp.1194},
file = {Planchon05.pdf:Planchon05.pdf:PDF},
keywords = {hydrology; water; measure ; flow velocity; salt tracing},
owner = {Fred. DARBOUX},
review = {Appareil pour mesurer la vitesse des �coulements minces par tra�age
au sel et mesure de la conductivit� �lectrique},
timestamp = {2007.09.28}
}
@ARTICLE{Playan94a,
author = {Play\'an, E. and Walker, W.~R. and Merkley, G.~P.},
title = {Two-Dimensional Simulation of Basin Irrigation. I: Theory},
journal = {Journal of Irrigation and Drainage Engineering},
year = {1994},
volume = {120},
pages = {837-856},
number = {5},
abstract = {Overland flow of water over a porous bed in two spatial dimensions
is governed by three partial differential equations accounting for
continuity of momentum in the x- and y-directions and continuity
of mass. A leapfrog explicit finite-difference numerical scheme was
applied to solve this system of equations for the initial and boundary
conditions that characterize level-basin irrigation. The numerical
procedure is stable and robust for different applications, and can
accommodate three different inflow configurations: line, corner,
and fan. These configurations simulate inflow from an overflowing
canal on a field boundary and at point sources from a corner or in
the middle of a straight boundary, respectively. A numerical test
was performed to assess the effect of grid fineness on the results
of the simulation and on central-processing-unit time requirement.
Data from two field tests were used to validate the model in quasi-one-dimensional
and two-dimensional conditions.},
doi = {10.1061/(ASCE)0733-9437(1994)120:5(837)},
file = {Playan94a.pdf:Playan94a.pdf:PDF},
keywords = {Basins; Surface irrigation; Two-dimensional models; Hydrodynamics;
Finite differences},
owner = {olivier},
publisher = {ASCE},
timestamp = {2009.07.19},
url = {http://link.aip.org/link/?QIR/120/837/1}
}
@ARTICLE{Playan94b,
author = {Play\'an, E. and Walker, W.~R. and Merkley, G.~P.},
title = {Two-Dimensional Simulation of Basin Irrigation. II: Applications},
journal = {Journal of Irrigation and Drainage Engineering},
year = {1994},
volume = {120},
pages = {857-870},
number = {5},
abstract = {The development of a two-dimensional hydrodynamic simulation model
of basin irrigation is reported in a companion paper. This article
presents four applications of the model. Two hypothetical case studies
are used to illustrate the ability of the model to accommodate multiple
inflows and irregular field shapes including internal high spots.
The model is applied to study the effect of field shape on irrigation
performance. The particular case of a rectangular basin irrigated
from a corner is considered. Results show that one-dimensional models
can underestimate the time of advance by up to 20%. Finally, the
model is applied to explore the effects of spatially varied infiltration
on irrigation performance. A series of infiltration observation points
is used to estimate the infiltration rate in unmeasured locations.
The model is used to simulate a hypothetical case study involving
the design of a square level-basin irrigation field with spatially
varied infiltration irrigated from a corner. Results show that irrigation
performance changes dramatically with the location of the corner
inflow.},
doi = {10.1061/(ASCE)0733-9437(1994)120:5(857)},
file = {Playan94b.pdf:Playan94b.pdf:PDF},
keywords = {Basins; Surface irrigation; Hydrodynamics; Finite differences; Two-dimensional
models},
owner = {olivier},
publisher = {ASCE},
timestamp = {2009.07.19},
url = {http://link.aip.org/link/?QIR/120/857/1}
}
@ARTICLE{Plumerault10,
author = {Plumerault, L.-R. and Astruc, D. and Thual, O.},
title = {High-Reynolds shallow flow over an inclined sinusoidal bottom},
journal = {Physics of Fluids},
year = {2010},
volume = {22},
number = {054110},
abstract = {An experimental study of a turbulent free-surface shallow ﬂow over
an inclined sinusoidal bottom with a ﬁxed corrugation amplitude is
presented. A parametric analysis is performed by varying both the
inclination angle and the Reynolds number. We show that a “pulsewaves”
regime, dominant for Reynolds smaller than 4000, coexists with a
“roll-waves” regime, which becomes dominant above this value. The
relative energy of the waves is quantiﬁed in the parameter space.
At Reynolds numbers larger than 8000, these wave instabilities disappear.},
doi = {͓doi:10.1063/1.3407668},
file = {Plumerault10.pdf:Plumerault10.pdf:PDF},
keywords = {roll waves; periodic bottom},
owner = {olivier},
timestamp = {2010.07.01}
}
@BOOK{Ponce89,
title = {Engineering Hydrology: Principles and Practices},
publisher = {Prentice-Hall, Inc., Englewood Cliffs, New Jersey},
year = {1989},
editor = {Prentice-Hall, Inc., Englewood Cliffs, New Jersey},
author = {Ponce, Victor Miguel},
file = {Ponce89.pdf:Ponce89.pdf:PDF},
owner = {olivier},
timestamp = {2010.06.29}
}
@ARTICLE{Ponce92,
author = {Ponce, V. M.},
title = {Reply},
journal = {Water Resources Research},
year = {1992},
volume = {28},
pages = {1735},
number = {6},
month = Jun,
file = {Ponce92.pdf:Ponce92.pdf:PDF},
owner = {olivier},
timestamp = {2010.02.06}
}
@ARTICLE{Ponce91a,
author = {Ponce, Victor M.},
title = {The {K}inematic {W}ave {C}ontroversy},
journal = {Journal of Hydraulic Engineering},
year = {1991},
volume = {117},
pages = {511-525},
number = {4},
month = Apr,
file = {Ponce91a.pdf:Ponce91a.pdf:PDF},
owner = {olivier},
timestamp = {2010.02.06}
}
@ARTICLE{Ponce91b,
author = {Ponce, V. M.},
title = {New {P}erspective on the {V}edernikov {N}umber},
journal = {Water Resources Research},
year = {1991},
volume = {27},
pages = {1777-1779},
number = {7},
month = Jul,
file = {Ponce91b.pdf:Ponce91b.pdf:PDF},
owner = {olivier},
timestamp = {2010.02.06}
}
@INPROCEEDINGS{Ponce79,
author = {Ponce, V. M.},
title = {On the classification of open channel flow regimes},
booktitle = {Fourth National Hydrotechnical Conference, Vancouver, B.C., Canada},
year = {1979},
file = {Ponce79.pdf:Ponce79.pdf:PDF},
owner = {olivier},
timestamp = {2010.04.21}
}
@ARTICLE{Ponce97,
author = {Ponce, V.~M. and {Cordero-Bra{\~n}a}, O.~I. and Hasenin, S.~Y.},
title = {Generalized conceptual modeling of dimensionless overland flow hydrographs},
journal = {Journal of Hydrology},
year = {1997},
volume = {200},
pages = {222--227},
abstract = {The rising and recession limbs of conceptual dimensionless overland
flow hydrographs are calculated for specific values of the rating
exponent in the range 1 {\leq} m {\leq} 3, including a linear reservoir
(m = 1); 100% turbulent Chezy friction (m = 3/2); 100% turbulent
Manning friction (m = 5/3); 67% turbulent Chezy (or 75% turbulent
Manning) (m = 2); and 100% laminar flow (m = 3). These conceptual
overland flow hydrographs show finite amounts of diffusion, increasing
with decreasing rating exponent, unlike the kinematic wave hydrograph,
which is nondiffusive.},
file = {Ponce97.pdf:Ponce97.pdf:PDF},
keywords = {dimensionless; overland flow; hydrographs; conceptual modeling},
owner = {olivier},
timestamp = {2008.05.03}
}
@ARTICLE{Ponce99,
author = {Ponce, Victor M. and Klabunde, Amy C.},
title = {Parking {L}ot {S}torage {M}odeling {U}sing {D}iffusion {W}aves},
journal = {Journal of Hydrologic Engineering},
year = {1999},
volume = {4, Technical Note No. 15231},
pages = {371--376},
number = {4},
month = Oct,
abstract = {The feasibility of temporarily holding storm water in parking lots
is examined by using a diffusion wave model of catchment dynamics.
Four extreme storm types are applied to four typical parking lot
sizes to assess the sensitivity of the resulting storm hydrograph
to the choice of design slope. Results show the promise of parking
lot storage in urban storm water management.},
file = {Ponce99.pdf:Ponce99.pdf:PDF},
keywords = {diffusion wave; hydrograph},
owner = {olivier},
timestamp = {2010.04.22}
}
@ARTICLE{Ponce78,
author = {Ponce, Victor Miguel and Li, Ruh-Ming and Simons, Daryl B.},
title = {Applicability of {K}inematic and {D}iffusion {M}odels},
journal = {Journal of the {H}ydraulics {D}ivision, ASCE},
year = {1978},
volume = {No. HY3, Proc. Paper 13635},
pages = {353--360},
month = Mar,
file = {Ponce78.pdf:Ponce78.pdf:PDF},
owner = {olivier},
timestamp = {2010.04.21}
}
@ARTICLE{Ponce93,
author = {Ponce, Victor M. and Maisner, Michael P.},
title = {Verification of {T}heory of {R}oll-{W}ave {F}ormation},
journal = {Journal of Hydraulic Engineering},
year = {1993},
volume = {119},
pages = {768-773},
number = {6},
month = Jun,
file = {Ponce93.pdf:Ponce93.pdf:PDF},
owner = {olivier},
timestamp = {2010.02.08}
}
@MISC{Ponce97b,
author = {Ponce, V.~M. and Porras, P.~J.},
title = {Discussion to "Free-surface stability criterion as affected by velocity
distribution", by C.-L. Chen, Journal of Hydraulic Engineering, ASCE,
123(7), 666-667},
year = {1997},
file = {Ponce97b.pdf:Ponce97b.pdf:PDF},
keywords = {Vedernikov},
owner = {olivier},
timestamp = {2010.04.22}
}
@ARTICLE{Ponce77,
author = {Ponce, Victor~Miguel and Simons, Daryl~B.},
title = {Shallow {W}ave {P}ropagation in {O}pen {C}hannel {F}low},
journal = {Journal of the Hydraulics Division, ASCE},
year = {1977},
volume = {103, No. HY12, Proc. Paper 13392},
pages = {1461-1476},
month = Dec,
file = {Ponce77.pdf:Ponce77.pdf:PDF},
keywords = {Attenuation; canals; celerity; dynamic characteristics; kinematics;
propagation; rivers; water flow; waves},
owner = {olivier},
timestamp = {2010.04.21}
}
@ARTICLE{Pop10,
author = {Pop, I. S. and Sep\'ulveda, M. and Radu, F. A. and Vera Villagr\'an,
O. P.},
title = {Error estimates for the finite volume discretization for the porous
medium equation},
journal = {Journal of Computational and Applied Mathematics},
year = {2010},
volume = {234},
pages = {2135--2142},
abstract = {We analyze the convergence of a numerical scheme for a class of degenerate
parabolic problems modelling reactions in porous media, and involving
a nonlinear, possibly vanishing diffusion. The scheme involves the
Kirchhoff transformation of the regularized nonlinearity, as well
as an Euler implicit time stepping and triangle based finite volumes.
We prove the convergence of the approach by giving error estimates
in terms of the
discretization and regularization parameter.},
doi = {10.1016/j.cam.2009.08.071},
file = {Pop10.pdf:Pop10.pdf:PDF},
keywords = {degenerate parabolic equation; porous medium; finite volumes; error
estimates; Richards},
owner = {olivier},
timestamp = {2011.02.24}
}
@ARTICLE{Popinet11,
author = {Popinet, St\'ephane},
title = {Quadtree-adaptative tsunami modelling},
journal = {submitted},
abstract = {The well-balanced, positivity-preserving scheme of Audusse et al,
2004, for the solution of the Saint-Venant equations with wetting
and drying, is generalised to an adaptive quadtree spatial discretisation.
The scheme is validated using an analytical solution for the oscillation
of a ﬂuid in a parabolic container, as well as the classic Monai
tsunami laboratory benchmark. An eﬃcient database system able to
dynamically reconstruct a multiscale bathymetry based on extremely
large datasets is also described. This combination of methods is
sucessfully applied to the adaptive modelling of the 2004 Indian
ocean tsunami. Adaptivity is shown to signiﬁcantly decrease the exponent
of the power law describing computational cost as a function of spatial
resolution. The new exponent is directly related to the fractal dimension
of the geometrical structures characterising tsunami propagation.
The implementation of the method as well as the data and scripts
necessary to reproduce the results presented are freely available
as part of the open-source Gerris Flow Solver framework.},
file = {Popinet11.pdf:Popinet11.pdf:PDF},
keywords = {tsunami; hydrostatic reconstruction; shallow water},
owner = {olivier},
timestamp = {2011.03.16}
}
@ARTICLE{Pukhnachova97,
author = {Pukhnachova, T.~P.},
title = {Problem of determining the roughness factor for flow in an open channel},
journal = {Journal of Applied Mechanics and Technical Physics},
year = {1997},
volume = {38},
pages = {412--416},
number = {3},
file = {Pukhnachova97.pdf:Pukhnachova97.pdf:PDF},
owner = {olivier},
timestamp = {2008.05.03}
}
@MASTERSTHESIS{Que03,
author = {Que, Yin Tik},
title = {{BGK} {K}inetic {S}cheme for the {S}hallow-{W}ater {E}quations},
school = {{H}ong {K}ong {U}niversity of {S}cience \& {T}echnology},
year = {2003},
file = {Que03.pdf:Que03.pdf:PDF},
owner = {olivier},
timestamp = {2010.04.17}
}
@ARTICLE{Que06,
author = {Que, Y.-T. and Xu, Kun},
title = {The numerical study of roll-waves in inclined open channels and solitary
wave run-up},
journal = {International Journal for Numerical Methods in Fluids},
year = {2006},
volume = {50},
pages = {1003-1027},
abstract = {In this paper, we introduce a finite-volume kinetic BGK scheme and
its applications to the study of roll and solitary waves. The current
scheme is based on the numerical of the gas-kinetic Bhatnagar-Gross-Krook
model in the flux evaluation across each cell interface. An intrinsic
connection between the BGK model and time-dependent, non-linear,
non-homogeneous shallow water equations enables us to solve shallow-water
equations automatically with our kinetic scheme. The analytical solution,
experimental measurements, and numerical calculations for problems
associated with roll-waves down an inclined open channel and solitary
waves incident on a sloped beach are also presented.},
doi = {10.1002/fld.1102},
file = {Que06.pdf:Que06.pdf:PDF},
keywords = {gas-kinetic scheme; shallow water equations;roll wave; solitary wave},
owner = {olivier},
timestamp = {2009.08.02}
}
@ARTICLE{Raats01,
author = {Raats, Peter A. C.},
title = {Developments in soil-water physics since the mid 1960s},
journal = {Geoderma},
year = {2001},
volume = {100},
pages = {355 - 387},
number = {3-4},
abstract = {The theory for movement of water in unsaturated soils published by
Richards 70 years ago is still an important starting point for the
analysis of most soil physical problems. Over the last quarter century,
the interest in finding new solutions of the Richards equation by
either analytical or numerical methods was intense, particularly
with regard to field situations. Experimental methods became more
diverse and sophisticated: electromagnetic methods for measuring
water content and salinity are now reliable and widely available,
inverse methods for inferring the soil physical properties have matured.
But during this period, we see also a widening of the scope of soil
physics beyond the classical theory of Richards with further studies
of various multiphase aspects--particularly, simultaneous movement
of water and air, simultaneous transport of heat and moisture, flow
of water and transport of solutes in structured soils--, of water
movement in soils subject to swelling and shrinkage, and of transport
of solutes in unsaturated soils. The latter two subjects became manageable
by replacing the traditional spatial descriptions by material descriptions
in which, respectively, the solid phase serves as the reference continuum
for the water and the water serves as the reference continuum for
the solutes. Progress was driven not only by a healthy theoretical,
computational, and experimental basis, but also by productive interaction
with adjoining disciplines and by challenging societal problems.},
doi = {DOI: 10.1016/S0016-7061(01)00028-3},
file = {Raats01.pdf:Raats01.pdf:PDF},
issn = {0016-7061},
keywords = {Soil water; Soil physics; Analytical solutions; Physical characterization;
Field studies; Material coordinates; infiltration; Richards; transport},
owner = {olivier},
timestamp = {2010.06.03},
url = {http://www.sciencedirect.com/science/article/B6V67-43PR4DH-6/2/809b4fed35fef3d9eadfe3a941297d8f}
}
@ARTICLE{Rabbani97,
author = {Rabbani, M. Ghulam and Warner, James W.},
title = {A finite-element linked model for analysis of solute transport in
3-D space of multilayer subsurface systems},
journal = {Journal of Hydrology},
year = {1997},
volume = {199},
pages = {163--182},
number = {1-2},
abstract = {The computational burden and instability of the fully 3-D saturated-unsaturated
unified approach can be lessened considerably by using the linked
model of the quasi 3-D approach. This approach is applicable to a
multi-layer subsurface system consisting of aquifers and aquitards.
In this approach, 1-D vertical flow and solute transport is assumed
in the vadose zone and aquitards, and 2-D horizontal flow and quasi
3-D solute transport are assumed in the aquifers to simulate flow
and transport in 3-D space. In this paper, the aquifers are sliced
into sublayers. In a aquifer with 2-D flow, transport in the horizontal
direction is assumed to be caused by advection and dispersion while
transport in the vertical direction is assumed to be caused solely
by dispersion. As a mathematical simplicity, the equations for vertical
flow and transport in the vadose zone and confining layers and the
equations for flow and transport in the aquifer are solved separately
in two different solution packages. During this time-marching analysis,
the output in terms of source/sink obtained from one solution package
is coupled with the equations in the other solution package. This
linked model quasi 3-D approach was tested with other widely used
numerical models and analytical solutions, and was found stable and
technically robust.},
doi = {DOI: 10.1016/S0022-1694(96)03239-8},
file = {Rabbani97.pdf:Rabbani97.pdf:PDF},
issn = {0022-1694},
keywords = {Richard; transport},
owner = {olivier},
timestamp = {2010.06.15},
url = {http://www.sciencedirect.com/science/article/B6V6C-3SWM82P-S/2/583ec041e2bda1a5a5491b1295b54e6d}
}
@ARTICLE{Raff05,
author = {Raff, D.~A. and Ramirez, J.~ A.},
title = {A physical, mechanistic and fully coupled hillslope hydrology model},
journal = {International Journal for Numerical Methods in Fluids},
year = {2005},
volume = {49},
pages = {1193--1212},
doi = {10.1002/fld.1016},
file = {Raff05.pdf:Raff05.pdf:PDF},
keywords = {shallow water equations; Richards infiltration; erosion/sedimentation;
hillslope evolution},
owner = {olivier},
timestamp = {2008.05.05}
}
@BOOK{Davis01,
title = {C++ pour les {N}uls},
publisher = {First {I}nteractive},
year = {2001},
author = {Randy {D}avis, Stephen},
owner = {olivier},
timestamp = {2009.11.25}
}
@ARTICLE{Rawls82,
author = {Rawls, W.~J. and Brakensiek, D.~L. and Saxton, K.~E.},
title = {Estimation of Soil Water Properties},
journal = {TRANSACTIONS of the ASAE},
year = {1982},
volume = {25},
pages = {1316--1320 \& 1328},
number = {5},
file = {Rawls82.pdf:Rawls82.pdf:PDF},
keywords = {soil properties; Mein-Larson},
owner = {olivier},
timestamp = {2010.04.26}
}
@ARTICLE{Regalado05,
author = {Regalado, C.~M. and Ritter, A. and \'Alvarez-Bene\'i, J. and Mu\
noz-Carpena, R.},
title = {Simplified {M}ethod to {E}stimate the {G}reen-{A}mpt {W}etting {F}ront
{S}uction and {S}oil {S}orptivity with the {P}hilip-{D}unne {F}alling-{H}ead
{P}ermeameter},
journal = {Vadose Zone Journal},
year = {2005},
volume = {4},
pages = {291--299},
abstract = {Wetting front suction and soil sorptivity (S ) are relevant parameters
to water movement in the vadose zone. Both may be estimated with
the Philip–Dunne falling-head permeameter, given the moisture increment
(\Delta\theta) and measured times (tmed and tmax) during an infiltration
event. Previous studies have shown that the Philip–Dunne falling
head permeameter can be used for estimating saturated hydraulic conductivity
(Ks), but its potential to estimate the soil’s sorptivity has received
little attention. We investigate the ability of the Philip–Dunne
method to estimate S and the Green–Ampt’s suction at the wetting
front, \Psi, by performing a parameter sensitivity analysis, focusing
on the boundary conditions that limit the search space of physically
sound solutions, and studying the shape factors used in Philip’s
analysis to reduce the three-dimensional flux of water in the soil
to one dimension. Finally, a useful approximate solution is provided
that allows computing both Ks and the Green–Ampt’s suction at the
wetting front, \Psi, (and hence the macroscopic capillary length
parameter, \alpha*) from only two infiltration times, tmed and tmax,
without having to resort to such a costly measurement as the soil
moisture increment, \Delta\theta, required by the original method.},
file = {Regalado05.pdf:Regalado05.pdf:PDF},
keywords = {Green-Ampt;Philip-Dunne},
owner = {olivier},
timestamp = {2010.04.24}
}
@ARTICLE{RezaNajafi03,
author = {Reza Najafi, Mohammad},
title = {Watershed modeling of rainfall excess transformation into runoff},
journal = {Journal of Hydrology},
year = {2003},
volume = {270},
pages = {273--281},
abstract = {In this paper an attempt is made to present a distributed physiographic
conceptual model that uses the principles of ﬂow continuity and momentum.
For this purpose, the watershed under study is divided into subwatersheds
keeping in view the drainage patterns and characteristics. Then the
main tributaries are identiﬁed and their drainage areas are delineated
to form tributary subwatersheds. The main channel subwatersheds have
taken care of the remaining area in the vicinity of the main channel.
The kinematic wave theory is applied for the overland runoff computations
from these subwatersheds. Further, the overland ﬂows are superimposed
onto the main channel. The dynamic wave theory is used to route the
ﬂows through the main channel to compute the watershed responses
at the outlet. The proposed model is tested onto a natural watershed.
The computations were performed for few storm events. Comparison
of the signiﬁcant parameters of the computed and the observed hydrographs
shows that the maximum relative error in prediction is 5.8%. Thus,
the results are satisfactory. Better results can be obtained when
measured rainfall-excess data are available or a more realistic loss
index is adopted for rainfall-excess separation.},
file = {RezaNajafi03.pdf:RezaNajafi03.pdf:PDF},
keywords = {Watershed modeling; Conceptual model; Surface runoff; Flow routing;
Dynamic wave; Kinematic wave},
owner = {olivier},
timestamp = {2010.04.25}
}
@ARTICLE{Rhebergen08,
author = {Rhebergen, S. and Bokhove, O. and van der Vegt, J.J.W.},
title = {Discontinuous Galerkin finite element methods for hyperbolic nonconservative
partial differential equations},
journal = {Journal of Computational Physics},
year = {2008},
volume = {227},
pages = {1887--1922},
number = {3},
abstract = {We present space- and space-time discontinuous Galerkin finite element
(DGFEM) formulations for systems containing nonconservative products,
such as occur in dispersed multiphase flow equations. The main criterium
we pose on the weak formulation is that if the system of nonconservative
partial differential equations can be transformed into conservative
form, then the formulation must reduce to that for conservative systems.
Standard DGFEM formulations cannot be applied to nonconservative
systems of partial differential equations. We therefore introduce
the theory of weak solutions for nonconservative products into the
DGFEM formulation leading to the new question how to define the path
connecting left and right states across a discontinuity. The effect
of different paths on the numerical solution is investigated and
found to be small. We also introduce a new numerical flux that is
able to deal with nonconservative products. Our scheme is applied
to two different systems of partial differential equations. First,
we consider the shallow water equations, where topography leads to
nonconservative products, in which the known, possibly discontinuous,
topography is formally taken as an unknown in the system. Second,
we consider a simplification of a depth-averaged two-phase flow model
which contains more intrinsic nonconservative products.},
doi = {DOI: 10.1016/j.jcp.2007.10.007},
file = {Rhebergen08.pdf:Rhebergen08.pdf:PDF},
issn = {0021-9991},
keywords = {Nonconservative products; Discontinuous Galerkin finite element methods;
Numerical fluxes; Arbitrary Lagrangian Eulerian (ALE) formulation;
Two-phase flows; HLL; analyrical solution},
owner = {olivier},
timestamp = {2010.06.18},
url = {http://www.sciencedirect.com/science/article/B6WHY-4PXDM93-1/2/cb2a0c5b3fd704448ae181eda52a9fc4}
}
@ARTICLE{Ricchiuto10,
author = {Ricchiuto, M.},
title = {On the C-property and Generalized C-property of Residual Distribution
for the Shallow Water Equations},
journal = {J Sci Comput},
year = {2010},
volume = {DOI 10.1007/s10915-010-9369-y},
abstract = {In this paper we consider the discretization of the Shallow Water
equations by means of Residual Distribution (RD) schemes. We review
the conditions allowing the exact preservation of some exact steady
solutions. These conditions are shown to be related both to the type
of spatial approximation and to the quadrature used to evaluate the
cell residual. Numerical examples are shown to validate the theory.},
file = {Ricchiuto10.pdf:Ricchiuto10.pdf:PDF},
keywords = {residual distribution; shallow water; C-property; generalized C-property;
unstructured meshes},
owner = {olivier},
timestamp = {2010.06.20}
}
@ARTICLE{Richards31,
author = {Richards, L.~A.},
title = {Capillary conduction of liquids through porous mediums},
journal = {Physics},
year = {1931},
volume = {1},
pages = {318--333},
month = nov,
file = {Richards31.pdf:Richards31.pdf:PDF},
keywords = {Infiltration},
owner = {Fred. DARBOUX},
timestamp = {2006.08.17}
}
@ARTICLE{Richardson94,
author = {Richardson, J.~R. and Julien, P.~Y.},
title = {Suitability of simplified overland flow equations},
journal = {Water Resources Research},
year = {1994},
volume = {30},
pages = {665--671},
number = {3},
month = mar,
file = {Richardson94.pdf:Richardson94.pdf:PDF},
owner = {olivier},
timestamp = {2008.05.08}
}
@ARTICLE{Ritter92,
author = {Ritter, A.},
title = {Die fortpflanzung der wasserwellen},
journal = {Zeitschrift des Vereines deuscher Ingenieure},
year = {1892},
volume = {36(33)},
pages = {947--954},
file = {Ritter92.pdf:Ritter92.pdf:PDF},
keywords = {dam-break; analytical solution},
owner = {olivier},
timestamp = {2011.04.23}
}
@PHDTHESIS{Roche06,
author = {Roche, N.},
title = {Mod{\'e}lisation du ruissellement sur surfaces rugueuses},
school = {Universit{\'e} Joseph Fourier},
year = {2006},
abstract = {Dans l'\'etude du ruissellement et de l'{\'e}rosion {\`a} l'{\'e}chelle
des bassins versants, la r{\'e}sistance hydraulique {\`a} l'{\'e}coulement
d'une surface est {\'e}valu{\'e}e par l'interm{\'e}diaire d'un coefficient
de frottement. Nous avons {\`a} notre disposition de nombreuses expressions
de ces coefficients issues de tout aussi nombreuses {\'e}tudes exp{\'e}rimentales
ou th{\'e}oriques. Cependnat, la plupart de ces coefficients ont
{\'e}t{\'e} {\'e}tablis sous l'hypoth{\`e}se implicite de micro rugosit{\'e}.
C'est-{\`a}-dire que la lame d'eau est consid{\'e}r{\'e}e suffisamment
importante pour que l'influence des asp{\'e}rit{\'e}s de la surface
sur l'{\'e}coulement se borne {\`a} leur effet sur la friction. La
diversit{\'e} des tailles des rugosit{\'e}s sur les surfaces naturelles,
fait qu'une telle hypoth{\`e}se est rarement v{\'e}rifi{\'e}e. Dans
ce travail, nous proposons de consid{\'e}rer une s{\'e}quence de
r{\'e}seaux hydrauliques fonctions du degr{\'e} d'inondation de la
surface. En nous appuyant sur ces r\'eseaux, nous pr\'esentons des
mod{\`e}les hydrauliques afin de d{\'e}terminer le coefficient de
frottement de la surface en fonction du taux d'inondation. Les mod{\'e}lisateurs
ayant besoin d'associer un coefficient de frottement {\`a} un type
de surface, nous avons voulu g{\'e}n{\'e}raliser nos r{\'e}sultats
en appliquant notre d{\'e}marche {\`a} des surfaces al{\'e}atoires
de m{\^e}mes caract{\'e}ristiques statistiques que la surface originale.
Ce faisant, nous avons mis en {\'e}vidence l'influence de la r{\'e}partition
spatiale des rugosit{\'e}s. Si nous n'avons pas pu valider exp{\'e}rimentalement
notre mod{\`e}le num{\'e}rique en raison du peu de r{\'e}sultats
pour les faibles taux d'inondation, nous avons mis en{\'e}vidence
que la transition entre les r{\'e}gimes d'inondation partielle et
marginale se traduit par une brusque augmentation de la croissance
des d{\'e}bits.},
file = {Roche06.pdf:Roche06.pdf:PDF},
keywords = {mod{\'e}lisation hydrologique; variabilit{\'e} hydro-climatique; Afrique
de l'Ouest; analyses de sensibilit{\'e} et d'incertitudes; AMMA;
GR4J; TOPMODEL},
owner = {olivier},
timestamp = {2008.04.28}
}
@ARTICLE{Rosatti06,
author = {Rosatti, G. and Fraccarollo, L.},
title = {A well-balanced approach for flows over mobile-bed with high sediment-transport},
journal = {Journal of Computational Physics},
year = {2006},
volume = {220},
pages = {312--338},
abstract = {In this paper we deal with the numerical computation of one-dimensional,
unsteady, free-surface ﬂows over mobile-bed. We focus on ﬂows characterized
by high concentration of sediments and strong interaction between
ﬂow and bottom dynamics, as in hyper-concentrated- and debris-ﬂows.
These features are fully considered in the adopted system of equations.
Challenging in its numerical approximation is the preservation of
the coupling and the treatment of a non-conservative ﬂux in the momentum
equation. In order to devise a new Godunov-type approach, we analyzed
in detail the Riemann problem associated with the mobile-bed phenomena
and the peculiar features of its wave relations. The scheme we developed
is based on two supports: well-balanced treatment of the variable
updating at the new time-level and ﬂux evaluation by three-wave approximations
of the intercell Riemann-problem that, without any split, embody
the eﬀect of the non-conservative term. The properties of the new
numerical strategy (named AWB) are assessed by comparison with exact
solutions of Riemann problems, built by handling an inverse technique.
Finally, AWB has been applied to cases of practical interest, where
wave interaction and friction eﬀects makes the ﬂow more complex.
The obtained results point out that the new method is able to predict
faithfully the overall behaviour of the solution and of any type
of waves. The use of AWB, in this one-dimensional frame, is therefore
fostered in representing rapid transients in river/torrent ﬂows with
movable bed.},
doi = {10.1016/j.jcp.2006.05.012},
file = {Rosatti06.pdf:Rosatti06.pdf:PDF},
keywords = {well-balanced scheme; Riemann solvers; non-conservative term; mobile-bed
models; sediment transport},
owner = {olivier},
timestamp = {2011.02.24}
}
@ARTICLE{Rosatti08,
author = {Rosatti, G. and Murillo, J. and Fraccarollo, L.},
title = {Generalized Roe schemes for 1D two-phase, free-surface flows over
a mobile bed},
journal = {Journal of Computational Physics},
year = {2008},
volume = {227},
pages = {10058--10077},
abstract = {The problem of two-phase, free-surface ﬂows over a mobile bed is characterized
by a hyperbolic partial differential equations system that shows
nonconservative terms and highly nonlinear relations between primitive
and conserved variables. Weak solutions of the present problem were
obtained resorting both to the distribution theory and to the integral
formulation of momentum conservation: the comparison of these two
approaches allowed us to give a physical insight into the meaning
of the nonconservative term across a discontinuity. Starting from
this result, we derived the conditions necessary to obtain generalized,
well-balanced Roe solvers without using the concept of a family of
paths. Two numerical schemes based on the same set of matrices have
been developed, one in terms of conserved variables and one in terms
of primitive variables. The friction-source term has also been included
by using an upwind approach. The capabilities and limits of the proposed
schemes have been analyzed by comparison with exact solutions of
Riemann problems and with numerical solutions obtained with the AWB-3SRS
scheme.},
doi = {10.1016/j.jcp.2008.08.007},
file = {Rosatti08.pdf:Rosatti08.pdf:PDF},
keywords = {two-phase flows; free-surface; mobile bed; nonconservative product;
generalized Roe solvers; weak solutions; well-balanced approach},
owner = {olivier},
timestamp = {2011.02.24}
}
@ARTICLE{Rose83,
author = {Rose, C.W. and Parlange, J.-Y. and Sander, G.C. and Campbell, S.Y.
and Barry, D.A.},
title = {Kinematic flow approximation to runoff on a plane: An approximate
analytic solution},
journal = {Journal of Hydrology},
year = {1983},
volume = {62},
pages = {363 - 369},
number = {1-4},
abstract = {A new theory is given which relates excess rainfall to runoff for
overland flow on a plane. The theory assumes that rate of change
of water flux with distance down the plane is constant at any time,
but its variation with time is such that runoff from the plane is
exact. It follows that mass of water is conserved for the entire
runoff event, but not exactly at all times within the event. The
magnitude of the error in the solution due to this approximation
is investigated by comparison with the more complex exact theory.
If runoff from the plane is measured, the theory allows simple direct
estimation of excess rainfall as a function of time. Alternatively,
if rainfall and infiltration rates are known then runoff can be calculated.
This approximate theory and the exact theory are also compared by
using them to estimate infiltration rate into a small planar catchment
from measured rates of rainfall and runoff. The accuracy and great
simplicity of the approximate theory makes it useful in practice.},
doi = {DOI: 10.1016/0022-1694(83)90113-0},
file = {Rose83.pdf:Rose83.pdf:PDF},
issn = {0022-1694},
keywords = {hydrograph; rain; exact; kinematic},
owner = {olivier},
timestamp = {2010.06.05},
url = {http://www.sciencedirect.com/science/article/B6V6C-487D1M6-1P/2/95501427f5e473aaab3526f45089b6d2}
}
@ARTICLE{Rose07,
author = {Rose, C.W. and Yu, B. and Ghadiri, H. and Asadi, H. and Parlange,
J.Y. and Hogarth, W.L. and Hussein, J.},
title = {Dynamic erosion of soil in steady sheet flow},
journal = {Journal of Hydrology},
year = {2007},
volume = {333},
pages = {449--458},
abstract = {Summary An approximate analytic solution is given for the ﬁrst time
to previously published equations describing the characteristics
of dynamic soil erosion caused by overland ﬂow. The solution describes
both the variation in time in total sediment concentration since
the commencement of uniform overland ﬂow, and also the dynamic change
in the settling velocity characteristics (and size distribution)
of eroding sediment. Following calibration for each of the three
soils investigated in order to determine unknown but physically-deﬁned
model parameters, prediction based on this theory was found to provide
good agreement with experimental data. Under steady-state conditions
achieved at long time, the solution agrees with the exact solution
for transport limiting conditions, and provides a simple expression
for sediment concentration in other situations where soil strength
affects the sediment concentration ultimately achieved.},
file = {Rose07.pdf:Rose07.pdf:PDF},
keywords = {soil erosion; overland flow; dynamic erosion processes; dynamic theory;
settling velocity},
owner = {olivier},
timestamp = {2010.06.13}
}
@ARTICLE{Rouhipour99,
author = {Rouhipour, H. and Rose, C.~W. and Yu, B. and Ghadiri, H.},
title = {Roughness coefficients and velocity estimation in well-inundated
sheet and rilled overland flow without strongly eroding bed forms},
journal = espl,
year = {1999},
volume = {24},
pages = {233--245},
number = {3},
month = mar,
abstract = {Even with the flow of water over a soil surface in which roughness
elements are well inundated, and in less erosive situations where
erosional bed forms are not pronounced, the magnitude of resistance
coefficients in equations such as those of Darcy-Weisbach, Chezy
or Manning vary with flow velocity (at least). Using both original
laboratory and field data, and data from the literature, the paper
examines this question of the apparent variation of resistance coefficients
in relation to flow velocity, even in the absence of interaction
between hydraulics and resulting erosional bed forms. Resistance
equations are first assessed as to their ability to describe overland
flow velocity when tested against these data sources. The result
is that Manning's equation received stronger support than the Darcy-Weisbach
or Chezy equations, though all equations were useful. The second
question addressed is how best to estimate velocity of overland flow
from measurements of slope and unit discharge, recognizing that the
apparent flow velocity variation in resistance coefficients is probably
a result of shortcomings in all of the listed resistance equations.
A new methodology is illustrated which gives good agreement between
estimated and measured flow velocity for both well-inundated sheet
and rill flow. Comments are given on the predictive use of this methodology.},
file = {Rouhipour99.pdf:Rouhipour99.pdf:PDF},
keywords = {shallow flow hydraulics; roughness coefficients; flow velocity; Manning's
equation; Darcy-Weisbach; sheet flow; rill flow; HYDRAULICS; EROSION;
RESISTANCE}
}
@MASTERSTHESIS{Rousseau08,
author = {Rousseau, M.},
title = {Mod{\'e}lisation des {\'e}coulements {\`a} surface libre : {\'e}tude
du ruissellement des eaux de pluie.},
school = {Université de Nantes, disponible sur : http://dumas.ccsd.cnrs.fr/dumas-00494243/fr/},
year = {2008},
month = {septembre},
file = {Rousseau08.pdf:Rousseau08.pdf:PDF},
keywords = {Saint-Venant;well-balanced scheme;hydrostatic reconstruction;overland
flow;analytical solutions},
owner = {olivier},
timestamp = {2008.10.01}
}
@ARTICLE{Russo05,
author = {Russo, G.},
title = {Central schemes for conservation laws with application to shallow
water equations},
journal = {S. Rionero, G. Romano (Eds.), Trends and Applications of Mathematics
to Mechanics: STAMM 2002, Springer Verlag, Italia SRL},
year = {2005},
pages = {225--246},
file = {Russo05.pdf:Russo05.pdf:PDF},
keywords = {shallow water; well-balanced; central scheme},
owner = {olivier},
timestamp = {2010.06.27}
}
@ARTICLE{Rybakin09,
author = {Rybakin, Boris and Shider, Natalia},
title = {Computer modeling of multidimensional problems of gravitational gas
dynamics on multiprocessor computers},
journal = {Computer Science Journal of Moldova},
year = {2009},
volume = {17},
pages = {3--13},
number = {1(49)},
abstract = {This article deals with a method, based on total variation diminishing
(TVD) scheme, for solving three-dimensional equations of gravitational
gas dynamics. For this method a parallel algorithm of the decision
is oﬀered. Equations of this kind are a powerful approach to simulating
astrophysical problems. Numerical schemes applied for their solving
must provide high-resolution capturing of shocks, prevent spurious
oscillations and specify the behavior of the matter in the neighborhood
of small perturbations beyond shock fronts. Diﬀerence schemes have
to combine the properties of high resolution in the regions of small
perturbations and of monotonicity in the domains of steep gradients
in order to satisfy such contradictory conditions.},
file = {Rybakin09.pdf:Rybakin09.pdf:PDF},
keywords = {minmod; superbee; van Leer; TVD},
owner = {olivier},
timestamp = {2010.06.09}
}
@ARTICLE{Sahmim07,
author = {Sahmim,Slah and Benkhaldoun, Fayssal and Alcrudo, Francisco},
title = {A sign matrix based scheme for non-homogeneous PDE's with an analysis
of the convergence stagnation phenomenon},
journal = {Journal of Computational Physics},
year = {2007},
volume = {226},
pages = {1753 - 1783},
number = {2},
abstract = {This work is devoted to the analysis of a finite volume method recently
proposed for the numerical computation of a class of non-homogenous
systems of partial differential equations of interest in fluid dynamics.
The stability analysis of the proposed scheme leads to the introduction
of the sign matrix of the flux jacobian. It appears that this formulation
is equivalent to the VFRoe scheme introduced in the homogeneous case
and has a natural extension here to non-homogeneous systems. Comparative
numerical experiments for the Shallow Water and Euler equations with
source terms, and a model problem of two-phase flow (Ransom faucet)
are presented to validate the scheme. The numerical results present
a convergence stagnation phenomenon for certain forms of the source
term, notably when it is singular. Convergence stagnation has been
also shown in the past for other numerical schemes. This issue is
addressed in a specific section where an explanation is given with
the help of a linear model equation, and a cure is demonstrated.},
doi = {DOI: 10.1016/j.jcp.2007.06.017},
file = {Sahmim07.pdf:Sahmim07.pdf:PDF},
issn = {0021-9991},
keywords = {Finite volumes; Riemann problems; SRNH scheme; source terms; shallow
water equations; Euler equations; two-phase flow; C-property; exact
solution},
owner = {olivier},
timestamp = {2010.06.06},
url = {http://www.sciencedirect.com/science/article/B6WHY-4P2YWYC-3/2/7bac8b025392f6b1b16b30c68529b309}
}
@PHDTHESIS{Saint-Cast02,
author = {Saint-Cast, Fr\'ed\'eric},
title = {Mod\'elisation de la morphodynamique des corps sableux en milieu
littoral},
school = {Universit\'e de Bordeaux I},
year = {2002},
abstract = {: This thesis presents physical modeling and numerical resolution
of the coastal hydrodynamics and sediment dynamics coupling in order
to investigate sand bancs
morphodynamics in the presence of breaking waves. The 2D-Horizontal
hydrodynamics model provides the waves-induced current. The sediment
transport can be deduced, and then, the sediment ﬂuxes balance gives
the sand bed evolution. Under few assumptions, a simpliﬁed morphodynamics
model can explain sand waves behavior. Hydrodynamics is solved using
an implicit method to obtain quasi-steady mean currents, and bed
evolution is computed using non-oscillating explicit schemes. Finally,
the interest of this numerical simulation tool is emphasized on the
aquitan’s beach application.},
file = {Saint-Cast02.pdf:Saint-Cast02.pdf:PDF},
keywords = {2D-Horizontal hydrodynamics ; waves-induced current ; sediment transport
; morphodynamics ; beach instabilies ; sand waves ; Aquitan’s beach
; ﬁnite volume method ; implicit scheme ; coupled solving ; hyperbolic
conservation law ; non-oscillating explicit schemes},
owner = {olivier},
timestamp = {2009.07.21}
}
@PHDTHESIS{Salles06,
author = {Salles, Tristan},
title = {Mod\'elisation num\'erique du remplissage s\'edimentaire des canyons
et chenaux sous-marins par approche g\'en\'etique},
school = {Universit\'e de Bordeaux I},
year = {2006},
abstract = {In this thesis, we propose a numerical model developed to simulate
the sedimentary ﬁll of canyons and channel-levee complexes present
in deep turbiditic environments and resulting from gravity currents.
The model is based on an innovative numerical method inspired from
Cellular Automata paradigm. Processes which control the evolution
of the system are described thanks to ﬂows and particles behaviour
rules. Those rules are established empirically from observations
or physical laws simpliﬁcation. Sedimentary system is described by
a three-dimensionnal meshed domain. The system is built with series
of unitary events.
Considering the Cellular Automata approach, two versions are developed
and consisted in coupling as best as possible the impact of ﬂow eﬀects
on deposits nature and architecture. The ﬁrst version allows a dynamic
description of the sea bed evolution under the activity of gravity
ﬂows. For a given simulation, a single event is considered and morphology
of the sea bed and sediments distribution are estimated at each iteration.
The model was calibrated by rhe application to the case study of
the turbulent surge that occured during the 1999 storm in Capbreton
canyon and using core control. The second version simulates deposits
architecture accumulated by a succession of steady states. Because
of the long time scales involved in geological modeling, classical
models can barely take into account detailed physical processes governing
sedimentation. A possible way to average physical processes over
time is then to consider geological events as successive quasi steady
states for which sediment transport has permanent values. The cellular
automata paradigm can be an interesting approach to quickly obtain
such stationary states at the expense of the mathematical rigor of
classical physical models. Obtained results improves a ﬁrst step
towards quantitative understanding of the impact of external parameters
on catastrophic gravity ﬂow dynamics and on the organization of subsequent
deposits.},
file = {Salles06.pdf:Salles06.pdf:PDF},
keywords = {gravity ﬂows ; multi-lithology numerical model ; cellular automata
; deposits architecture.},
owner = {olivier},
timestamp = {2009.07.21}
}
@ARTICLE{Salvucci94,
author = {Salvucci, Guido Daniel and Entekhabi, Dara},
title = {Explicit expressions for {G}reen-{A}mpt (delta function diffusivity)
infiltration rate and cumulative storage},
journal = {Water Resources Research},
year = {1994},
volume = {30},
pages = {2661--2663},
number = {9},
abstract = {The sharp wetting front model of infiltration (Green and Ampt, 1911;
Philip, 1954) yields through simple integration an exact solution
relating the infiltration rate (i), cumulative infiltration (I),
and time (t). The relation, however, is implicit for i or I: i.e.,
it is of the form t=A[I-Bln(1+I/B)]. Numerical iteration is required
to find the infiltration rate, and furthermore, analytic manipulations
are limited using this traditional formulation of the Green-Ampt
infiltration. In this note we present an accurate expression for
the infiltration rate in the form of a rapidly converging series
in the variable thau=t/(t+khi). Truncating the series ... .},
file = {Salvucci94.pdf:Salvucci94.pdf:PDF},
keywords = {Green-Ampt; Mein-larsen},
owner = {olivier},
timestamp = {2010.04.23}
}
@ARTICLE{Samouelian07,
author = {Samou\"elian, A. and Vogel, H.-J. and Ippisch, O.},
title = {Upscaling hydraulic conductivity based on the topology of the sub-scale
structure},
journal = {Advances in Water Resources},
year = {2007},
volume = {30},
pages = {1179--1189},
abstract = {The hydraulic conductivity of heterogeneous porous media depends on
the distribution function and the geometry of local conductivities
at the smaller scale. There are various approaches to estimate the
eﬀective conductivity Keﬀ at the larger scale based on information
about the small scale heterogeneity. A critical geometric property
in this ‘upscaling’ procedure is the spatial connectivity of the
small-scale conductivities. We present an approach based on the Euler-number
to quantify the topological properties of heterogeneous conductivity
ﬁelds, and we derive two key parameters which are used to estimate
Keﬀ. The required coeﬃcients for the upscaling formula are obtained
by regression based on numerical simulations of various heterogeneous
ﬁelds. They are found to be generally valid for various diﬀerent
isotropic structures. The eﬀective unsaturated conductivity function
Keﬀ (wm) could be predicted satisfactorily. We compare our approach
with an alternative based on percolation theory and critical path
analysis which yield the same type of topological parameters. An
advantage of using the Euler-number in comparison to percolation
theory is the fact that it can be obtained from local measurements
without the need to analyze the entire structure. We found that for
the heterogeneous ﬁeld used in this study both methods are equivalent.},
file = {Samouelian07.pdf:Samouelian07.pdf:PDF},
keywords = {porous media; effective hydraulic properties; hydraulic conductivity;
unsaturated flow; upscaling; topology; connectivity; heterogeneous
structure; van Genuchten; Mualem; Richards},
owner = {olivier},
timestamp = {2010.06.13}
}
@INPROCEEDINGS{Sampson09,
author = {Sampson, Joe},
title = {A numerical solution for moving boundary shallow water flow above
parabolic bottom topography},
booktitle = { Proceedings of the 14th Biennial Computational Techniques and Applications
Conference, CTAC-2008},
year = {2009},
editor = {Geoffry N. Mercer and A. J. Roberts},
volume = {50},
series = {ANZIAM J.},
pages = {C898--C911},
month = jun,
abstract = {A numerical method has been applied to the nonlinear shallow water
wave equations for unforced linear frictional flow above parabolic
bottom topography and is found to be accurate. This solution involves
moving shorelines. The motion decays over time. The numerical scheme
used is adapted from the Selective Lumped Mass numerical scheme.
The wetting and drying algorithm used in the numerical scheme is
different to that in the Selective Lumped Mass scheme. The numerical
scheme is finite element in space, using fixed triangular elements,
finite difference in time and is explicit. The numerical solution
compares well with an analytical solution.},
file = {Sampson09.pdf:Sampson09.pdf:PDF},
keywords = {Algorithms; Numerical methods; Shallow water; Shorelines; Wave equations},
owner = {olivier},
timestamp = {2009.06.25},
url = {http://anziamj.austms.org.au/ojs/index.php/ANZIAMJ/article/view/1351}
}
@PHDTHESIS{Sampson08,
author = {Sampson, Joe},
title = {Some solutions of the shallow water wave equations},
school = {Faculty of Engineering and Industrial Sciences Swinburne University
of Technology Melbourne, Australia},
year = {2008},
abstract = {This thesis is concerned with the solution of the shallow water wave
equations. To solve the equations for a real life domain of flow
a numerical solution is required. Analytical solutions are useful
for testing numerical solutions. Previous research in this area is
examined. Existing analytical solutions of the nonlinear shallow
water equations involving moving boundaries do not include bottom
friction. Existing analytical solutions of the nonlinear shallow
water equations involving fixed boundaries can be modifed. The SLM
(Selective Lumped Mass) scheme for numerically solving the shallow
water equations has been used to accurately model tides both in bays
with fixed boundaries and bays with moving boundaries. The SLM scheme
for domains with moving boundaries has not been fully explained in
published papers. Analytical solutions are established for moving
boundary shallow water equations involving nonlinear continuity for
unforced frictional flow in parabolic canals, circular paraboloids
and elliptical paraboloids, and both for forced frictional flow and
unforced frictionless flow in a parabolic canal. Analytical solutions
are established for one dimensional nonlinear frictionless shallow
water wave flow in a basin of constant depth, with a fixed boundary
and with a sinusoidal input at the open boundary. The SLM scheme
is coded in Visual C ++ and validated against an analytical solution,
a convergence study is carried out for the SLM scheme and a computer
program is written in Visual C ++ to generate finite element meshes.
The SLM scheme is used to model one dimensional nonlinear shallow
water flow in a basin of constant depth, with fixed boundary and
with sinusoidal input at the open boundary; results obtained were
close to those in the analytical solution. The SLM scheme when applied
to a moving boundary domain has been modifed, with the resultant
scheme used to model forced frictionless flow and forced frictional
flow in a parabolic canal, with results close to those of the analytical
solutions developed. The SLM scheme is applied to model accurately
the existing tidal heights and currents in Port Phillip Bay, Victoria,
Australia. The SLM scheme is applied to model the effect of proposed
channel deepening on the tides in Port Phillip Bay; the effect is
small, increasing the tidal heights by at most seven millimetres.
The conclusion of this thesis is that successful analytical and numerical
solutions of the shallow water equations are developed both for domains
with fixed boundaries and domains with moving boundaries.},
file = {Sampson08.pdf:Sampson08.pdf:PDF},
institution = {Swinburne Research Bank [http://researchbank.swinburne.edu.au:8080/fedora/oai]
(Australia)},
keywords = {Water waves -- Mathematical models, Wave equations -- Numerical models,
Fluid mechanics -- Mathematics, Numerical analysis},
location = {http://www.scientificcommons.org/35457835},
owner = {olivier},
timestamp = {2009.06.25},
url = {http://hdl.handle.net/1959.3/35957}
}
@ARTICLE{Sampson07a,
author = {Sampson, Joe and Easton, Alan and Singh, Manmohan},
title = {A new moving boundary shallow water wave numerical model},
year = {2007},
abstract = {A new moving boundary shallow water wave equation numerical model
is presented. The model is adapted from the Selective Lumped Mass
(SLM) numerical model. The wetting and drying scheme used is different
to that in the SLM model. The SLM model is finite element in space,
using fixed triangular elements, finite difference in time and is
explicit. The numerical model has been tested against an analytical
solution with good agreement between the numerical and analytical
solutions. The numerical model proposed is useful for comparing against
analytical moving boundary solutions. The analytical solution is
presented for the first time, being for the case of frictionless
one dimensional moving boundary nonlinear shallow water wave flow
with cosine forcing in a bed with quadratically varying depth. The
analytical solution, which is explicit, is useful for testing numerical
models.},
file = {Sampson07a.pdf:Sampson07a.pdf:PDF},
institution = {ARROW Discovery Service [http://search.arrow.edu.au/apps/ArrowUI/OAIHandler]
(Australia)},
keywords = {Algorithms, Numerical methods, Shallow water, Shorelines, Wave equations},
location = {http://www.scientificcommons.org/47354869},
owner = {olivier},
publisher = {Cambridge University Press},
timestamp = {2009.06.25},
url = {http://hdl.handle.net/1959.3/57398}
}
@ARTICLE{Sampson07b,
author = {Sampson, Joe and Easton, Alan and Singh, Manmohan},
title = {Moving boundary shallow water flow in a region with quadratic bathymetry},
year = {2007},
abstract = {Exact solutions of the nonlinear shallow water wave equations for
forced flow involving linear bottom friction in a region with quadratic
bathymetry have been found. These solutions also involve moving shorelines.
The motion decays over time. In the solution of the three simultaneous
nonlinear partial differential shallow water wave equations it is
assumed that the velocity is a function of time only and along one
axis. This assumption reduces the three simultaneous nonlinear partial
differential equations to two simultaneous linear ordinary differential
equations. The analytical model has been tested against a numerical
solution with good agreement between the numerical and analytical
solutions. The analytical model is useful for testing the accuracy
of a moving boundary shallow water numerical model.},
file = {Sampson07b.pdf:Sampson07b.pdf:PDF},
institution = {ARROW Discovery Service [http://search.arrow.edu.au/apps/ArrowUI/OAIHandler]
(Australia)},
keywords = {Model equations, Nonlinear shallow water, Numerical solutions, Quadratic
bathymetry, Shallow water, Shorelines},
location = {http://www.scientificcommons.org/41546042},
owner = {olivier},
publisher = {Australian Mathematical Society},
timestamp = {2009.06.25},
url = {http://hdl.handle.net/1959.3/47084}
}
@ARTICLE{Sampson06,
author = {Sampson, Joe and Easton, Alan and Singh, Manmohan},
title = {Moving boundary shallow water flow above parabolic bottom topography},
year = {2006},
abstract = {Exact solutions of the two dimensional nonlinear shallow water wave
equations for flow involving linear bottom friction and with no forcing
are found for flow above parabolic bottom topography. These solutions
also involve moving shorelines. The motion decays over time. In the
solution of the three simultaneous nonlinear partial differential
shallow water wave equations it is assumed that the velocity is a
function of time only and along one axis. This assumption reduces
the three simultaneous nonlinear partial differential equations to
two simultaneous linear ordinary differential equations . The solutions
found are useful for testing numerical solutions of the nonlinear
shallow water wave equations which include bottom friction and whose
flow involves moving shorelines.},
file = {Sampson06.pdf:Sampson06.pdf:PDF},
institution = {ARROW Discovery Service [http://search.arrow.edu.au/apps/ArrowUI/OAIHandler]
(Australia)},
keywords = {230000 Mathematical Sciences},
location = {http://www.scientificcommons.org/23526429},
owner = {olivier},
publisher = {Australian Mathematical Society},
timestamp = {2009.06.25},
url = {http://hdl.handle.net/1959.3/5688}
}
@ARTICLE{Sampson05,
author = {Sampson, Joe and Easton, Alan and Singh, Manmohan},
title = {Modelling the effect of proposed channel deepening on the tides in
{P}ort {P}hillip {B}ay},
year = {2005},
abstract = {The Victorian State Government is investigating a proposal to deepen
the channels into Port Phillip Bay in order to bring larger ships
into the Bay. The Port of Melbourne Corporation, the Victorian State
Government authority responsible for the channel deepening, has concluded
that the largest increase in tidal height due to the channel deepening
will be eight millimetres. This paper is an independent study on
the effect of the channel deepening on the astronomical tides. The
levels of tides for the existing topography and for the topography
including the proposed channel deepening have been computed. Our
results show that the effect of channel deepening on the astronomical
tides will be to increase the maximum tidal height at most locations.
We calculate that the largest increase will be nine millimetres,
confirming the results of the Port of Melbourne Corporation.},
file = {Sampson05.pdf:Sampson05.pdf:PDF},
institution = {ARROW Discovery Service [http://search.arrow.edu.au/apps/ArrowUI/OAIHandler]
(Australia)},
keywords = {Mathematical Sciences (230000), Physical Sciences (240000)},
location = {http://www.scientificcommons.org/33260923},
owner = {olivier},
publisher = {Australian Mathematical Society},
timestamp = {2009.06.25},
url = {http://hdl.handle.net/1959.3/2405}
}
@ARTICLE{Sanders02,
author = {Sanders, Brett F.},
title = {Non-reflecting boundary flux function for finite volume shallow-water
models},
journal = {Advances in Water Resources},
year = {2002},
volume = {25},
pages = {195--202},
abstract = {An approach to implement non-reﬂecting boundary conditions in ﬁnite-volume
based shallow-water models is presented. Shallow-water models are
routinely applied to sections of rivers, estuaries, and coastal zones,
introducing computational boundaries where no physical control is
present, and necessitating a condition that supplies information
to the model while it simultaneously allows disturbances from the
interior to pass out unhampered. The approach presented here builds
upon the ﬁnite-volume convention of constructing a Riemann problem
at the interface between cells and then solving it with a ﬂux function.
Hence, non-reﬂecting boundary conditions are achieved using a non-reﬂecting
ﬂux function on cell faces aligned with open boundaries. Numerical
tests show that the non-reﬂecting ﬂux function performs extremely
well when waves advance toward the boundary with a small incident
angle (approximately less than 45° from the boundary normal direction),
while very minor reﬂections are present when the incident angle is
larger. The presence of minor reﬂections, when the incident angle
is large, is consistent with non-reﬂecting conditions previously
implemented in ﬁnite-diﬀerence based schemes.},
file = {Sanders02.pdf:Sanders02.pdf:PDF},
keywords = {boundary condition; shallow water; inflow; outflow; soft boundary},
owner = {olivier},
timestamp = {2011.02.23}
}
@ARTICLE{Savat77,
author = {Savat, J.},
title = {The hydraulics of sheet flow on a smooth surface and the effect of
simulated rainfall},
journal = {Earth Surface Processes},
year = {1977},
volume = {2},
pages = {125--140},
file = {Savat77.pdf:Savat77.pdf:PDF},
owner = {olivier},
timestamp = {2009.01.11}
}
@ARTICLE{Schmitz93,
author = {Schmitz, Gerd H.},
title = {A conservative 2D subsurface flow model for curvilinear coordinate
systems},
journal = {Advances in Water Resources},
year = {1993},
volume = {16},
pages = {241--253},
number = {4},
abstract = {A mass conservative finite difference scheme to describe 2D unsaturated/saturated
subsurface flow is developed. The development takes into account
important findings of Celia et al. (Water Resour. Res., 26(7) (1990)
1483-96) and extends their mass conservative 1D approach to two space
dimensions. Moreover, using the theory of metric coefficients, the
numerical model is not restricted to cartesian coordinates but is
generally formulated for arbitrary orthogonal coordinate systems,
thus accounting for curved boundaries of a computational domain.
For flux boundary conditions convenient formulae avoid the cumbersome
use of imaginary points outside the computational domain without
reducing the order of magnitude of the approximation error. A flexible
iteration strategy caters, on the one hand, for accuracy and stability
when simulating sharp wet fronts and, on the other hand, for an economical
calculation. The model was compared with the outcome of a laboratory
experiment which investigated the transient development of the infiltration
pattern in initially dry sand as a result of filling a circular cavity.},
doi = {DOI: 10.1016/0309-1708(93)90041-D},
file = {Schmitz93.pdf:Schmitz93.pdf:PDF},
issn = {0309-1708},
keywords = {subsurface flow; Richards equation; mixed formulation; two-dimensional
approach; conservative finite difference shceme; curvilinear coordinates;
metric coefficients; sharp wet-front simulation},
owner = {olivier},
timestamp = {2010.06.14},
url = {http://www.sciencedirect.com/science/article/B6VCF-48765HW-P/2/50aef3bf686ae7c577e7f3999c9036be}
}
@ARTICLE{Secomb78,
author = {Secomb, T. W.},
title = {Flow in a channel with pulsating walls},
journal = {J. Fluid Mech.},
year = {1978},
volume = {88, part 2},
pages = {273--288},
abstract = {In this paper calculations are made of the two-dimensional flow field
of an incompressible viscous fluid in a long parallel-sided channel
whose walls pulsate in a prescribed way. The study covers all values
of the unsteadiness parameter alpha and the steady-streaming Reynolds
number. The wall motion is, in general, assumed to be of small amplitude
and sinusoidal. Particular attention is given to the steady component
of the flow at second order in the amplitude parameter epsilon. The
results for the corresponding problem in axisymmetric geometry are
given in an appendix.
Next the following problem is considered: the calculation of the wall
motion which will result, in response to prescribed unsteady pressures
imposed at the ends of the channel and outside its walls, if the
walls are assumed to respond elastically to variations in transmural
pressure. It is found that the system has a natural frequency of
oscillation, and that resonance will occur if this frequency is close
to a multiple of the frequency of the external pressure fluctuations.
Finally the preceding work is applied in a discussion of blood flow
in the coronary arteries of large mammals.},
file = {Secomb78.pdf:Secomb78.pdf:PDF},
keywords = {blood flow},
owner = {olivier},
timestamp = {2011.03.05}
}
@MASTERSTHESIS{Seguin99,
author = {Seguin, N.},
title = {G{\'e}n{\'e}ration et validation de {R}ozavel, un code {\'e}quilibre
en hydraulique 2{D}},
school = {Universit{\'e} Bordeaux I},
year = {1999},
month = jun,
file = {Seguin99.pdf:Seguin99.pdf:PDF},
owner = {olivier},
timestamp = {2008.05.05}
}
@ARTICLE{Serna04,
author = {Serna, Susana and Marquina, Antonio},
title = {Power ENO methods: a fifth-order accurate Weighted Power ENO method},
journal = {Journal of Computational Physics},
year = {2004},
volume = {194},
pages = {632--658},
abstract = {In this paper we introduce a new class of ENO reconstruction procedures,
the Power ENO methods, to design high-order accurate shock capturing
methods for hyperbolic conservation laws, based on an extended class
of limiters, improving the behavior near discontinuities with respect
to the classical ENO methods. Power ENO methods are deﬁned as a correction
of classical ENO methods [J. Comput. Phys. 71 (1987) 231], by applying
the new limiters on second-order diﬀerences or higher. The new class
of limiters includes as a particular case the minmod limiter and
the harmonic limiter used for the design of the PHM methods [see
SIAM J. Sci. Comput. 15 (1994) 892]. The main features of these new
ENO methods are the substantially reduced smearing near discontinuities
and the good resolution of corners and local extrema. We design a
new ﬁfth-order accurate Weighted Power ENO method that improves the
behavior of Jiang–Shu WENO5 [J. Comput. Phys. 126 (1996) 202]. We
present several one- and two-dimensional numerical experiments for
scalar and systems of conservation laws, including linear advections
and one- and two-dimensional Riemann problems for the Euler equations
of gas dynamics, comparing our methods with the classical and weighted
ENO methods, showing the advantages and disadvantages.},
file = {Serna04.pdf:Serna04.pdf:PDF},
keywords = {conservation law; ENO; weighted ENO; Total Variation Bounded; minmod;
mineno; harmod; hareno},
owner = {olivier},
timestamp = {2010.06.20}
}
@ARTICLE{Sheldon08,
author = {Sheldon, Shane A. and Fiedler, Fritz R.},
title = {Direct {N}umerical {S}imulation of {H}ortonian {R}unoff {R}esulting
from {H}eterogeneous {S}atured {H}ydraulic {C}onductivity},
journal = {Journal of Hydrologic Engineering},
year = {2008},
volume = {13},
pages = {948--959},
number = {10},
month = Oct,
abstract = {Abstract: A two-dimensional rainfall-runoff model is used to systematically
explore the aggregate effect of spatially heterogeneous saturated
hydraulic conductivity, Ks, on Hortonian runoff generation. The fully
dynamic model integrates overland ﬂow and inﬁltration to allow for
the “interactive inﬁltration” process ͑run-on͒. Rainfall events varying
in time and intensity were simulated on synthetic hillslopes with
random and spatially correlated Ks ﬁelds. Model grid size discretization
recommendations are developed to fully capture the variation in Ks
and avoid limiting the spatial interactive inﬁltration opportunities
as found in analysis of the effects of model grid size on spatially
uncorrelated hillslopes. Our results show that on highly correlated
Ks ﬁelds, relative to the hillslope length, the inﬁltration due to
interaction is less than half that of uncorrelated ﬁelds for low
intensity events. Previous ﬁndings, are also substantiated and further
explored, with explicit consideration of model discretization, that
the variation in Ks increases interaction by increasing the inﬁltration
opportunity time, simultaneously, increasing runoff. Finally we investigate
the rainfall durations, which produce maximum interaction, and ﬁnd
interaction peaks for rainfall events approximately 1.5 times longer
than the hillslope average time to ponding.},
doi = {10.1061/͑ASCE͒1084-0699͑2008͒13:10͑948͒},
file = {Sheldon08.pdf:Sheldon08.pdf:PDF},
keywords = {Hydrologic models; Runoff; Inﬁltration; Hydrologic conductivity; Heterogeneity;
Simulation},
owner = {olivier},
timestamp = {2010.04.24}
}
@ARTICLE{Sherwin03,
author = {Sherwin, S. J. and Formaggia, L. and Peir\'o, J. and Franke, V.},
title = {Computational modelling of 1D blood flow with variable mechanical
properties and its application to the simulation of wave propagation
in the human arterial system},
journal = {International Journal for Numerical Methods in Fluids},
year = {2003},
volume = {43},
pages = {673--700},
abstract = {In this paper we numerically investigate a one-dimensional model of
blood ow in human arteries using both a discontinuous Galerkin and
a Taylor–Galerkin formulation. The derivation of the model and the
numerical schemes are detailed and applied to two model numerical
experiments. We ÿrst study the effect of an intervention, such the
implantation of a vascular prosthesis (e.g. a stent), which leads
to an abrupt variation of the mechanical characteristics of an artery.
We then discuss the simulation of the propagation of pressure and
velocity waveforms in the human arterial tree using a simpliÿed model
consisting of the 55 main arteries.},
doi = {10.1002/fld.543},
file = {Sherwin03.pdf:Sherwin03.pdf:PDF},
keywords = {1D blood flow; computational haemodynamics; discontinuous Galerkin
methods; Taylor-Galerkin methods; fluid-structure interaction},
owner = {olivier},
timestamp = {2011.03.10}
}
@ARTICLE{Shih09,
author = {Shih, H.-M. and Yang, Chih~Ted},
title = {Estimating overland flow erosion capacity using unit stream power},
journal = {International Journal of Sediment Research},
year = {2009},
volume = {24},
pages = {46 - 62},
number = {1},
abstract = {Soil erosion caused by water flow is a complex problem. Both empirical
and physically based approaches were used for the estimation of surface
erosion rates. Their applications are mainly limited to experimental
areas or laboratory studies. The maximum sediment concentration overland
flow can carry is not considered in most of the existing surface
erosion models. The lack of erosion capacity limitation may cause
over estimations of sediment concentration. A correlation analysis
is used in this study to determine significant factors that impact
surface erosion capacity. The result shows that the unit stream power
is the most dominant factor for overland flow erosion which is consistent
with experimental data. A bounded regression formula is used to reflect
the limits that sediment concentration cannot be less than zero nor
greater than a maximum value. The coefficients used in the model
are calibrated using published laboratory data. The computed results
agree with laboratory data very well. A one dimensional overland
flow diffusive wave model is used in conjunction with the developed
soil erosion equation to simulate field experimental results. This
study concludes that the non-linear regression method using unit
stream power as the dominant factor performs well for estimating
overland flow erosion capacity.},
doi = {DOI: 10.1016/S1001-6279(09)60015-9},
file = {Shih09.pdf:Shih09.pdf:PDF},
issn = {1001-6279},
keywords = {Overland flow},
owner = {olivier},
timestamp = {2009.11.14},
url = {http://www.sciencedirect.com/science/article/B8JJR-4W26FGM-4/2/93a0b1f5dff080fd1c8dad36039c09b1}
}
@ARTICLE{Shu88,
author = {Shu, C.-W. and Osher, Stanley},
title = {Efficient implementation of essentially non-oscillatory shock-capturing
schemes},
journal = {Journal of Computational Physics},
year = {1988},
volume = {77},
pages = {439 - 471},
number = {2},
abstract = {In the computation of discontinuous solutions of hyperbolic conservation
laws, TVD (total-variation-diminishing), TVB (total-variation-bounded),
and the recently developed ENO (essentially non-oscillatory) schemes
have proven to be very useful. In this paper two improvements are
discussed: a simple TVD Runge-Kutta type time discretization, and
an ENO construction procedure based on fluxes rather than on cell
averages. These improvements simplify the schemes considerably-especially
for multi-dimensional problems with forcing terms. Preliminary numerical
results are also given.},
doi = {DOI: 10.1016/0021-9991(88)90177-5},
issn = {0021-9991},
owner = {olivier},
timestamp = {2009.11.10},
url = {http://www.sciencedirect.com/science/article/B6WHY-4DD1T6W-MM/2/bef99e4b67bd7132c8af1984c34ce57e}
}
@ARTICLE{Sidorchuk08,
author = {Sidorchuk, A. and Schmidt, J. and Cooper, G.},
title = {Variability of shallow overland flow velocity and soil aggregate
transport observed with digital videography},
journal = {Hydrological Processes},
year = {2008},
volume = {n/a},
pages = {n/a},
number = {n/a},
abstract = {Field experiments at Tiramoana station 30 km north of Christchurch,
New Zealand using an erosion plot 16.5 m long, 0.6 m wide, and with
a slope of 14-14.5 deg on rendzina soil aimed to measure the variability
of flow velocity and of soil aggregates transport rate in shallow
overland flow. Discharge/cross-section area ratio was used to estimate
mean velocity, and high-speed digital video camera and image analysis
provided information about flow and sediment transport variability.
Six flow runs with 0.5-3.0 L s-1 discharges were supercritical with
Froude numbers close to or more than 1. Mean flow velocity followed
Poiseuille law, float numbers were more than 1.5 and hydraulic resistance
was an inverse proportional function of the Reynolds number, which
is typical for laminar flows. Hence actual velocity varied through
time significantly and the power spectrum was of lsquored-noisersquo,
which is typical for turbulent flow. Sediment transport rates had
even higher variability, and soil aggregates transport was a compound
Poisson process},
doi = {10.1002/hyp.7006},
file = {Sidorchuk08.pdf:Sidorchuk08.pdf:PDF},
keywords = {soil aggregates erosion, high-speed digital video, image analysis,
velocity variability, laminar to turbulent flow, sediment transport
variability, compound Poisson process, experiment, field, measurement},
owner = {Fred. DARBOUX},
timestamp = {2008.08.08}
}
@ARTICLE{Sielecki70,
author = {Sielecki, Anita and Wurtele, M.G.},
title = {The numerical integration of the nonlinear shallow-water equations
with sloping boundaries},
journal = {Journal of Computational Physics},
year = {1970},
volume = {6},
pages = {219 - 236},
number = {2},
abstract = {The nonlinear shallow-water equations in a rotating frame are integrated
numerically over a sloping bottom with free lateral boundary conditions
in such a way that the fluid determines its own level. Three different
finite-difference schemes are tested and found to give equivalent
results. The results are compared with nonlinear analytic solutions
in one and two dimensions, and a high order of accuracy is achieved.
The techniques used could be of importance in the operational forecasting
of storm surges at irregular coast lines.},
doi = {DOI: 10.1016/0021-9991(70)90022-7},
file = {Sielecki70.pdf:Sielecki70.pdf:PDF},
issn = {0021-9991},
keywords = {Analytic solutions; exact; rotating; shallow water; Carrier and Greenspan;
Ball; Stoker},
owner = {olivier},
timestamp = {2010.06.16},
url = {http://www.sciencedirect.com/science/article/B6WHY-4DD1V8M-100/2/b63890497bae64b7be9713dac3eb167c}
}
@ARTICLE{Singh98,
author = {Singh, V. and Bhallamudi, S.~M.},
title = {Conjunctive surface-subsurface modeling of overland flow},
journal = {Advances in Water Resources},
year = {1998},
volume = {21},
pages = {567--579},
abstract = {In this paper, details of a conjunctive surface-subsurface numerical
model for the simulation of overland flow are presented. In this
model, the complete onedimensional Saint-Venant equations for the
surface flow are solved by a simple, explicit, essentially non-oscillating
(ENO) scheme. The two-dimensional Richards equation in the mixed
form for the subsurface flow is solved using an efficient strongly
implicit finite-difference scheme. The explicit scheme for the surface
flow component results in a simple method for connecting the surface
and subsurface components. The model is verified using the experimental
data and previous numerical results available in the literature.
The proposed model is used to study the two-dimensionality effects
due to non-homogeneous subsurface characteristics. Applicability
of the model to handle complex subsurface conditions is demonstrated.},
doi = {DOI: 10.1016/S0309-1708(97)00020-1},
file = {Singh98.pdf:Singh98.pdf:PDF},
issn = {0309-1708},
keywords = {Overland flow; Saint-Venant equations; Richards equation; Conjunctive
model},
owner = {olivier},
timestamp = {2009.01.11},
url = {http://www.sciencedirect.com/science/article/B6VCF-3TDH36C-3/2/980779e9479d0b96f3a3e25e06db7637}
}
@ARTICLE{Singh02,
author = {Singh, V.~P.},
title = {Is hydrology kinematic?},
journal = {Hydrological processes},
year = {2002},
volume = {16},
pages = {667--716},
abstract = {A wide range of phenomena, natural as well as man-made, in physical,
chemical and biological hydrology exhibit characteristics similar
to those of kinematic waves. The question we ask is : can these phenomena
be described using the theory of kinematic waves . Since the range
of phenomena is wide, another question we ask is : how prevalent
are kinematic waves ? If they are widely pervasive, does that mean
hydrology is kinematic or close to it ? This paper addresses these
issues, which are perceived to be fundamental to advancing the state-of-the-art
of water science and engineering.},
doi = {10.1002/hyp.306},
file = {Singh02.pdf:Singh02.pdf:PDF},
keywords = {biological hydrology; chemical hydrology; physical hydrology; kinematic
wave theory; kinematics; flux laws},
owner = {olivier},
timestamp = {2008.04.29}
}
@ARTICLE{Singh01,
author = {Singh, V.~P.},
title = {Kinematic wave modelling in water resources: a historical perspective},
journal = {Hydrological Processes},
year = {2001},
volume = {15},
pages = {671--706},
abstract = {The history of the kinematic wave theory and its applications in water
resources are traced. It is shown that the theory has found its niche
in water resources and its applications are so widespread that they
may well constitute what may be termed `kinematic wave hydrology'.
Few theories have been applied in hydrology and water resources as
extensively as the kinematic wave theory. This theory, however, is
not without limitations and when it is applied they must be so recognized.},
doi = {10.1002/hyp.99},
file = {Singh01.pdf:Singh01.pdf:PDF},
owner = {olivier},
timestamp = {2008.05.08}
}
@ARTICLE{Singh75,
author = {Singh, Vijay P.},
title = {Hybrid formulation of kinematic wave models of watershed runoff},
journal = {Journal of Hydrology},
year = {1975},
volume = {27},
pages = {33 - 50},
number = {1-2},
abstract = {Current kinematic wave models of watershed runoff incorporate either
numerical or analytical solutions, depending upon the type of input
(rainfall pattern) and representation of watershed geometry. Numerical
solutions are time-consuming; analytic solutions are not always feasible.
This paper formulates these models in terms of an approach called
hybrid approach which is part numerical and part analytical. By applying
it to a set of rainfall-runoff events on a natural watershed, it
is demonstrated that this approach is computationally far more efficient
than a totally numerical one, and is applicable where analytical
solutions are not feasible.},
doi = {DOI: 10.1016/0022-1694(75)90097-9},
file = {Singh75.pdf:Singh75.pdf:PDF},
issn = {0022-1694},
keywords = {kinematic wave; watershed runoff; converging section; Wooding; composite
section; cascade of N planes; hydrograph},
owner = {olivier},
timestamp = {2010.06.16},
url = {http://www.sciencedirect.com/science/article/B6V6C-487FBF8-VJ/2/70fbc85295b9d1a991115c0151a7edd9}
}
@ARTICLE{Singh81,
author = {Singh, Vijay P. and Agiralioglu, Necati},
title = {Diverging overland flow},
journal = {Advances in Water Resources},
year = {1981},
volume = {4},
pages = {117--124},
number = {3},
abstract = {This study investigates divering overland flow utilizing kinematic
wave theory, which does not appear to have been dealt with previously.
Explicit analytical solutions are derived in dimensionless form for
space-time invariant rainfall. Analytical solutions do not seem to
be tractable for time-varying rainfall. Depending upon the duration
of rainfall, equilibrium and partial equilibrium cases are distinguished
explicitly. The effect of divergence parameter on the hydrograph
shape is shown. The adequacy of kinematic approximation for characterization
of diverging overland flow is tested against laboratory watershed
results. The diverging overland flow model is found to yield results
which compare well with observations and with those of a plane model.},
doi = {DOI: 10.1016/0309-1708(81)90042-7},
file = {Singh81.pdf:Singh81.pdf:PDF},
issn = {0309-1708},
keywords = {kinematic wave; analytical solution; infiltration},
owner = {olivier},
timestamp = {2010.06.18},
url = {http://www.sciencedirect.com/science/article/B6VCF-487HP22-1M/2/6f0cd99136f35307b72f4617f1833acb}
}
@ARTICLE{Sivakumar09,
author = {Sivakumar, P. and Hyams, D. G. and Taylor, L. K. and Briley, W. R.},
title = {A primitive-variable Riemann method for solution of the shallow water
equations with wetting and drying},
journal = {Journal of Computational Physics},
year = {2009},
volume = {228},
pages = {7452--7472},
abstract = {A Riemann ﬂux that uses primitive variables rather than conserved
variables is developed for the shallow water equations with nonuniform
bathymetry. This primitive-variable ﬂux is both conservative and
well behaved at zero depth. The unstructured ﬁnite-volume discretization
used is suitable for highly nonuniform grids that provide resolution
of complex geometries and localized ﬂow structures. A source-term
discretization is derived for non-uniform bottom that balances the
discrete ﬂux integral both for still water and in dry regions. This
primitive-variable formulation is uniformly valid in wet and dry
regions with embedded wetting and drying fronts. A fully nonlinear
implicit scheme and both nonlinear and time-linearized explicit schemes
are developed for the time integration. The implicit scheme is solved
by a parallel Newton-iterative algorithm with numerically computed
ﬂux Jacobians. A concise treatment of characteristic-variable boundary
conditions with source terms is also given. Computed results obtained
for the one-dimensional dam break on wet and dry beds and for normal-mode
oscillations in a circular parabolic basin are in very
close agreement with the analytical solutions. Other results for a
forced breaking wave with friction interacting with a sloped bottom
demonstrate a complex wave motion with wetting, drying and multiple
interacting wave fronts. Finally, a highly nonuniform, coastline-conforming
unstructured grid is used to demonstrate an unsteady simulation that
models an artiﬁcial coastal ﬂooding due to a forced wave entering
the Gulf of Mexico.},
doi = {10.1016/j.jcp.2009.07.002},
file = {Sivakumar09.pdf:Sivakumar09.pdf:PDF},
keywords = {shallow water equations; wet/dry front; Riemann flux; primitive variables;
boundary conditions; parallel implicit algorithm; unstructured grid;
Gulf of Mexico; dam break; Thacker},
owner = {olivier},
timestamp = {2011.02.23}
}
@ARTICLE{Smaoui08,
author = {Smaoui, Hassan and Zouhri, Lahcen and Ouahsine, Abdellatif},
title = {Flux-limiting techniques for simulation of pollutant transport in
porous media: Application to groundwater management},
journal = {Mathematical and Computer Modelling},
year = {2008},
volume = {47},
pages = {47 - 59},
number = {1-2},
abstract = {The objective of this work is to present a numerical study of contaminant
migration in saturated porous media. For this purpose, the advection-diffusion
equation describing the evolution of contaminant plumes in a 2D horizontal
aquifer (Atlantic margin, Rharb Basin of Morocco) is discretized
employing a Total Variation Diminishing method (TVD), which provides
an efficient way to eliminate spurious numerical oscillations. The
stationary velocity field is computed by the ModFlow code using the
finite difference method discretization. The initial concentration
needed to determine the solution was specified using data from well
samples. Numerical examples showing the implementation of the algorithm
to describe groundwater contamination by the chloride in the aquifer
are presented. This high accuracy method (TVD) constitutes an approach
in the water management and allows us to envisage risks of pollution
and to manage the groundwater resource from the durable development
perspective.},
doi = {DOI: 10.1016/j.mcm.2007.02.006},
file = {Smaoui08.pdf:Smaoui08.pdf:PDF},
issn = {0895-7177},
keywords = {Groundwater; TVD; advection; diffusion; flux limiters; numerical modelling;
numerical scheme; infiltration; pollutant},
owner = {olivier},
timestamp = {2010.06.03},
url = {http://www.sciencedirect.com/science/article/B6V0V-4NC38T2-H/2/5996adb68e2dae3cdcca767c20aa418f}
}
@ARTICLE{Smith11,
author = {Smith, Matthew R. and Lin, K.-M. and Hung, C.-T. and Chen, Y.-S.
and Wu, J.-S.},
title = {Development of an improved spatial reconstruction technique for the
HLL method and its applications},
journal = {Journal of Computational Physics},
year = {2011},
volume = {230},
pages = {477--493},
abstract = {The integral form of the conventional HLL ﬂuxes are presented by taking
integrals around the control volume centred on each cell interface.
These integrals are demonstrated to reduce to the conventional HLL
ﬂux through simpliﬁcation by assuming spatially constant conserved
properties. The integral ﬂux expressions are then modiﬁed by permitting
the analytical inclusion of spatially linearly varying conserved
quantities. The newly obtained ﬂuxes (which are named HLLG ﬂuxes
for clariﬁcation, where G stands for gradient inclusion) demonstrate
that conventional reconstructions at cell interfaces are invalid
and can produce unstable results when applied to conventional HLL
schemes. The HLLG method is then applied to the solution of the Euler
Equations and Shallow Water Equations for various common benchmark
problems and ﬁnally applied to a 1D ﬂuid modeling for an argon RF
discharge at low pressure. Results show that the correct inclusion
of ﬂow gradients is shown to demonstrate superior transient behavior
when compared to the existing HLL solver and conventional spatial
reconstruction without signiﬁcantly increasing computational expense.},
doi = {10.1016/j.jcp.2010.09.023},
file = {Smith11.pdf:Smith11.pdf:PDF},
keywords = {computational fluid dynamics (CFD); finite volume methods (FVM); total
variable diminishing (TVD) schemes; plasma simulation; minmod; HLL;
dam break; HLLG},
owner = {olivier},
timestamp = {2011.02.23}
}
@ARTICLE{Smith07,
author = {Smith, Mark~W. and Cox, Nicholas~J. and Bracken, Louise~J.},
title = {Applying flow resistance equations to overland flows},
journal = {Progress in Physical Geography},
year = {2007},
volume = {31},
pages = {363--387},
number = {4},
month = aug,
abstract = {Resistance to flow determines routing velocities and must be adequately
represented both within stream channels and over hillslopes when
making predictions of streamflow and soil erosion. The limiting assumptions
inherent in flow resistance equations can be relaxed if the spatial
and temporal scale over which they are applied is restricted. This
requires a substantial methodological advance in the study of overland
flows over natural surfaces. It is suggested that terrestrial laser
scanning will allow a greater understanding of overland flow hydraulics
and present opportunities to investigate resistance to flow over
complex morphologies. The Darcy-Weisbach, ChÃ©zy and Manning equations
are the most widely used empirical equations for the calculation
of flow velocity in runoff and erosion models. These equations rest
on analyses originally developed for one-dimensional pipe flows and
assume conditions which are not met by overland flows. The following
assumptions are brought into question: flow can be described as uniform;
flow is parallel to the surface; flow is of a constant width and
the boundary to the flow is longitudinally uniform; grain roughness
is homogeneous over the wetted perimeter and can be considered as
random; form roughness and other sources of flow resistance can be
ignored; resistance is independent of flow depth; and resistance
can be modelled as a function of the Reynolds number. A greater appreciation
of the processes contributing to resistance to overland flows must
be developed. This paper also presents a brief history of the development
of flow resistance equations.},
doi = {10.1177/0309133307081289},
file = {Smith07.pdf:Smith07.pdf:PDF},
keywords = {flow threads; friction coefficients; hillslope hydrology; hydraulic
resistance; hydraulics; overland flow; surface roughness; SOIL-EROSION
MODEL; GRAVEL-BED RIVERS; COARSE-GRAINED CHANNELS; ESTIMATING MANNINGS-N;
VELOCITY PROFILES; TURBULENT-FLOW; SHEET FLOW; ROUGHNESS COEFFICIENTS;
HYDRAULIC RESISTANCE; SHEAR-STRESS},
owner = {olivier},
timestamp = {2008.10.07}
}
@PHDTHESIS{Sochala08,
author = {Sochala, P.},
title = {M\'ethodes num\'eriques pour les \'ecoulements souterrains et couplage
avec le ruissellement},
school = {\'Ecole Nationale des Ponts et Chauss\'ees},
year = {2008},
month = dec,
abstract = {Accurate and robust numerical schemes are proposed to simulate subsurface
flows and their coupling with surface runoff. Subsurface flows are
modelled by the (unsteady) Richards’ equation discretized by a BDF
in time and a discontinuous Galerkin method with symmetric interior
penalty in space. Infiltration column test cases confirm the robustness
of our schemes. Firstly, we consider Signorini conditions for Richards
equation to model buried drains or the water table reaching the ground
surface ; thus we assume that exfiltrated water immediately exits
the system. Secondly, runoff flow is taken into account through coupling
conditions enforcing water flux equality and pressure continuity
at the interface. Overland flows are modelled by the kinematic wave
approximation of the shallow water equations, which is discretized
by a Godunov method. Both schemes, that for the subsurface flow and
that for the overland flow, are mass conservative and can be coupled
within a multiple time step procedure. To ensure total water mass
conservation for the whole system, interface fluxes must be carefully
designed. We specify the form of these fluxes for BDF1 and BDF2.
Accuracy and robustness of our schemes are assessed on drainage,
exfiltration and hortonian runoff test cases. Finally, we apply the
methology to investigate the hydrological behavior of a small-scale
drained watershed.},
file = {Sochala08.pdf:Sochala08.pdf:PDF},
keywords = {Richards’ equation; kinematic wave approximation; discontinuous finite
elements; coupling algorithms; mass conservation},
owner = {olivier},
timestamp = {2009.01.11}
}
@ARTICLE{Sochala09,
author = {P. Sochala and A. Ern and S. Piperno},
title = {Mass conservative BDF-discontinuous Galerkin/explicit finite volume
schemes for coupling subsurface and overland flows},
journal = {Computer Methods in Applied Mechanics and Engineering},
year = {2009},
volume = {198},
pages = {2122 - 2136},
number = {27-29},
abstract = {Robust and accurate schemes are designed to simulate the coupling
between subsurface and overland flows. The coupling conditions at
the interface enforce the continuity of both the normal flux and
the pressure. Richards' equation governing the subsurface flow is
discretized using a backward differentiation formula and a symmetric
interior penalty discontinuous Galerkin method. The kinematic wave
equation governing the overland flow is discretized using a Godunov
scheme. Both schemes individually are mass conservative and can be
used within single-step or multi-step coupling algorithms that ensure
overall mass conservation owing to a specific design of the interface
fluxes in the multi-step case. Numerical results are presented to
illustrate the performances of the proposed algorithms.},
doi = {DOI: 10.1016/j.cma.2009.02.024},
file = {Sochala09.pdf:Sochala09.pdf:PDF},
issn = {0045-7825},
keywords = {Surface-subsurface coupled flows},
owner = {olivier},
timestamp = {2010.05.14},
url = {http://www.sciencedirect.com/science/article/B6V29-4VPM5B6-2/2/fae6d540a1dcc0fc110116f2bd8123a0}
}
@PHDTHESIS{SoriaUgalde03,
author = {Soria Ugalde, Jos\'e Miguel},
title = {Identification des param\`etres hydrodynamiques du sol par mod\'elisation
inverse des flux d'infiltration : application aux \'echelles locale
et hydrologique},
school = {Institut national polytechnique de Grenoble},
year = {2003},
month = Dec,
abstract = {La mod\'elisation des transferts d’eau dans la zone non satur\'ee
utilise des m\'ethodes et des techniques de la physique du sol fond\'ees
sur la solution de l’équation de Richards. Cependant, il existe un
d\'esaccord entre la taille des mesures fournies par la physique
du sol et la taille des domaines de mod\'elisation hydrologique,
probl\`eme auquel s’ajoute la forte variabilit\'e des propri\'et\'es
hydrodynamiques du sol dans le temps et dans l’espace. L’objectif
de ce travail a \'et\'e de d\'evelopper une m\'ethodologie permettant
l’estimation des param\`etres hydrodynamiques pour la mod\'elisation
des transferts d’eau 1D \`a diff\'erentes \'echelles hydrologiques.
Dans ce contexte, la variabilit\'e du sol dans un domaine hydrologique
est prise en compte par la mesure des signaux de flux agr\'eg\'es
\`a l’\'echelle requise. Deux m\'ethodes de mod\'elisation inverse
de flux ont \'et\'es d\'evelopp\'ees pour l’estimation des param\`etres
hydrodynamiques "\'equivalents" des domaines hydrologiques. Les m\'ethodes
sont fond\'ees sur l’approche "Beerkan" qui utilise des informations
texturales du sol et l’inversion num\'erique des flux d’infiltration.
La premi\`ere m\'ethode utilise des mod\`eles analytiques d’infiltration
simples ce qui permet une inversion num\'erique stable et une solution
unique. La deuxi\`eme m\'ethode d\'eveloppe un "mod\`ele num\'erique"
non dimensionnel, tr\`es pr\'ecis, qui prend en compte des conditions
initiales et aux limites plus complexes que la premi\`ere ainsi que
le cas 3D axisym\'etrique. De plus, une solution approximative du
front d’infiltration qui utilise les donn\'ees des flux d’infiltration
I(t) est d\'evelopp\'ee.},
file = {SoriaUgalde03.pdf:SoriaUgalde03.pdf:PDF},
keywords = {param\`etres hydrodynamiques; mod\`elisation inverse; agr\'egation
des flux; \'echelles hydrologiques; \'equation de Richards; front
d'infiltration; sols non satur\'es; hydraulic parameters; inverse
modelling; flux aggregation; hydrological scales; Richards' equation;
infiltration wetting front; unsatured soils},
owner = {olivier},
timestamp = {2010.06.05}
}
@ARTICLE{Souchere98,
author = {Souch\`ere, V. and King, D. and Daroussin, J. and Papy, F. and Capillon,
A.},
title = {Effects of tillage on runoff directions: consequences on runoff contributing
areas within agricultural catchments.},
journal = {Journal of Hydrology},
year = {1998},
volume = {206},
pages = {256--267},
number = {3-4},
month = may,
abstract = {In areas of intensive agriculture, e.g. 'Pays de Caux' in France,
which was the study area, field observations have shown that runoff
directions were modified by agricultural activities. In order to
account for factors responsible for modifications of the runoff direction
(roughness, tillage direction and agricultural patterns, e.g. dead
furrow or dirt tracks), we constructed a discriminant function based
on field observations. This function enables us to decide whether
flow direction for slopes of up to 15% was imposed by slope direction
or tillage direction. It can be applied to any location, provided
there are known roughness, known slope intensity, known aspect and
known tillage azimuth. In order to examine the effects of these agricultural
activities at the catchment scale, we compared two models by analysing
the same hydrological variables: the area contributing to runoff
and the flow network. The first model (Topo) was built according
to the runoff direction derived from a Digital Elevation Model (DEM).
The second model (Tillage) was constructed by combining information
from the DEM, and information from rules based on field observations
or resulting from statistical analysis. For 23 basic catchments,
the result of the comparison between the two models (Topo and Tillage)
showed that a major part of the catchments and the drainage network
was affected by modifications related to the introduction of man-made
agricultural factors. For example, for 20 of 23 catchments, the runoff
flows over more than 50% of the surface of such areas were produced
along the direction imposed by tillage. The introduction of tillage
effect brings about modifications of both. the shape and size of
catchments.},
doi = {10.1016/S0022-1694(98)00103-6},
file = {Souchere98.pdf:Souchere98.pdf:PDF},
keywords = {runoff; tillage direction; catchment; erosion},
owner = {Fred. DARBOUX},
review = {Effet des sillons sur la r�partition spatiale du ruissellement dans
un bassin-versant},
timestamp = {2007.09.28}
}
@ARTICLE{Stagnitti01,
author = {F. Stagnitti and Ling Li and A. Barry and G. Allinson and J. -Y.
Parlange and T. Steenhuis and E. Lakshmanan},
title = {Modelling solute transport in structured soils: performance evaluation
of the ADR and TRM models},
journal = {Mathematical and Computer Modelling},
year = {2001},
volume = {34},
pages = {433 - 440},
number = {3-4},
abstract = {The movement of chemicals through the soil to the groundwater or discharged
to surface waters represents a degradation of these resources. In
many cases, serious human and stock health implications are associated
with this form of pollution. The chemicals of interest include nutrients,
pesticides, salts, and industrial wastes. Recent studies have shown
that current models and methods do not adequately describe the leaching
of nutrients through soil, often underestimating the risk of groundwater
contamination by surface-applied chemicals and overestimating the
concentration of resident solutes. This inaccuracy results primarily
from ignoring soil structure and nonequilibrium between soil constituents,
water, and solutes. A multiple sample percolation system (MSPS),
consisting of 25 individual collection wells, was constructed to
study the effects of localized soil heterogeneities on the transport
of nutrients (NO-3, Cl-, PO3-4) in the vadose zone of an agricultural
soil predominantly dominated by clay. Very significant variations
in drainage patterns across a small spatial scale were observed (one-way
ANOVA, p < 0.001 indicating considerable heterogeneity in water flow
patterns and nutrient leaching. Using data collected from the multiple
sample percolation experiments, this paper compares the performance
of two mathematical models for predicting solute transport, the advective-dispersion
model with a reaction term (ADR), and a two-region preferential flow
model (TRM) suitable for modelling nonequilibrium transport. These
results have implications for modelling solute transport and predicting
nutrient loading on a larger scale.},
doi = {DOI: 10.1016/S0895-7177(01)00074-7},
file = {Stagnitti01.pdf:Stagnitti01.pdf:PDF},
issn = {0895-7177},
keywords = {Advective-dispersion equation; Preferential flow; Numerical methods;
Solute transport; Nutrients; Nitrate; Chloride; Phosphate; Pollution},
owner = {olivier},
timestamp = {2010.06.04},
url = {http://www.sciencedirect.com/science/article/B6V0V-43GK1S0-M/2/0339eea0149e3d2f9b8ec1bb2406d7bf}
}
@ARTICLE{Stergiopulos92,
author = {Stergiopulos, N. and Young, D. F. and Rogge, T. R.},
title = {Computer simulation of arterial flow with applications to arterial
and aortic stenoses},
journal = {J. Biomechanics},
year = {1992},
volume = {25},
pages = {1477--1488},
number = {12},
abstract = {A computer model for simulating pressure and flow propagation in the
human arterial system is developed. The model is based on the one-dimensional
flow equations and includes nonlinearities arising from geometry
and material properties. Fifty-five arterial segments, representing
the various major arteries, are combined to form the model of the
arterial system. Particular attention is paid to the development
of peripheral pressure and flow pulses under normal flow conditions
and under conditions of arterial and aortic stenoses. Results show
that the presence of severe arterial stenoses significantly affects
the nature of the distal pressure and flow pulses. Aortic stenoses
also have a profond effect on central and peripheral pressure pulse
formation. Comparison with the published experimental data suggests
that the model is capable of simulating arterial flow under normal
flow conditions as well as conditions of stenotic obstructions in
a satisfactory manner.},
file = {Stergiopulos92.pdf:Stergiopulos92.pdf:PDF},
keywords = {blood flow; aortic stenoses; arterial flow},
owner = {olivier},
timestamp = {2011.03.03}
}
@ARTICLE{Stettler81,
author = {Stettler, J.~C. and Niederer, P. and Anliker, M.},
title = {Theoretical analysis of arterial hemodynamics including the influence
of bifurcations -- Part I: Mathematical Model and Prediction of Normal
Pulse Patterns},
journal = {Annals of Biomedical Engineering},
year = {1981},
volume = {9},
pages = {145--164},
abstract = {Based on earlier theoretical studies, a new mathematical model is
developed for the prediction of the pressure and flow pulses propagating
in the arterial system. This model permits a more realistic simulation
of bifurcation and stenoses than was possible previously. By making
use of a computer, it allows us to calculate the pulse shapes along
branching arteries. It is based on the assumption that each arterial
conduit can be represented by a suitable combination of three basic
segments, namely segments with no or only small-calibre side branches,
short segments with big side branches, and short segments with pathological
changes of the conduit. Along segments of the first type, the pulse
propagation is calculated with the aid of the method of characteristics
and a first order integration. For the other two types, the linearized
mass balance and momentum equations are utilized together with the
boundary conditions to determine the pressure and flow values at
the ends of the segment. A standard case for the human arterial conduit
extending from the heart to the foot, with eight major branches,
is defined using published data and prescribing the ejection pattern
from the heart. The computed pulse shapes and their changes with
propagation exhibit the characteristic features observed in man under
normal conditions.},
file = {Stettler81.pdf:Stettler81.pdf:PDF},
keywords = {blood flow; artery},
owner = {olivier},
timestamp = {2010.11.26}
}
@BOOK{Stoker57,
title = {Water Waves: The Mathematical Theory with Applications},
publisher = {Interscience Publishers, New York, USA},
year = {1957},
author = {Stoker, J. J.},
keywords = {waves; shallow water; dam-break},
owner = {olivier},
timestamp = {2011.03.05}
}
@ARTICLE{Stomph02,
author = {Stomph, T. J. and De Ridder, N. and Steenhuis, T. S. and Van De Giesen,
N. C.},
title = {Scale effects of hortonian overland flow and rainfall-runoff dynamics:
laboratory validation of process-based model},
journal = {Earth Surface Processes and Landforms},
year = {2002},
volume = {27},
pages = {847--855},
abstract = {Hortonian runoff was measured in the laboratory from uniform slopes
of lengths of 1.5, 3.0, and 6.0 m for steady, highintensity rainstorms
with durations of 1.0 to 7.5 min. A clear reduction in runoff per
unit slope length was found as slope lengths were increased. This
effect becomes more pronounced with decreasing storm duration. The
runoff data were used to validate a simple process-based model that
combines the Philip-two-term infiltration equation with the kinematic
wave overland flow principle. The predicted and experimental results
agreed well. Laboratory findings were extrapolated with the aid of
the model to slopes and rainfall durations similar to those found
under West African conditions. The calculated reduction of runoff
per unit length is similar to reported observations. Thus, this process-based
model can largely explain the phenomenon of runoff reduction with
increasing slope length.},
doi = {10.1002/esp.356},
file = {Stomph02.pdf:Stomph02.pdf:PDF},
keywords = {runoff; model validation; laboratory experiments; slope length; scale},
owner = {olivier},
timestamp = {2008.05.03}
}
@ARTICLE{Stomph01,
author = {Stomph, T.~J. and De Ridder, N. and Van De Giesen, C.},
title = {A flume design for the study of slope length effects on runoff},
journal = {Earth Surface Processes and Landforms},
year = {2001},
volume = {26},
pages = {647--655},
abstract = {Recent publications from field and simulation studies indicate that
runoff per unit area decreases as the length of the slope being observed
is increased. This scale effect has been observed and documented
for slopes with a uniform infiltration capacity as well as for slopes
along which infiltration capacity is variable. This paper presents
the design and testing of a laboratory flume for the study of the
processes that lead to this scale effect, particularly for the case
of slopes covered with crops. The features of the flume include reliable
experimental control of soil water content prior to rainfall, high
intensity rainfall without erosion, uniform crop growth along the
slope, and the option of varying the infiltration rate independently
of rainfall and soil characteristics.},
file = {Stomph01.pdf:Stomph01.pdf:PDF},
keywords = {slope length; runoff; scale effect; laboratory experiments; flume},
owner = {olivier},
timestamp = {2008.05.08}
}
@ARTICLE{Strupczewski96,
author = {Strupczewski, W.~G. and Szymkiewicz, R.},
title = {Analysis of paradoxes arising from the {C}hezy formula with constant
roughness: {II}. Flow area-discharge curve},
journal = {Hydrological Sciences Journal},
year = {1996},
volume = {41},
pages = {675--682},
abstract = {The Chezy formula for steady flow in a uniform symmetrical channel
with constant slope-friction factor is mathematically examined. The
problem of the determination of the channel shape above a reference
level for a given rating curve of flow area vs discharge with a constant
ratio (m) of slope to mean velocity above a reference level is posed
and then solved. It is shown that there is a double solution of the
problem. One solution (being of main interest) is unlimited and gives
a shape widening with depth, while the other has an upper bound and
yields a shape narrow-ing with depth. It is shown that a solution
to the problem exists for a negative value of m. A relationship is
examined between the width-to-depth ratio of a rectangular initial
shape and a shape above a reference level for m values close to zero.
In particular, the solutions for negative values of m, i.e. for discharge
decreasing with increasing flow area, are evidently against common
sense.},
file = {Strupczewski96.pdf:Strupczewski96.pdf:PDF},
owner = {olivier},
timestamp = {2008.05.03}
}
@INCOLLECTION{Sudicky03,
author = {Sudicky, Edward A. and Vanderkwaak, Joel E. and Jones, Jon P. and
Keizer, Jon P. and Mclaren, Robert G. and Matanga, George B.},
title = {Fully-integrated modelling of surface and subsurface water flow and
solute transport: Model overview and application},
booktitle = {Water Resources Perspectives: Evaluation, Management and Policy},
publisher = {Elsevier},
year = {2003},
editor = {Abdulrahman S. Alsharhan and Warren W. Wood},
volume = {50},
series = {Developments in Water Science},
pages = {313 - 318},
abstract = {A physically-based, fully-integrated model has been recently developed
that considers water and solute transport on the two-dimensional
land surface and three-dimensional dual continua (i.e. porous mediummacropore)
subsurface under variably-saturated conditions. The two-dimensional
form of the nonlinear diffusion-wave equation, together with Manning's
equation to compute overland flow velocities, are employed on the
surface, while Richards' equation and Darcy's law are assumed to
hold in the subsurface. Two- and three-dimensional forms of the advection-dispersion
equation are used to describe solute transport on the surface and
within the subsurface, respectively. Linkage between the various
continua is through first-order, physically based flux relationships
or through pressure head and concentration continuity assumptions.
Full coupling of the flow regimes is achieved by solving and assembling
one system of discrete algebraic equations such that surface water
depths and subsurface pressure heads, as well as water fluxes between
continua, are determined simultaneously. Likewise, one system of
advective-dispersive transport equations is solved to obtain the
solute concentrations in the surface and subsurface flow domains.
Robust and efficient discretization and solution techniques are utilized
to achieve a high degree of computational efficiency. The model is
applied to the Laurel Creek watershed in Southern Ontario, which
is about 75 km2 in area and includes both urban and rural land uses.
Through past and ongoing field studies, the watershed is resonably
well characterized and is being monitored on an ongoing basis. In
addition to diverse land use and surface cover and more than 100m
of topographic relief, the watershed is underlain by a complex interconnected
sequence of sand and gravel aquifers used for water supply that are
separated by discontinuous clayey aquitards.},
doi = {DOI: 10.1016/S0167-5648(03)80027-8},
file = {Sudicky03.pdf:Sudicky03.pdf:PDF},
issn = {0167-5648},
keywords = {Darcy; Richards},
owner = {olivier},
timestamp = {2010.06.15},
url = {http://www.sciencedirect.com/science/article/B8G6B-4NV9Y9J-Y/2/faea0d479a6564ef67f2d59001002458}
}
@ARTICLE{Sulis10,
author = {Sulis, Mauro and Meyerhoff, Steven B. and Paniconi, Claudio and Maxwell,
Reed M. and Putti, Mario and Kollet, Stefan J},
title = {A comparison of two physics-based numerical models for simulating
surface water-groundwater interactions},
journal = {Advances in water resources},
year = {2010},
volume = {33},
pages = {456--467},
abstract = {Problems in hydrology and water management that involve both surface
water and groundwater are best addressed with simulation models that
can represent the interactions between these two ﬂow regimes. In
the current generation of coupled models, a variety of approaches
is used to resolve surface–subsurface interactions and other key
processes such as surface ﬂow propagation. In this study we compare
two physics-based numerical models that use a 3D Richards equation
representation of subsurface ﬂow. In one model, surface ﬂow is represented
by a fully 2D kinematic approximation to the Saint–Venant equations
with a sheet ﬂow conceptualization. In the second model, surface
routing is performed via a quasi-2D diffusive formulation and surface
runoff follows a rill ﬂow conceptualization. The coupling between
the land surface and the subsurface is handled via an explicit exchange
term resolved by continuity principles in the ﬁrst model (a fully-coupled
approach) and by special treatment of atmospheric boundary conditions
in the second (a sequential approach). Despite the signiﬁcant differences
in formulation between the two models, we found them to be in good
agreement for the simulation experiments conducted. In these numerical
tests, on a sloping plane and a tilted V-catchment, we examined saturation
excess and inﬁltration excess runoff production under homogeneous
and heterogeneous conditions, the dynamics of the return ﬂow process,
the differences in hydrologic response under rill ﬂow and sheet ﬂow
parameterizations, and the effects of factors such as grid discretization,
time step size, and slope angle. Low sensitivity to vertical discretization
and time step size was found for the two models under saturation
excess and homogeneous conditions. Larger sensitivity and differences
in response were observed under inﬁltration excess and heterogeneous
conditions, due to the different coupling approaches and spatial
discretization schemes used in the two models. For these cases, the
sensitivity to vertical and temporal resolution was greatest for
processes such as reinﬁltration and ponding, although the differences
between the hydrographs of the two models decreased as mesh and step
size were progressively reﬁned. In return ﬂow behavior, the models
are in general agreement, with the largest discrepancies, during
the recession phase, attributable to the different parameterizations
of diffusion in the surface water propagation schemes. Our results
also show that under equivalent parameterizations, the rill and sheet
ﬂow conceptualizations used in the two models produce very similar
responses in terms of hydrograph shape and ﬂow depth distribution.},
file = {Sulis10.pdf:Sulis10.pdf:PDF},
keywords = {subsurface hydrology; surface hydrology; groundwater modeling; boundary
conditions; surface-subsurface interactions; coupled systems; kinematic
wave; diffusion wave; Richards},
owner = {olivier},
timestamp = {2010.06.13}
}
@ARTICLE{Swartzendruber00,
author = {Swartzendruber, D.},
title = {Derivation of a two-term infiltration equation from the Green-Ampt
model},
journal = {Journal of Hydrologic},
year = {2000},
volume = {236},
pages = {247--251},
abstract = {For a uniform and inﬁnitely deep soil at constant initial volumetric
soil water content u n, the soil surface is subjected instantaneously
to a ponded-water head that increases with the square root of time
t 1/2 after the initial ponding of water. An integration procedure
is used in a rigorous derivation of the one-dimensional Green–Ampt
ﬂux equation. The resulting ordinary differential equation is solved
exactly to yield the two-term inﬁltration equation wherein the coefﬁcient
of t is the sated hydraulic conductivity, but the ponded-head t 1/2
function must be the same as the one found earlier by a different
but exact mathematical derivation. The present ﬁndings reveal and
describe this previously unknown kinship between the Green–Ampt inﬁltration
model and the two-term inﬁltration equation, and underscore in still
another way the serious limitations of the two-term equation.},
file = {Swartzendruber00.pdf:Swartzendruber00.pdf:PDF},
keywords = {Green–Ampt model; Inﬁltration; Unsaturated zone; Hydrology},
owner = {olivier},
timestamp = {2010.04.25}
}
@ARTICLE{Szpilka03,
author = {Szpilka, C.~M. and Kolar, R.~L.},
title = {Numerical analogs to Fourier and dispersion analysis: development,
verification, and application to the shallow water equations},
journal = {Advances in Water Resources},
year = {2003},
volume = {26},
pages = {649-662},
abstract = {Herein, we present numerical analogs to traditional Fourier and dispersion
analyses and validate them with well-characterized phase behavior
for classic ﬁnite diﬀerence and ﬁnite element (FE) discretizations
of the shallow water equations. Basically, the procedure is to introduce
a single wave with known amplitude and phase into the domain, propagate
the wave approximately one wavelength using some discretization scheme,
and then note its ﬁnal amplitude and phase. The ﬁnal state of the
wave is then compared with the expected wave form predicted by the
continuum equations to determine the propagation behavior of the
discretization. After validating the technique, we then examine two
case studies: (1) slope limiting schemes within the ﬁnite volume
framework and (2) lumping coeﬃcients within the selective lumping
FE framework. Of the three common slope limiters that we examined,
the Superbee limiter has the most promising phase behavior, as it
is the least dissipative while maintaining minimal phase error. Using
our numerical technique, we were also able to verify the range of
values that has been found to be most accurate in practice for the
selective lumping coeﬃcient.},
file = {Szpilka03.pdf:Szpilka03.pdf:PDF},
keywords = {Shallow water equations; Finite volume method; Fourier analysis; Dispersion
analysis; Numerical phase analysis},
owner = {olivier},
timestamp = {2010.01.26}
}
@ARTICLE{saintvenant71,
author = {de {S}aint-{V}enant, {A}dh\'emar {J}ean-{C}laude},
title = {Th\'eorie du mouvement non-permanent des eaux, avec application aux
crues des rivi\`eres et \`a l'introduction des mar\'ees dans leur
lit},
journal = {Comptes Rendus de l'Acad\'emie des {S}ciences},
year = {1871},
volume = {73},
pages = {147-154},
file = {saintvenant71.pdf:saintvenant71.pdf:PDF},
owner = {olivier},
timestamp = {2010.03.14}
}
@ARTICLE{Toth06,
author = {T\'oth, G\'abor and De Zeeuw, Darren L. and Gombosi, Tamas I. and
Powell, Kenneth G.},
title = {A parallel explicit/implicit time stepping scheme on block-adaptive
grids},
journal = {Journal of Computational Physics},
year = {2006},
volume = {217},
pages = {722 - 758},
number = {2},
abstract = {We present a parallel explicit/implicit time integration scheme well
suited for block-adaptive grids. The basic idea of the algorithm
is that the time stepping scheme can differ in the blocks of the
grid for a given time step: an explicit scheme is used in the blocks
where the local stability requirement is not violated and an implicit
scheme is used in the blocks where the explicit scheme would be unstable.
The implicit scheme is second order in time. The non-linear system
of equations is linearized with Newton linearization. The linear
system is solved with a preconditioned Krylov subspace iterative
scheme. The Schwarz type preconditioning is also based on the block
structure of the grid. We discuss load balancing for parallel execution
and the optimal choice of the time step for speed and robustness.
The parallel efficiency of the scheme is demonstrated for the equations
of magnetohydrodynamics with a geophysics application in three dimensions.
The control of the numerical divergence of the magnetic field in
combination with the explicit/implicit time stepping scheme is also
discussed.},
doi = {DOI: 10.1016/j.jcp.2006.01.029},
file = {Toth06.pdf:Toth06.pdf:PDF},
issn = {0021-9991},
keywords = {Models; numerical methods; numerical approximation; time dependent
initial-boundary value problems; parallel computation; compressible
fluids and gas dynamics; magnetohydrodynamics},
owner = {olivier},
timestamp = {2010.06.03},
url = {http://www.sciencedirect.com/science/article/B6WHY-4JDVP88-2/2/1a91b9bb4e1d42ef5d53a4b47f703870}
}
@ARTICLE{Tabuada95,
author = {Tabuada, M.A. and Rego, Z.J.C. and Vachaud, G. and Pereira, L.S.},
title = {Modelling of furrow irrigation. Advance with two-dimensional infiltration},
journal = {Agricultural Water Management},
year = {1995},
volume = {28},
pages = {201--221},
abstract = {A complete hydrodynamic furrow irrigation model (TRIDISUL) with two-dimensional
infiltration is presented and applied to blocked furrows. Richards’
equation in its two-dimensional form is used to quantify the infiltrated
volume in all sections along the furrow. To this equation an implicit
method is used and the system of equations is solved with the Gauss-Seidel
method. Saint Venant equations are solved using the Newton-Raphson
method and the double sweep algorithm. This model allows the simulation
of the interactions between the height of the water above the furrow
bed and soil water movement during the advance, supply, recession
and redistribution phases. It can give information on the position
of the wetting front in the soil through time, allowing the quantification
of the water stored in the root zone. It is therefore possible to
choose the best inflow discharge, spacing between furrows and furrow
shape to obtain the best irrigation efficiency.},
file = {Tabuada95.pdf:Tabuada95.pdf:PDF},
keywords = {furrow irrigation; two-dimensional infiltration; Richard's equation
in furrow irrigation; Saint-Venant},
owner = {olivier},
timestamp = {2010.06.13}
}
@ARTICLE{Tabuada95b,
author = {Tabuada, M.A. and Rego, Z.J.C. and Vachaud, G. and Pereira, L.S.},
title = {Two-dimensional infiltration under furrow irrigation: modelling,
its validation and applications},
journal = {Agricultural Water Management},
year = {1995},
volume = {27},
pages = {105-123},
abstract = {A model of water movement in soil during furrow irrigation using Richards
equation in its bidimensional form is presented. This model was developed
and tested for two types of soil and short closed furrows. It gives
information on the position of the wetting front in the soil with
time, thus allowing quantification of the water stored in the root
zone and computing the percolation losses during a given time interval
and relative to any given soil depth. In this model, an implicit
method is used and the resulting equation set is solved with the
Gauss-Seidel method. The model considers the initial conditions of
the soil before irrigation and the boundary conditions defined by
the water level in the furrow. Also, the model can be used to simulate
infiltration in different sections, thus providing better information
concerning the uniformity and efficiency of the irrigation.},
file = {Tabuada95b.pdf:Tabuada95b.pdf:PDF},
keywords = {two-dimensional infiltration; furrow irrigation; soil water diffusivity;
two dimensional flow; water content distribution; Richards},
owner = {olivier},
timestamp = {2010.06.13}
}
@ARTICLE{Takken99,
author = {Takken, I. and Beuselinck, L. and Nachtergaele, J. and Govers, G.
and Poesen, J. and Degraer, G.},
title = {Spatial evaluation of a physically-based distributed erosion model
(LISEM)},
journal = {Catena},
year = {1999},
volume = {37},
pages = {431--447},
number = {3-4},
month = oct,
abstract = {Generally, spatially distributed erosion models are 'validated' using
only data on runoff and sediment load collected at the catchment
outlet. This implies that one of the most important aspects of such
models, i.e. the prediction of the spatial variation of erosion and
deposition within the catchment is not at all tested. After an extreme
event. in a small agricultural catchment in the Belgium loam belt,
erosion and deposition patterns were mapped by measuring rill and
gully volumes and the thickness of sediment deposits. Volumes of
interrill erosion were estimated. From these data, the erosion and
deposition budget was calculated. The physically based soil erosion
model LISEM was then used to simulate the event. Model parameters
which could not be derived from the field data were estimated using
guidelines for LISEM proposed for South Limburg (Netherlands), an
area very near and similar to the Belgian catchment. The model was
calibrated on total erosion within the catchment by varying the infiltration
parameters. The results of the simulations show that the model predicts
reasonably well the overall sediment delivery ratio of the event
(ca. 60%). However, the observed variation in erosion rates for different
crop types is not well-predicted. In general, LISEM strongly overpredicts
erosion rates on fields with an important vegetation cover. Furthermore,
the correlation between predicted and measured erosion rates per
crop type at locations of the measured rill transects is weak. The
predicted pattern of deposition is generally similar to the mapped
deposition pattern. Discrepancies are mainly due to the fact that,
in some cases, important (unpredicted) deposition was observed upstream
of vegetation barriers or alongside roads. The study clearly shows
that it is not possible to evaluate the performance of spatially
distributed erosion models by using catchment outlet data alone.
Such a 'validation' can mask important spatial variations within
the catchment which are not accurately predicted. It is therefore
possible to obtain a good agreement between observed and simulated
outlet data, while the spatial pattern erosion and deposition within
the catchment is not well-described.},
file = {Takken99.pdf:Takken99.pdf:PDF},
owner = {Fred. DARBOUX},
review = {Sur la r�partition spatiale du ruissellement dans un bassin-versant},
timestamp = {2007.09.28}
}
@ARTICLE{Takken00,
author = {Takken, I. and Govers, G.},
title = {Hydraulics of interill overland flow on rough, bare soil surfaces},
journal = {Earth Surface Processes and Landforms},
year = {2000},
volume = {25},
pages = {1387--1402},
abstract = {A set of laboratory experiments on bare, rough soil surfaces was carried
out to study the relationship between soil surface roughness and
its hydraulic resistance. Existing models relating roughness coefficients
to a measure of surface roughness did not predict the hydraulic resistance
well for these surfaces. Therefore, a new model is developped to
predict the hydraulic resistance of the surface, based on detailed
surface roughness data. Roughness profiles perpendicular to the flow
are used to calculate the wet cross-sectional area and hydraulic
radius given a certain water level. The algorithm of Savat is then
applied to calculate the hydraulic resistance. The value for the
equivalent roughness, which is used in the algorithm of Savat, could
be predicted from the roughness profiles. Here, the tortuosity of
the submerged part of the surface was used, which means that the
calculated roughness depends on flow depth. The roughness increased
with discharge, due to the fact that rougher parts of the surface
became submerged at higher discharges. Therefore, a single measure
of surface roughness (e.g. random roughness) is not sufficient to
predict the hydraulic resistance. The proposed model allows the extension
of the flow over the surface with increasing discharge to be taken
into account, as well as the roughness within the submerged part
of the surface. Therefore, the model is able to predict flow velocities
reasonably well fromdischarge and roughness data only.},
file = {Takken00.pdf:Takken00.pdf:PDF},
keywords = {interrill flow; surface roughness; hydraulic resistance; modelling},
owner = {olivier},
timestamp = {2008.05.01}
}
@ARTICLE{Takken05,
author = {Takken, Ingrid and Govers, Gerard and Jetten, Victor and Nachtergaele,
Jeroen and Steegen, An and Poesen, Jean},
title = {The influence of both process descriptions and runoff patterns on
predictions from a spatially distributed soil erosion model},
journal = espl,
year = {2005},
volume = {30},
pages = {213--229},
number = {2},
month = feb,
abstract = {Spatially distributed, process-based erosion models have been built
to predict both erosion and deposition rates and patterns. However,
predictions by these models often do not meet our expectations. There
are several possible reasons for this, which can be subdivided into
three groups: (i) process descriptions within the models may be incomplete
or incorrect, leading to structural errors (model error); (ii) parameterization
is difficult leading to a high degree of uncertainty regarding model
inputs (input error); and (iii) the spatial implementation of the
model (the spatial discretization and the routing methods used) may
be inadequate. Hitherto, most studies of erosion model performance
have focused on input parameter uncertainty: the effects of process
description and spatial implementation of the model have often been
neglected. In this study an attempt is made to compare some aspects
of the effects of process description, parameter uncertainty and
model implementation on model performance. A series of model runs
was carried out to evaluate to what extent the predictions of the
spatially distributed erosion model LISEM are affected by the description
of the hydraulic resistance, the parameter values used to characterize
hydraulic resistance as well as the routing algorithm used to generate
the runoff pattern. The process description used for overland flow
resistance and velocity has a clear effect on the erosion and deposition
rates predicted by the model. However, relatively minor variations
in a single parameter value (hydraulic roughness) appear to affect
model output more strongly than variations in the process description
itself. The use of different routing algorithms leads to notably
different erosion and deposition patterns, but total erosion and
deposition rates are much less affected.},
doi = {10.1002/esp.1176},
file = {Takken05.pdf:Takken05.pdf:PDF},
keywords = {hydraulic resistance ; interrill ; rill ; runoff pattern ; erosion},
owner = {Fred. DARBOUX},
review = {Sur la r�partition spatiale du ruissellement dans un bassin-versant},
timestamp = {2007.09.28}
}
@ARTICLE{Takken01b,
author = {Takken, I. and Govers, G. and Jetten, V. and Nachtergaele, L. and
Steegen, A. and Poesen, J.},
title = {Effects of tillage on runoff and erosion patterns},
journal = {Soil \& Tillage Research},
year = {2001},
volume = {61},
pages = {55--60},
number = {1--2},
month = aug,
abstract = {Historically, research on water runoff and soil erosion has been conducted
mainly at the plot scale, with slope gradient being one of the dominant
controlling factors. However, tillage-induced roughness can also
significantly impact runoff and erosion, and therefore runoff patterns
on a field scale can be very different from the runoff pattern that
would be predicted from topography alone. A model and methodology
were developed to account for oriented tillage effects on runoff
patterns. Results suggests that the prediction of soil erosion and
deposition within a field, as well as total soil loss from a field,
can be significantly improved by combining the effects of tillage-induced
runoff patterns with detailed topographic data.},
file = {Takken01b.pdf:Takken01b.pdf:PDF},
keywords = {Tillage; Oriented roughness; Runoff pattern; Erosion pattern; Modeling;
Tilled soil surfaces; Depressional storage; Infiltration; Catchments;
Roughness},
owner = {Fred. DARBOUX},
review = {Effet des sillons sur la r\'epartition spatiale du ruissellement dans
un bassin-versant},
timestamp = {2007.09.28}
}
@ARTICLE{Takken01c,
author = {Takken, Ingrid and Govers, Gerard and Steegen, An and Nachtergaele,
Jeroen and Gu\'erif, J\'erome},
title = {The prediction of runoff flow directions on tilled fields},
journal = {Journal of Hydrology},
year = {2001},
volume = {248},
pages = {1--13},
number = {1--4},
month = jul,
abstract = {On tilled fields runoff directions may be affected by tillage induced
oriented roughness, causing runoff to flow along tillage lines instead
of topographic direction. That this has an important effect on runoff
and erosion patterns was already reported [Ludwig et al., Catena
25 (1995); Desmet and Govers, Catena 29 (1997); Souchere et al.,
J. Hydrol. 206 (1998); Takken et al., Catena 37 (1999)]. However,
limited research has been carried out to develop models that can
be used to predict whether flow will be in tillage or topographic
direction. In this study a wide range of data was collected on runoff
patterns observed in an agricultural catchment in the Belgian loess
belt. The data show that for more than 75% of the mapped areas on
hillslopes the flow was in direction of tillage. The data were analysed
to develop two logistic regression models to predict runoff direction.
The first model uses topographic slope, the angle between the tillage
orientation and aspect direction and the degree of oriented roughness
as input. In the second model, the effect of discharge on the flow
direction is also considered using unit contributing area as a substitute
variable. However, the application of the second model is complicated
and error-prone. Furthermore, application of both models to a validation
dataset showed only a minor increase in model performance when upslope
area is included (95 vs. 93% of correct predictions). Therefore,
it may be better to predict flow directions without taking discharge
into account. The model without unit contributing area predicted
very well the spatial variation of flow directions within a field
surveyed by [Desmet and Govers, Catena 29 (1997)]. Including this
logistic model in runoff and erosion models will result in much better
predictions of runoff and erosion patterns than can be obtained by
using the traditional approach of calculating a runoff pattern based
on topography only.},
doi = {10.1016/S0022-1694(01)00360-2},
file = {Takken01c.pdf:Takken01c.pdf:PDF},
keywords = {Tillage; Oriented roughness; Runoff pattern; Erosion pattern; Modelling},
owner = {Fred. DARBOUX},
review = {Effet des sillons sur la r\'epartition spatiale du ruissellement dans
un bassin-versant},
timestamp = {2007.09.28}
}
@ARTICLE{Takken01a,
author = {Takken, I. and Jetten, V. and Govers, G. and Nachtergaele, J. and
Steegen, A.},
title = {The effect of tillage-induced roughness on runoff and erosion patterns},
journal = {Geomorphology},
year = {2001},
volume = {37},
pages = {1--14},
number = {1--2},
month = mar,
file = {Takken01a.pdf:Takken01a.pdf:PDF},
keywords = {modelling; tillage direction; runoff pattern; erosion pattern},
owner = {Fred. DARBOUX},
review = {Effet des sillons sur la r\'epartition spatiale du ruissellement dans
un bassin-versant},
timestamp = {2007.09.28}
}
@ARTICLE{Tambroni10,
author = {Tambroni, N. and Ferrarin, C. and Canestrelli, A.},
title = {Benchmark on the numerical simulations of the hydrodynamic and morphodynamic
evolution of tidal channels and tidal inlets},
journal = {Continental Shelf Research},
year = {2010},
volume = {30},
pages = {963--983},
abstract = {A correct understanding of the hydrodynamics and morphodynamics of
tidal basins is of fundamental importance for the fate of the Venice
Lagoon, Italy. If on one hand, the development of sophisticated numerical
models is called for in order to reproduce the complexity of the
mechanisms governing the morphodynamic evolution of many natural
environments, including lagoons, on the other hand, a clear knowledge
of the reliability and limits of the results provided by these models
is crucial in order to establish the condition under which they can
be safely applied. To this aim, researchers involved in numerical
modeling in the framework of the recent Corila research programmes,
agreed to perform an accurate comparison of results provided by three
different numerical models, applying them to the test case offered
by the experimental investigations performed under controlled conditions
by Tambroni et al. (2005a). Here, we consider the following numerical
models: (i) a 2D ﬁnite element hydrodynamic model coupled with a
2D ﬁnite volume morphodynamic model (Deﬁna, 2000; Canestrelli et
al., 2007); (ii) a 2D ﬁnite element morphodynamic model (Ferrarin
et al., 2008); (iii) a 2D depth-averaged model for the inlet region,
coupled with a 1D model for the channel (Tambroni et al., 2005b).
A ﬁrst set of simulations concerns the ﬁxed bed case and shows that
all the models provide similar results: in particular, they are able
to predict the observed free surface oscillations satisfactorily,
while comparison with the measured velocity ﬁeld is less satisfactory.
Moreover, as far as the ﬂow ﬁeld at the inlet is concerned, the models
describe accurately the potential ﬂow into the channel during the
ﬂood phase, while they are not able to adequately reproduce the occurrence
of the ﬁne structure of the shear layers shed by the inlet edges
during the ebb phase. This limit is related to the shallow water
character of the models. As for the morphodynamics, the long term
equilibrium conﬁgurations of the bottom of the channel and of the
near inlet region show qualitative agreement with the experimental
observations, although in this case the differences between the results
provided by the distinct numerical approaches are more marked.},
doi = {10.1016/j.csr.2009.12.005},
file = {Tambroni10.pdf:Tambroni10.pdf:PDF},
keywords = {2D numerical modelling; tidal channels; tidal inlets morphodynamics;
Saint-Venant Exner; shallow water},
owner = {olivier},
timestamp = {2011.02.23}
}
@ARTICLE{Tang06,
author = {Tang, Shao-Qiang and Qian, Jing and Xiao, Jun},
title = {Wave interactions in Suliciu model for dynamic phase transitions},
journal = {Applied Mathematics and Mechanics},
year = {2006},
volume = {27},
pages = {91--98},
abstract = {Elementary waves in Suliciu model for dynamic phase transitions are
obtained through traveling wave analysis. For any given initial data
with two pieces of constant states, the Riemann solutions are constructed
as a combination of elementary waves. When the initial proﬁle contains
three pieces of constant states, the solution may be constructed
from the Riemann solutions, with each two adjacent states connected
by elementary waves. A new Riemann problem forms when these two waves
collide. Through the exploration of these Riemann problems, the outcome
of wave interactions may be classiﬁed in a suitable parametric space.},
doi = {10.1007/s10483-006-0112-z},
file = {Tang06.pdf:Tang06.pdf:PDF},
keywords = {phase transition; Suliciu model; wave interaction},
owner = {olivier},
timestamp = {2011.02.23}
}
@ARTICLE{Tardy91,
author = {Tardy, Y. and Meister, J.~J. and Perret, F. and Brunner, H.~R. and
Arditi, M.},
title = {Non-invasive estimate of the mechanical properties of peripheral
arteries from ultrasonic and photoplethysmographic measurements},
journal = {Clin. Phys. Physiol. Meas.},
year = {1991},
volume = {12},
pages = {39--54},
number = {1},
abstract = {The non-linear elastic response of arteries implies that their mechanical
properties depend strongly on blood pressure. Thus, dynamic measurements
of both the diameter and pressure curves over the whole cardiac cycle
are necessary to characterise properly the elastic behaviour of an
artery. We propose a novel method of estimating these mechanical
properties based on the analysis of the arterial diameter against
pressure curves derived from ultrasonic and photoplethysmographic
measurements. An ultrasonic echo tracking device has been developed
thet allows continuous recording of the internal diameter of peripheral
arteries. It measures the diameter 300 times per second with a resolution
of 2.5um. This system is linked to a commercially available light-plethysmograph
which continuously records the finger arterial pressure (0.25kPa
accuracy). Because of the finite pulse wave velocity, the separation
between the diameter and the pressure measurement sites causes a
hysteresis to appear in the recorded diameter-pressure curve. Using
a model based on haemodynamic considerations, the delay between the
diameter variations and the finger arterial pressure is first eliminated.
As the pulse wave velocity depnds on the pressure, the delay is determined
for each pressure value. The relationship between pressure and diameter
is then described by a non-linear mathematical expression with three
parameters, which best fits the recorded data. The dynamic local
behaviour of the vessel is fully characterised by these parameters.
Compliance, distensibility and pulse wave velocity can then be calculated
at each pressure level. Thus, the mechanical behaviour of peripheral
human arteries can now be characterised non-invasively over the pressure
range of the whole cardiac cycle. The results obtained in vivo on
human radial and brachial arteries show that a thorough analysis
of the compliance-pressure curves and their modifications (curving,
shift) is needed in order to compare two different vessels in a meaningful
way.},
file = {Tardy91.pdf:Tardy91.pdf:PDF},
keywords = {blood flow},
owner = {olivier},
timestamp = {2010.11.26}
}
@ARTICLE{Tassi07,
author = {Tassi, P.A. and Bokhove, O. and Vionnet, C.A.},
title = {Space discontinuous Galerkin method for shallow water flows--kinetic
and HLLC flux, and potential vorticity generation},
journal = {Advances in Water Resources},
year = {2007},
volume = {30},
pages = {998 - 1015},
number = {4},
abstract = {In this paper, a second order space discontinuous Galerkin (DG) method
is presented for the numerical solution of inviscid shallow water
flows over varying bottom topography. Novel in the implementation
is the use of HLLC and kinetic numerical fluxes1 in combination with
a dissipation operator, applied only locally around discontinuities
to limit spurious numerical oscillations. Numerical solutions over
(non-)uniform meshes are verified against exact solutions; the numerical
error in the L2-norm and the convergence of the solution are computed.
Bore-vortex interactions are studied analytically and numerically
to validate the model; these include bores as #breaking##waves# in
a channel and a bore traveling over a conical and Gaussian hump.
In these complex numerical test cases, we correctly predict the generation
of potential vorticity by non-uniform bores. Finally, we successfully
validate the numerical model against measurements of steady oblique
hydraulic jumps in a channel with a contraction. In the latter case,
the kinetic flux is shown to be more robust.},
doi = {DOI: 10.1016/j.advwatres.2006.09.003},
file = {Tassi07.pdf:Tassi07.pdf:PDF},
issn = {0309-1708},
keywords = {Discontinuous Galerkin; Finite elements; Shallow water flows; Discontinuity
detector; Bore-vortex interactions; Potential vorticity generation;
analytical solution},
owner = {olivier},
timestamp = {2010.06.06},
url = {http://www.sciencedirect.com/science/article/B6VCF-4MC0TP5-1/2/4f2bde469e62a2fa3cee9fb1f452d131}
}
@MASTERSTHESIS{Tatard05,
author = {Tatard, Lucile},
title = {Mod\'elisation num\'erique de la vitesse de ruissellement sur sol
nu ; implications sur la mod\'elisation de l'\'erosion / Numerical
modelling of flow velocities on a bare sandy soil; implications for
modelling soil erosion},
school = {Universit\'e {P}ierre \& {M}arie {C}urie},
year = {2005},
file = {Tatard05.pdf:Tatard05.pdf:PDF},
owner = {olivier},
timestamp = {2009.09.30}
}
@ARTICLE{Tatard08,
author = {Tatard, L. and Planchon, O. and Wainwright, J. and Nord, G. and Favis-Mortlock,
D. and Silvera, N. and Ribolzi, O. and Esteves, M. and Huang, Chi-hua},
title = {Measurement and modelling of high-resolution flow-velocity data under
simulated rainfall on a low-slope sandy soil},
journal = {Journal of Hydrology},
year = {2008},
volume = {348},
pages = {1-12},
number = {1-2},
month = jan,
abstract = {The study presented here is focussed on the question of the hydraulic
nature of the threshold that allows a rill to start. A rainfall-simulation
experiment was carried out to produce high-resolution flow-velocity
data. The experiment employed a 10 m × 4 m experimental plot with
a 1% slope, which had been previously eroded and had a small rill
formed in the middle. The experiment consisted of a 2 h 15′-long
rainfall at a constant intensity of 69 mm h−1. Surface elevation
was measured before rainfall at a horizontal resolution of 2.5 cm
across, and 5 cm along the slope direction. During rainfall, flow-velocities
were measured at 68 locations on the plot with the salt velocity
gauge technology, an automated, miniaturized device based on the
inverse modelling of the propagation of a salt plume. The experiment
led to the collection of flow-velocity measurements which are novel
in three ways: (i) the small size of the measured section, which
was only 10-cm long and 1-cm wide, (ii) the wide range of measured
flow-velocities, which ranged from 0.006 m s−1 to 0.27 m s−1 and,
(iii) the large number of measured locations. The flow-velocity field
was simulated with three models: PSEM_2D solves the Saint-Venant
equations in 2D, MAHLERAN uses a 1D kinematic wave in the slope direction
coupled with a 2D flow-routing algorithm, and Rillgrow2, which involves
an empirical runoff algorithm that is close in principle to the diffusion-wave
equation in 2D. The Darcy–Weisbach friction factor (ff) and the infiltration
parameters were calibrated in all cases to investigate the capabilities
of the different models to reproduce flow hydraulics compatible with
the onset of rilling. In a first set of numerical experiments, ff
was set uniform, and calibration used only the hydrograph. The comparison
of simulated and observed flow-velocity field showed that PSEM_2D
was the most satisfying model, at the cost of longer computational
time. MAHLERAN gave surprisingly good results with regards to the
simplicity of the model and its low computational needs. However,
all models largely underestimated the highest velocity values, located
in the rill. Furthermore, none of the models was able to simulate
the Reynolds (Re) and Froude (Fr) numbers. The next numerical experiment
was done with PSEM_2D. Non-uniform ff values were calibrated by fitting
the simulated flow-velocity field to the observed one. The latter
simulation produced realistic simulations of Re and Fr. The hydraulic
conditions at the transition from interrill flow to rill flow are
discussed. The results support the theory that supercritical flows
are a necessary condition for a rill to emerge from a smooth surface.},
doi = {10.1016/j.jhydrol.2007.07.016},
file = {Tatard08.pdf:Tatard08.pdf:PDF},
keywords = {Rainfall-simulation; Water erosion; Erosion models; Rill; Interrill;
Senegal; experiment; Velocity measurement; depth measurement},
owner = {olivier},
timestamp = {2008.10.16}
}
@ARTICLE{Taylor74,
author = {Taylor, C. and Al-Mashidani, G. and Davis, J.~M.},
title = {A finite element approach to watershed runoff},
journal = {Journal of Hydrology},
year = {1974},
volume = {21},
pages = {231--246},
abstract = {A numerical finite element based implicit recurrence relationship
is developed for the analysis of watershed direct runoff problems.
The algorithm is presented in a two dimensional form for the full
momentum and continuity equations and unidimensionally for the kinematic
wave theory. Since the whole domain is represented and solved as
a single set of matrix equations, the advent of shocks for domains
where appreciable changes in slope and/or resistance to flow occur,
is immediately distinguishable.},
file = {Taylor74.pdf:Taylor74.pdf:PDF},
keywords = {kinematic; Saint-Venant; hydrograph},
owner = {olivier},
timestamp = {2010.05.03}
}
@BOOK{Telles05,
title = {C++ {T}rucs et {A}stuces pour les {N}uls},
publisher = {First {I}nteractive},
year = {2005},
author = {Telles, Matthew},
owner = {olivier},
timestamp = {2009.11.25}
}
@ARTICLE{Teyssier06,
author = {Teyssier, Romain and Fromang, S\'ebastien and Dormy, Emmanuel},
title = {Kinematic dynamos using constrained transport with high order Godunov
schemes and adaptive mesh refinement},
journal = {Journal of Computational Physics},
year = {2006},
volume = {218},
pages = {44 - 67},
number = {1},
abstract = {We propose to extend the well-known MUSCL-Hancock scheme for Euler
equations to the induction equation modeling the magnetic field evolution
in kinematic dynamo problems. The scheme is based on an integral
form of the underlying conservation law which, in our formulation,
results in a #finite-surface# scheme for the induction equation.
This naturally leads to the well-known #constrained##transport# method,
with additional continuity requirement on the magnetic field representation.
The second ingredient in the MUSCL scheme is the predictor step that
ensures second order accuracy both in space and time. We explore
specific constraints that the mathematical properties of the induction
equations place on this predictor step, showing that three possible
variants can be considered. We show that the most aggressive formulations
(referred to as C-MUSCL and U-MUSCL) reach the same level of accuracy
as the other one (referred to as Runge-Kutta), at a lower computational
cost. More interestingly, these two schemes are compatible with the
adaptive mesh refinement (AMR) framework. It has been implemented
in the AMR code RAMSES. It offers a novel and efficient implementation
of a second order scheme for the induction equation. We have tested
it by solving two kinematic dynamo problems in the low diffusion
limit. The construction of this scheme for the induction equation
constitutes a step towards solving the full MHD set of equations
using an extension of our current methodology.},
doi = {DOI: 10.1016/j.jcp.2006.01.042},
file = {Teyssier06.pdf:Teyssier06.pdf:PDF},
issn = {0021-9991},
keywords = {Magnetohydrodynamics and electrohydrodynamics; hydrodynamic and hydromagnetic
problems; finite difference methods; induction equation; magnetohydrodynamics;
Godunov scheme; adaptative mesh refinement; numerical schemes},
owner = {olivier},
timestamp = {2010.06.03},
url = {http://www.sciencedirect.com/science/article/B6WHY-4JHMJX2-3/2/4499999d24defe2d357cb3558a1a38f4}
}
@ARTICLE{Thacker81,
author = {Thacker,William~Carlisle},
title = {Some exact solutions to the nonlinear shallow-water wave equations},
journal = {Journal of Fluid Mechanics Digital Archive},
year = {1981},
volume = {107},
pages = {499-508},
number = {-1},
abstract = {These exact solutions correspond to time-dependent motions in parabolic
basins. A characteristic feature is that the shoreline is not fixed.
It is free to move and must be determined as part of the solution.
In general, the motion is oscillatory and has the appropriate small-amplitude
limit. For the case in which the parabolic basin reduces to a flat
plane, there is a solution for a flood wave. These solutions provide
a valuable test for numerical models of inundating storm tides.},
doi = {10.1017/S0022112081001882},
eprint = {http://journals.cambridge.org/article_S0022112081001882},
file = {Thacker81.pdf:Thacker81.pdf:PDF},
owner = {olivier},
timestamp = {2009.07.04},
url = {http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=389055&fulltextType=RA&fileId=S0022112081001882}
}
@ARTICLE{Thanh08,
author = {Thanh, M.~D. and {F}azlul {K}arim, Md. and Ismail, A.~I.~Md.},
title = {Well-balanced scheme for shallow water equations with arbitrary topography},
journal = {Int. J. Dynamical Systems and Differential Equations},
year = {2008},
volume = {1},
pages = {196-204},
number = {3},
abstract = {We study the one-dimensional shallow water equations with arbitrary
topography.
We ﬁrst verify that traditional discretisations of the right-hand
side of the equation of the
balance of momentum give unsatisfactory results. We then show that
the equations can be
written in the divergence form for stationary waves. Motivated by
the encouraging results for
the well-balanced scheme for ﬂuid ﬂows in a nozzle with variable cross-section
in Kröner and
Thanh (2005), we construct a numerical scheme based on stationary
waves. This scheme is
constructed so that it maintains equilibrium states. Tests show that
our scheme is both stable
and fast.},
file = {Thanh08.pdf:Thanh08.pdf:PDF},
keywords = {shallow water; conservation law; well-balanced scheme; topography},
owner = {olivier},
timestamp = {2009.11.13}
}
@ARTICLE{Therrien01,
author = {Therrien, Ren\'e and Sudicky, E.A.},
title = {Well bore boundary conditions for variably saturated flow modeling},
journal = {Advances in Water Resources},
year = {2001},
volume = {24},
pages = {195--201},
abstract = {Well bore boundary conditions are incorporated in a three-dimensional
finite element model that solves the variably saturated groundwater
flow equation. One-dimensional line elements, which are used to discretize
the flow equation along the well screen, are superimposed onto three-dimensional
porous media elements. The use of line elements allows the inclusion
of well bore storage effects, and also avoids the need of a second
iteration step during the solution of the nonlinear flow equation
to achieve the correct head and flux distribution along the well
screen. Verification of the formulation is done by comparing results
from the numerical model to an analytical solution for pumping in
an unconfined aquifer. Simulation of convergent±divergent flow into
a heterogeneous unconfined aquifer illustrates that the model accounts
for the aquifer heterogeneity by producing a variable fluid flux
distribution along the well screen. This result has implications
for the correct modeling of contaminant transport to the well.},
file = {Therrien01.pdf:Therrien01.pdf:PDF},
keywords = {groundwater flow; variably saturated; modeling; well; boundary conditions;
Richards; van Genuchten},
owner = {olivier},
timestamp = {2010.06.14}
}
@ARTICLE{Therrien96,
author = {Therrien, Ren\'e and Sudicky, E.A.},
title = {Three-dimensional analysis of variably-saturated flow and solute
transport in discretely-fractured porous media},
journal = {Journal of Contaminant Hydrology},
year = {1996},
volume = {23},
pages = {1--44},
abstract = {A discrete fracture, saturated-unsaturated numerical model is developed
where the porous matrix is represented in three dimensions and fractures
are represented by two-dimensional planes. This allows a fully three-dimensional
description of the fracture network connectivity. Solute advection
and diffusion in the porous matrix are also directly accounted for.
The variably-saturated flow equation is discretized in space using
a control volume finite-element technique which ensures fluid conservation
both locally and globally. Because the relative permeability and
saturation curves for fractures may be highly nonlinear, and in strong
contrast to those of the matrix, the robust Newton-Raphson iteration
method is implemented according to the efficient procedure of Kropinski
(1990) and Forsyth and Simpson (1991) to solve the variably-saturated
flow equation. Upstream weighting of the relative permeabilities
is used to yield a monotone solution that lies in the physical range
and adaptive time stepping further enhances the efficiency of the
solution process, A time-marching Galerkin finite-element technique
is used to discretize the solute transport equation. Although the
methodology is developed in a finite-element frame-work, a finite-difference
discretization for both groundwater flow and solute transport can
be mimicked through a manipulation of the influence coefficient technique.
The use of an ILU-preconditioned ORTHOMIN solver permits the fast
solution of matrix equations having tens to hundreds of thousands
of unknowns. Verification examples are presented along with illustrative
problems that demonstrate the complexity of variably-saturated flow
and solute transport in fractured systems.},
file = {Therrien96.pdf:Therrien96.pdf:PDF},
keywords = {variably-saturated flow; Richards; van Genuchten; solute transport},
owner = {olivier},
timestamp = {2010.06.14}
}
@MASTERSTHESIS{Thoms97,
author = {Thoms, R. Brad},
title = {Simulating fully coupled overland and variably satured subsurface
flow using {MODFLOW}},
school = {OGI School of Science and Engineering at Oregon Health and Science
University},
year = {1997},
file = {Thoms97.pdf:Thoms97.pdf:PDF},
keywords = {kinematic wave; MODFLOW; Philip's solution; infiltration},
owner = {olivier},
timestamp = {2010.04.24}
}
@ARTICLE{Thual10,
author = {Thual, O. and Plumerault, L.-R. and Astruc, D.},
title = {Linear stability of the 1D Saint-Venant equations and drag parameterizations},
journal = {Journal of Hydraulic Research},
year = {2010},
volume = {48},
pages = {348--353},
number = {3},
abstract = {The stability of the homogeneous and steady ﬂow based on the one-dimensional
Saint-Venant equations for free surface and shallow-water ﬂows of
constant slope is derived and displayed through graphs. With a suitable
choice of units, the small and large drag limits, respectively, correspond
to the small and large spatio-temporal scales of a linear system
only controlled by the Froude number and two other dimensionless
numbers associated with the bottom drag parameterization. Between
the small drag limit, with the two families of marginal and non-dispersive
shallow-water waves, and the large drag limit, with the marginal
and non-dispersive waves of the kinematic wave approximation, dispersive
roll waves are detailed. These waves are damped or ampliﬁed, depending
on the value of the three control parameters. The spatial generalized
dispersion relations are also derived indicating that the roll-wave
instability is of the convective type for all drag parameterizations.},
doi = {doi:10.1080/00221686.2010.481837},
file = {Thual10.pdf:Thual10.pdf:PDF},
keywords = {convective instability; kinematic-wave approximation; roll-wave instability;
Saint-Venant equations; shallow water},
owner = {olivier},
timestamp = {2010.07.01}
}
@BOOK{Toro97,
title = {Riemann solvers and numerical methods for fluid dynamics},
publisher = {Springer-Verlag},
year = {1997},
author = {Toro, Eleuterio~F.},
pages = {xviii+592},
address = {Berlin},
note = {A practical introduction},
isbn = {3-540-61676-4},
mrclass = {76M20 (35L65 65M12 76N15)},
mrnumber = {MR1474503 (98h:76099)},
mrreviewer = {Randall J. LeVeque},
owner = {olivier},
timestamp = {2009.08.24}
}
@ARTICLE{Touma09,
author = {Touma, R.},
title = {Central unstaggered finite volume schemes for hyperbolic systems:
Applications to unsteady shallow water equations},
journal = {Applied Mathematics and Computation},
year = {2009},
volume = {213},
pages = {47 - 59},
number = {1},
abstract = {A class of central unstaggered finite volume methods for approximating
solutions of hyperbolic systems of conservation laws is developed
in this paper. The proposed method is an extension of the central,
non-oscillatory, finite volume method of Nessyahu and Tadmor (NT).
In contrast with the original NT scheme, the method we develop evolves
the numerical solution on a single grid; however ghost cells are
implicitly used to avoid the resolution of the Riemann problems arising
at the cell interfaces. We apply our method and solve classical one
and two-dimensional unsteady shallow water problems. Our numerical
results compare very well with those obtained using the original
NT method, and are in good agreement with corresponding results appearing
in the recent literature, thus confirming the efficiency and the
potential of the proposed method.},
doi = {DOI: 10.1016/j.amc.2009.02.059},
file = {Touma09.pdf:Touma09.pdf:PDF},
issn = {0096-3003},
keywords = {Unstaggered central schemes; shallow water equations; source terms;
non-oscillatory; limiters; finite volume methods},
owner = {olivier},
timestamp = {2010.06.03},
url = {http://www.sciencedirect.com/science/article/B6TY8-4VT5TH1-2/2/48bb37b35dfd37d153c5c5132dad87f1}
}
@ARTICLE{Tran08,
author = {Tran, Quang~Huy},
title = {Second-order slope limiters for the simultaneous linear advection
of (not so) independent variables},
journal = {Commun. Math. Sci.},
year = {2008},
volume = {6},
pages = {569-593},
number = {3},
abstract = {We propose a strategy to perform second-order enhancement using slope-limiters
for the simultaneous linear advection of several scalar variables.
Our strategy ensures a discrete min-max principle not only for each
variable but also for any number of non-trivial combinations of them,
which represent control variables. This problem arises in ﬂuid mechanics
codes using the Arbitrary Lagrange-Euler formalism, where the additional
monotonicity property on control variables is required by physical
considerations within the remap step.},
file = {Tran08.pdf:Tran08.pdf:PDF},
keywords = {Linear advection; min-max principle; slope reconstruction; Arbitrary
Lagrange-Euler (ALE) formalism},
owner = {olivier},
timestamp = {2009.07.27}
}
@ARTICLE{Troch02,
author = {Troch, Peter and van Loon, Emiel and Hilberts, Arno},
title = {Analytical solutions to a hillslope-storage kinematic wave equation
for subsurface flow},
journal = {Advances in Water Resources},
year = {2002},
volume = {25},
pages = {637--649},
number = {6},
abstract = {Hillslope response has traditionally been studied by means of the
hydraulic groundwater theory. Subsurface ﬂow from a one-dimensional
hillslope with a sloping aquifer can be described by the Boussinesq
equation [Mem. Acad. Sci. Inst. Fr. 23 (1) (1877) 252–260]. Analytical
solutions to Boussinesq’s equation are very useful to understand
the dynamics of subsurface ﬂow processes along a hillslope. In order
to extend our understanding of hillslope functioning, however, simple
models that nonetheless account for the three-dimensional soil mantle
in which the ﬂow processes take place are needed. This three-dimensional
soil mantle can be described by its plan shape and by the proﬁle
curvatures of terrain and bedrock. This plan shape and proﬁle curvature
are dominant topographic controls on ﬂow processes along hillslopes.
Fan and Bras [Water Resour. Res. 34 (4) (1998) 921–927] proposed
a method to map the three-dimensional soil mantle into a one-dimensional
storage capacity function. Continuity and a kinematic form of Darcy’s
law lead to quasi-linear wave equations for subsurface ﬂow solvable
with the method of characteristics. Adopting a power function of
the form proposed by Stefano et al. [Water Resour. Res. 36 (2) (2000)
607–617] to describe the bedrock slope, we derive more general solutions
to the hillslope-storage kinematic wave equation for subsurface ﬂow,
applicable to a wide range of complex hillslopes. Characteristic
drainage response functions for nine distinct hillslope types are
computed. These nine hillslope types are obtained by combining three
plan curvatures (converging, uniform, diverging) with three bedrock
proﬁle curvatures (concave, straight, convex). We demonstrate that
these nine hillslopes show quite diﬀerent dynamic behaviour during
free drainage and rainfall recharge events.},
doi = {DOI: 10.1016/S0309-1708(02)00017-9},
file = {Troch02.pdf:Troch02.pdf:PDF},
issn = {0309-1708},
keywords = {Hillslope hydrology; Subsurface flow; Kinematic wave approximation;
Method of characteristics; Boussinesq; Darcy; analytcal solutions},
owner = {olivier},
timestamp = {2010.06.15},
url = {http://www.sciencedirect.com/science/article/B6VCF-45BRPX8-1/2/1e0a13addb2db0100e027d60eb7a85ea}
}
@ARTICLE{Tsihrintzis00,
author = {Tsihrintzis, V.~A. and Madiedo, E.~E.},
title = {Resistance determination in marsh wetlands},
journal = {Water Resources Management},
year = {2000},
volume = {14},
pages = {285--309},
file = {Tsihrintzis00.pdf:Tsihrintzis00.pdf:PDF},
keywords = {Chezy equation; Darcy-Weisbach equation; hydraulic resistance; Manning's
equation; marsh; retardance curves; roughness; vegetation; wetland},
owner = {olivier},
timestamp = {2008.05.01}
}
@ARTICLE{Turitsyn93,
author = {Turitsyn, Sergei K.},
title = {Blow-up in the Boussinesq equation},
journal = {Physical Review E},
year = {1993},
volume = {47},
pages = {796--799},
abstract = {The Boussinesq equation is known to be the fundamental nonlinear model,
describing wave propagation in a weakly dispersive nonlinear medium.
In this paper, we prove the existence of the collapse dynamics for
the two basic forms of the Boussinesq equation in the case of the
periodic boundary conditions. The sufficient criterion of the blow-up
is found analytically.},
file = {Turitsyn93.pdf:Turitsyn93.pdf:PDF},
owner = {olivier},
timestamp = {2011.03.03}
}
@MASTERSTHESIS{Turner06,
author = {Turner, Ellen},
title = {Comparison of infiltration equations and their field validation by
rainfall simulation},
school = {Faculty of the Graduate School of the University of Maryland, College
Park},
year = {2006},
abstract = {Infiltration is a complex process with many factors contributing to
the rate. Different approximate equations for infiltration differ
in the parameters they require and predict different infiltration
rate curves. Five equations including those of Kostiakov, Horton,
Holtan, Philip and Green-Ampt were compared to determine which one
most accurately predicted measured infiltration rates from rainfall
simulation events at two different locations. Parameters were developed
from measured infiltration data and laboratory analyses of soil samples.
The Green-Ampt, Holtan and Philip equations with respective root mean
squared errors of 0.15, 0.17, and 0.19 cmh-1, provided the first,
second and third best estimates of infiltration rates, for observed
infiltration data at the University of Maryland’s Research and Education
Center in Upper Marlboro, Maryland. An atypical infiltration curve
was},
file = {Turner06.pdf:Turner06.pdf:PDF},
keywords = {infiltration rate equation; rainfall simulation; parameter calibration;
model validation; approximate infiltration model; Kostiakov; Horton;
Holtan; Philip; Smith and Parlange; Green-Ampt},
owner = {olivier},
timestamp = {2010.04.24}
}
@ARTICLE{Vazquez-Cendon99,
author = {V\`azquez-Cend\`on, M.~E.},
title = {Improved treatment of source terms in upwind schemes for the shallow
water equations in channels with irregular geometry},
journal = {Journal of Computational Physics},
year = {1999},
volume = {148},
pages = {497--526},
abstract = {This paper deals with the numerical solution of the shallow water
equations in channels with irregular geometry but with a locally
rectangular cross section. This type of channel leads to the presence
of source terms involving the gradient of the depth and the breadth
of the channel. Extensions of the Q-scheme of van Leer and Roe are
proposed which generate natural upwind discretizations of the source
terms. The consistency of the proposed schemes is analyzed. A stationary
solution that emphasizes the source terms considered is obtained
which is used to test the proposed extensions in terms of a conservation
property. A low-order asymptotic unsteady analytical solution for
a small Froude number is also obtained. The numerical results presented
confirm the improved properties of the proposed schemes for a transient
test problem.},
file = {Vazquez-Cendon99.pdf:Vazquez-Cendon99.pdf:PDF},
keywords = {upwind schemes; source terms; shallow water equations; channels with
irregular geometry},
owner = {olivier},
timestamp = {2008.05.04}
}
@MASTERSTHESIS{Lencina07,
author = {Valc\'{a}rcel Lencina, Ignacio},
title = {Comparison between {1D} and {2D} models to analyze the dam break
wave using the {FEM} method and the shallow water equations},
school = {Department of Land and Water Resources Engineering. Royal Institute
of Technology},
year = {2007},
address = {Stockholm, Suede},
month = may,
abstract = {The simulation of exceptional events characterised by high hydraulic
and hydrogeologic risk is an actual problem for the scientific community,
working in the topic of environmental protection. There have been
around 200 notable dam and reservoir failures worldwide in the twentieth
century. These failures have caused severe devastation in the valleys
downstream both in terms of lives lost and widespread damage to infrastructure
and property. The flood wave caused by a dam failure can result in
the loss of human lives and have a severe economic impact. Therefore,
significant efforts have been carried out over the years to produce
methods for determination of the extent and timing of the flood wave.
This work describes and compares two models for solving the dam break
problem using the FEM (finite element method). Both models are based
on solving the Shallow Water equations. The first model is one-dimensional
and the second is two-dimensional. Most simulation studies for the
dam break problem are currently attempted using one-dimensional models,
and we investigate here the possibility of moving to two-dimensional
simulations solving and comparing the two models with a finite element
analysis and solver software package called Comsol Multiphysics.
Comsol Multiphysics is a modelling package for the simulation of
any physical process describable with partial differential equations
(PDEs). The hydraulic analysis of the dam break problem from a different
point of view has been done in this work, that is, using a generic
tool not adapted to solve this kind of problems. This fact helps
us to understand the process entirely because of the necessity of
introducing all the conditions and equations. We are able in this
way to control all the details within the model, even though we have
other problems in relation with the generic nature of the program.
A simple example of the collapse of a dam is used to demonstrate
the capability of the two models. The instantaneous collapse over
wet bed has been studied. Some difficulties are encountered simulating
dry bed condition for the appearance of negative depths or velocity
overshoots. The important influence of the bathymetry has been also
demonstrated during the simulations.},
file = {Lencina07.pdf:Lencina07.pdf:PDF},
keywords = {Shallow water equations; dam-break simulation; finite elements method;
bathymetry},
owner = {Fred. DARBOUX},
pages = {39},
timestamp = {2008.07.24}
}
@ARTICLE{Valiani02,
author = {Valiani, A. and Caleffi, V. and Zanni, A.},
title = {Case {S}tudy : {M}alpasset {D}am-{B}reak {S}imulation using a {T}wo-{D}imensional
{F}inite {V}olume {M}ethods},
journal = {Journal of {H}ydraulic {E}ngineering},
year = {2002},
volume = {128},
pages = {460-472},
number = {5},
month = May,
file = {Valiani02.pdf:Valiani02.pdf:PDF},
owner = {olivier},
timestamp = {2010.02.17}
}
@INPROCEEDINGS{Valiani99a,
author = {Valiani, A. and Caleffi, V. and Zanni, A.},
title = {Finite volume scheme for {2D} shallow-water equations. {A}pplication
to {M}alpasset dam-break},
booktitle = {the $4^{th}$ {CADAM} {W}orkshop, {Z}aragoza},
year = {1999},
pages = {63-94},
file = {Valiani99a.pdf:Valiani99a.pdf:PDF},
owner = {olivier},
timestamp = {2010.02.17}
}
@INPROCEEDINGS{Valiani99b,
author = {Valiani, A. and Caleffi, V. and Zanni, A.},
title = {Finite {V}olume scheme for {2D} {S}hallow-{W}ater equations: {A}pplication
to a flood event in the {T}oce river},
booktitle = {the $4^{th}$ {CADAM} {W}orkshop, {Z}aragoza},
year = {1999},
pages = {185-206},
month = Nov,
file = {Valiani99b.pdf:Valiani99b.pdf:PDF},
owner = {olivier},
timestamp = {2010.02.17}
}
@ARTICLE{VanSteenhoven86,
author = {Van Steenhoven, A. A. and Van Dongen, M. E. H.},
title = {Model studies of the aortic pressure rise just after valve closure},
journal = {J. Fluid. Mech.},
year = {1986},
volume = {166},
pages = {93--113},
abstract = {Model experiments are performed in a long, thin-walled, fluid-filled,
latex tube in which the fluid is locally suddenly stopped, starting
from a steady flow, thus simulating the wave phenomenon generated
by the final closure of the aortic valve. The resulting waveform
is determined as it propagates upstream. The effect of a local step-wise
change in compliance close to the valve, representing the aortic
sinus section, is investigated. The observed phenomena are analysed
by means of a quasi-one-dimensional model, solved by the method of
characteristics, taking into account the influence of nonlinearities,
wall shear stress, viscoelastic wall properties and wave reflections.
The theoretical computations are well confirmed by the experimental
results. the pressure jump, induced by the valve closing, appeared
to be slightly affected by nonlinearities. The decrease of the pressure
jump while the propagating upstream and the gradual pressure increase
that follows the pressure jump are caused by the effect of wall shear
stress. The local change in compliance generates the expected wave
reflections and has a strong influence on the rise-time of the wave
front. The experiments confirmed the prediction that the wall viscoelasticity
is the dominant factor in the gradual decay of the slope of the wave.},
file = {VanSteenhoven86.pdf:VanSteenhoven86.pdf:PDF},
keywords = {blood flow},
owner = {olivier},
timestamp = {2011.03.03}
}
@ARTICLE{Varado06,
author = {Varado, N. and Braud, I. and Ross, P. J. and Haverkamp, R.},
title = {Assessment of an efficient numerical solution of the 1D Richards'
equation on bare soil},
journal = {Journal of Hydrology},
year = {2006},
volume = {323},
pages = {244--257},
abstract = {A new numerical scheme has been proposed by Ross [Ross, P.J., 2003.
Modeling soil water and solute transport—fast, simpliﬁed numerical
solutions. Agronomy Journal 95, 1352–1361] to solve the 1D Richards’
equation [Richards, L.A., 1931. Capillary conduction of liquids through
porous medium. Physics 1, 318–333]. This non-iterative solution uses
the description of soil properties proposed by Brooks and Corey [Brooks,
R.H., Corey, A.T., 1964. Hydraulic properties of porous media. Colorado
State University, Fort Collins]. It allows the derivation of an analytical
expression for the Kirchhoff potential used in the calculation of
water ﬂuxes. The degree of saturation is used as the dependent variable
when the soil is unsaturated and the Kirchhoff potential is used
in case of saturation. A space and time discretisation scheme leads
to a tridiagonal set of linear equations that is solved non-iteratively.
We propose in this paper an extensive test of this numerical method,
evaluated only on a single case by Ross. The tests are conducted
in two steps. First, the solution is
assessed against two analytical solutions. The ﬁrst one [Basha, H.A.,
1999. Multidimensional linearized nonsteady inﬁltration with prescribed
boundary conditions at the soil surface. Water Resources Research
35(1), 75–93] provides the water content proﬁle when simpliﬁed soil
characteristics such as the exponential law of Gardner [Gardner,
W.R., 1958. Some steady-state solutions of the unsaturated moisture
ﬂow equations with application to evaporation from a water table.
Soil Science 85, 228–232] are used. The Ross solution is compared
to this solution on eight different soils that were ﬁtted to this
law. Analytical solution with the Brooks and Corey models is not
available at the moment for the moisture proﬁle but some exist for
cumulative inﬁltration. Therefore, the second analytical solution,
used in this study, is the one developed by Parlange et al. [Parlange,
J.-Y., Haverkamp, R., Touma, J., 1985. Inﬁltration under ponded conditions:
1. Optimal analytical solution and comparison with experimental observations.
Soil Science 139(4), 305–311] and Haverkamp et al. [Haverkamp, R.,
Parlange, J.-Y., Starr, J.L., Schmitz, G., Fuentes, C., 1990. Inﬁltration
under ponded conditions: 3. A
predictive equation based on physical parameters. Soil Science 149(5),
292–300]. The various parameters of this solution are written for
the Brooks and Corey models and the cumulative inﬁltration calculated
by the Ross solution is compared to this analytical solution.
The second part of the test is a comparison with a reference model:
the SiSPAT (Simple Soil Plant Atmosphere Transfer) model, which provides
a reference iterative solution of the soil water ﬂow equation. A
wide range of simulations is performed, with various soil types (homogeneous
or not), various climate forcing and several initial conditions.
It allows the comparison of various variables such as deep drainage,
soil moisture proﬁle, surface ponding, and evaporation under non-uniform
initial moisture content and time varying climate forcing. We show
that the model provides robust and accurate solutions as compared
with the analytical solutions and with the SiSPAT model. This study
also shows that a ﬁner discretization than the one proposed by Ross
is necessary close to the soil surface to accurately model the cumulative
inﬁltration, especially for clayey soils.},
file = {Varado06.pdf:Varado06.pdf:PDF},
keywords = {unsatured zone; bare soil; Richards' equation; numerical scheme; soil
water flow; analytical solution},
owner = {olivier},
timestamp = {2010.06.06}
}
@ARTICLE{Vedernikov46,
author = {Vedernikov, V. V.},
title = {Characteristic features of a liquid flow in an open channel},
journal = {Comptes Rendus (Doklady) de l'{A}cad\'emie des {S}ciences de l'{URSS}},
year = {1946},
volume = {LII},
pages = {207-210},
number = {3},
file = {Vedernikov46.pdf:Vedernikov46.pdf:PDF},
owner = {olivier},
timestamp = {2010.02.12}
}
@ARTICLE{Velasco03,
author = {Velasco, D. and Bateman, A. and Redondo, J.~M. and Demedina, V.},
title = {An open channel flow experimental and theoretical study of resistance
and turbulent characterization over flexible vegetated lining},
journal = {Flow, Turbulence and Combustion},
year = {2003},
volume = {70},
pages = {69--88},
file = {Velasco03.pdf:Velasco03.pdf:PDF},
keywords = {canopy flows; plant turbulence},
owner = {olivier},
timestamp = {2008.05.01}
}
@ARTICLE{Venutelli05,
author = {Venutelli, M.},
title = {A constitutive explanation of {M}anning's formula},
journal = {Meccanica},
year = {2005},
volume = {40},
pages = {281--289},
abstract = {Manning's empirical formula for evaluating the mean velocity for a
steady uniform turbulent flow pressure conduits with circuler cross-section
and in a wide rectangular open channel, can be theoretically justified
by introducing a virtual viscosity or mixing turbulent coefficient,
depending on the velocity and the position of a particle according
to Boussinesq's hypothesis for the turbulent flow in a pipe. The
balance equation yields an ordinary differential equation whose integration
yield the distribution of the velocity.},
doi = {10.1007/s11012-005-6529-5},
file = {Venutelli05.pdf:Venutelli05.pdf:PDF},
keywords = {Manning's formula; turbulent flow; virtual viscosity; mechanics of
fluids},
owner = {olivier},
timestamp = {2008.05.01}
}
@PHDTHESIS{Vidal05,
author = {Vidal, J.~-P.},
title = {Assistance au calage de mod{\`e}les num{\'e}riques en hydraulique
fluviale--Apports de l'intelligence artificielle},
school = {Institut National Polytechnique de Toulouse},
year = {2005},
file = {Vidal05.pdf:Vidal05.pdf:PDF},
keywords = {calibration; numerical model; river hydraulics; knowledge-based system},
owner = {olivier},
timestamp = {2008.05.04}
}
@PHDTHESIS{Vincent99,
author = {Vincent, St\'ephane},
title = {Mod\'elisation d'\'ecoulements incompressibles de fluides non-miscibles},
school = {Bordeaux I},
year = {1999},
month = Dec,
file = {Vincent99.pdf:Vincent99.pdf:PDF},
keywords = {tension superficielle; Superbee; Navier-Stokes; Poiseuille; Saint-Venant;
solution analytique; droplet impact},
owner = {olivier},
timestamp = {2010.11.12}
}
@BOOK{Viollet02,
title = {M{\'e}canique des fluides appliqu{\'e}e, {\'e}coulements incompressibles
dans les circuits, canaux et rivi{\`e}res autour de structures et
dans l'environnement},
publisher = {Presses de l'Ecole Nationale des Ponts et Chauss{\'e}es},
year = {2002},
author = {Viollet, P.-L. and Chabard, J.-P. and Esposito, P. and Laurence,
D.},
abstract = {Cet ouvrage r\'epond aux besoins de l'ing\'enieur moderne, qui doit
en m\^eme temps poss\`eder une connaissance physique approfondie
des ph\'enom\`enes, avoir une bonne compr\'ehension des outils et
m\'ethodes avanc\'ees de mod\'elisation, auxquelles il peut \^etre
amen\'e \`a faire appel, et en m\^eme temps \^etre capable de d\'eterminer
rapidement les ordres de grandeur significatifs d'un probl\`eme.
La turbulence, omnipr\'esente dans les applications de la m\'ecanique
des fluides, est trait\'ee d\`es le d\'ebut du livre. Les domaines
plus particuli\`erement abord\'es ensuite pr\'esentent un panorama
complet des \'ecoulements incompressibles : \'ecoulements dans les
circuits et tuyauteries, autour de structures, \'ecoulements g\'eophysiques
et \'ecoulements \`a surface libre sous leurs diff\'erents aspects
: ph\'enom\`enes permanents et transitoires, \'el\'ements sur le
transport des s\'ediments. Le livre pr\'esente \'egalement de nombreuses
r\'ef\'erences \`a l'histoire de la m\'ecanique des fluides. Constituant
le cours de m\'ecanique des fluides appliqu\'ees de l'Ecole nationale
des ponts et chauss\'ees, il est accessible \`a un large public d'\'etudiants,
d'ing\'enieurs et de chercheurs.},
owner = {olivier},
timestamp = {2008.04.27}
}
@MASTERSTHESIS{Vothingoc08,
author = {Vo Thi Ngoc, Tuoi},
title = {One dimensional {S}aint-{V}enant system},
school = {Universit{\'e} d'Orl{\'e}ans},
year = {2008},
address = {France},
month = {@jun},
file = {Vothingoc08.pdf:Vothingoc08.pdf:PDF},
keywords = {shallow flow equations; analytic solution; MacDonald; ANR METHODE;
Saint-Venant; inverse method},
owner = {Fred. DARBOUX},
timestamp = {2008.08.11}
}
@ARTICLE{vandeVosse03b,
author = {van de Vosse, F.N. and de Hart, J. and van Oijen, C.H.G.A. and Bessems,
D.},
title = {Finite-element-based computational methods for cardiovascular fluid-structure
interaction},
journal = {Journal of Engineering Mathematics},
year = {2003},
volume = {47},
pages = {335--368},
abstract = {Abstract. In this paper a combined arbitrary Lagrange-Euler ﬁctitious
domain (ALE-FD) method for ﬂuid-structure interaction problems in
cardiovascular biomechanics is derived in terms of a weighted residual
ﬁnite-element formulation. For both ﬂuid ﬂow of blood and solid mechanics
of vascular tissue, the performance of tetrahedral and hexahedral
Crouzeix-Raviart elements are evaluated. Comparable convergence results
are found, although for the test cases considered the hexahedral
elements are more accurate. The possibilities that are offered by
the ALE-FD method are illustrated by means of a simulation of valve
dynamics in a simpliﬁed left ventricular ﬂow model.},
file = {vandeVosse03b.pdf:vandeVosse03b.pdf:PDF},
keywords = {arbitrary Lagrange-Euler; blood flow; fictious domain; fluid-structure
interaction; vascular-tissue mechanics},
owner = {olivier},
timestamp = {2011.03.16}
}
@ARTICLE{vandeVosse03,
author = {van~de~Vosse, F.~N.},
title = {Mathematical modelling of the cardiovascular system},
journal = {Journal of Engineering Mathematics},
year = {2003},
volume = {47},
pages = {175--183},
abstract = {This paper is an introduction to the special issue of the Journal
of Engineering Mathematic (Volume 47/3–4, 2003) on the mathematical
modelling of the cardiovascular system. This issue includes the 2003
James Lighthill Memorial Paper written by Pedley [1] on the mathematical
modelling of arterial fluid dynamics. This introduction is written
to bring cardiovascular biomechanics to readers with a background
in mathematical modelling and computational mechanics. The importance
of mathematical modelling for physiological understanding, diagnostics,
prosthesis development, patient selection and medical planning is
indicated and discussed shortly. A subdivision into models for cardiac
mechanics, pressure- and flow-wave propagation, mass transfer and
fully
three-dimensional fluid-structure interaction is made and references
are given to the different contributions of the issue.},
file = {vandeVosse03.pdf:vandeVosse03.pdf:PDF},
keywords = {arterial fluid dynamics; arterial pressure and flow waves; arterial
wall mass-transfer; cardiovascular biomechanics; cardiovascular fluid-structure
interaction; cardiac mechanics; model based diagnostics; medical
planning; blood flow},
owner = {olivier},
timestamp = {2010.11.27}
}
@ARTICLE{Walter07,
author = {Walter, M. Todd and Gao, Bin and Parlange, J.-Yves},
title = {Modeling soil solute release into runoff with infiltration},
journal = {Journal of Hydrology},
year = {2007},
volume = {347},
pages = {430--437},
abstract = {Despite empirical evidence that inﬁltration plays an important role
in controlling the transfer of chemicals from soil to surface runoff,
few mechanistic models have been tested under both inﬁltrating and
non-inﬁltrating conditions. We used previously published experimental
data to test a physically-based, solute transport model. The model’s
underlying conceptual basis is that near-surface soil chemicals are
ejected into runoff by raindrop impact and chemicals deeper in the
soil diffuse into this near-surface raindrop ‘‘exchange-layer.’’
The experiments consisted of three soil types (clay, loam, and ﬁne
sandy loam) subjected to three inﬁltration conditions (none, full
drainage, and reduced inﬁltration). Model parameters that could not
be directly determined from the descriptions of the experiments were
determined from previously published information or otherwise internally
constrained. The model’s governing equations were solved numerically
and the results agreed well with measured solute concentrations in
both runoff and soil-water for all the experiments. The results emphasize
the potentially important role of saturated, poorly draining parts
of the landscape in contributing solutes to streams and lakes via
overland ﬂow.},
file = {Walter07.pdf:Walter07.pdf:PDF},
keywords = {infiltration; raindrop impact; exchange-layer; diffusion; bromide;
physically-based model; runoff; soil-water; Richards; transport},
owner = {olivier},
timestamp = {2010.06.13}
}
@ARTICLE{Wang06,
author = {Wang, A. and Jin, C. and Liu, J. and Pei, T.},
title = {A modified hortonian overland flow model based on laboratory experiments},
journal = {Water Resources Management},
year = {2006},
volume = {20},
pages = {181--192},
abstract = {Overland flow, which is examined here, is an important hydrological
response to storms of a catchment. And it is also a main component
of hillslope hydrology. Through controlling of rainfall intensities
and changing of artificial slope angles. 49 overland flow hydrographs
are obtained from rainfall-runoff simulation experiments conducted
on a manmade hillside. Based on the measured overland flow processes,
the relationship between the average water depth on the hillslope
and that at the outlet, which is nearly a quadratic curve, is obtained.
the relationship is different from the assumption, in which the average
water depth on the hillslope is equal to that at the outlet, proposed
by Horton. Finally, a regression equation is also presented, which
provides both the theoretical and experimental basis to modify the
time delay of peak flow for a distributed rainfall-runoff modeling.},
doi = {10.1007/s11269-7375-5},
file = {Wang06.pdf:Wang06.pdf:PDF},
keywords = {manmade hillside; modification; overland flow; simulated experiment;
water surface profile},
owner = {olivier},
timestamp = {2008.05.01}
}
@ARTICLE{Wang02,
author = {Wang, G.-T. and Chen, Shulin and Boll, Jan and Stockle, C.~O. and
Mccool, D.~K.},
title = {Modelling overland flow based on {S}aint-{V}enant equations for a
discretized hillslope system},
journal = {Hydrological Processes},
year = {2002},
volume = {16},
pages = {2409--2421},
number = {12},
abstract = {Mathematical modelling of overland flow is a critical task in simulating
transport of water, sediment and other pollutants from land surfaces
to receiving waters. In this paper, an overland flow routing method
is developed based on the Saint-Venant equations using a discretized
hillslope system for areas with high roughness and steep slope. Under
these conditions, the momentum equation reduces to a unique relationship
between the flow depth and discharge. A hillslope is treated as a
system divided into several subplanes. A set of first-order non-linear
differential equations for subsequent subplanes are solved analytically
using Chezy's formula in lieu of the momentum equation. Comparison
of the analytical solution of the first-order non-linear ordinary
differential equations and a numerical solution using the Runge-Kutta
method shows a relative error of 0·3\%. Using runoff data reported
in the literature, comparison between the new approach and a numerical
solution of the full Saint-Venant equations showed a close agreement.},
address = {Biological System Engineering, Washington State University, Pullman,
WA 99164-6120, USA; Biological and Agricultural Engineering Department,
University of Idaho Moscow, ID 83844-0904, USA; Agricultural Research
Service, United State Department of Agriculture, Washington State
University, Pullman, WA 99164-6120, USA},
citeulike-article-id = {4123110},
citeulike-linkout-0 = {http://dx.doi.org/10.1002/hyp.1010},
citeulike-linkout-1 = {http://www3.interscience.wiley.com/cgi-bin/abstract/92013467/ABSTRACT},
doi = {10.1002/hyp.1010},
file = {Wang02.pdf:Wang02.pdf:PDF},
keywords = {kinematic-wave, overland-flow, st-venant},
owner = {olivier},
posted-at = {2009-03-03 10:57:39},
priority = {2},
timestamp = {2009.07.19},
url = {http://dx.doi.org/10.1002/hyp.1010}
}
@ARTICLE{Wang09,
author = {Wang, Wei and Shu, Chi-Wang and Yee, H. C. and Sj\¨ogreen, Bj\¨orn},
title = {High-order well-balanced schemes and applications to non-equilibrium
flow},
journal = {Journal of Computational Physics},
year = {2009},
volume = {228},
pages = {6682--6702},
abstract = {The appearance of the source terms in modeling non-equilibrium ﬂow
problems containing ﬁnite-rate chemistry or combustion poses additional
numerical difﬁculties beyond that for solving non-reacting ﬂows.
A well-balanced scheme, which can preserve certain non-trivial steady
state solutions exactly, may help minimize some of these difﬁculties.
In this paper, a simple one-dimensional non-equilibrium model with
one temperature is considered. We ﬁrst describe a general strategy
to design high-order well-balanced ﬁnite-difference schemes and then
study the well-balanced properties of the high-order ﬁnite-difference
weighted essentially non-oscillatory (WENO) scheme, modiﬁed balanced
WENO schemes and various total variation diminishing (TVD) schemes.
The advantages of using a well-balanced scheme in preserving steady
states and in resolving small perturbations of such states will be
shown. Numerical examples containing both smooth and discontinuous
solutions are included to verify the improved accuracy, in addition
to the well-balanced behavior.},
doi = {10.1016/j.jcp.2009.05.028},
file = {Wang09.pdf:Wang09.pdf:PDF},
keywords = {well-balanced schemes; non-equilibrium flow; chemical reactions; WENO
schemes; TVD schemes; nozzle flow; shock tube},
owner = {olivier},
timestamp = {2011.02.24}
}
@ARTICLE{Wang08,
author = {Wang, Wei and Shu, Chi-Wang and Yee, H. C. and Sj\¨ogreen, Bj\¨orn},
title = {On well-balanced schemes for non-equilibrium flow with stiff source
terms},
journal = {Stanford Center for Turbulence Research -- Annual Research Briefs},
year = {2008},
pages = {391--402},
abstract = {In the modeling of unsteady reactive problems, the interaction of
turbulence with ﬁnite-rate chemistry introduces a wide range of space
and time scales, leading to additional numerical diﬃculties. A main
diﬃculty stems from the fact that most numerical algorithms used
in reacting ﬂows were originally designed to solve non-reacting ﬂuids.
As a result, spatial stiﬀness due to reacting source terms and turbulence/chemistry
interaction are major stumbling blocks to numerical algorithm development.
One of the important numerical issues is the proper numerical treatment
of a system of highly coupled stiﬀ non-linear source terms, which
will result in possible spurious steady state numerical solutions
(see Lafon & Yee 1996).
It was shown in LeVeque (1998) that a well-balanced scheme, which
can preserve the steady state solution exactly, may solve this spurious
numerical behavior. The goal of this work is to consider a simple
1-D model with one temperature and three species as studied by Gnoﬀo,
Gupta & Shinn (1989) and to study the well-balanced property of various
popular linear and non-linear numerical schemes in the literature.
The diﬀerent
behaviors of those numerical schemes in preserving steady states and
in resolving small perturbations of such states will be shown.},
file = {Wang08.pdf:Wang08.pdf:PDF},
keywords = {well-balanced schemes; non-equilibrium flow; WENO schemes; TVD schemes},
owner = {olivier},
timestamp = {2011.02.24}
}
@ARTICLE{Wang97,
author = {Wang, Zhi and Feyen, Jan and Nielsen, Donald R. and van Genuchten,
Martinus T.},
title = {Two-phase flow infiltration equations accounting for air entrapment
effects},
journal = {Water Resources Research},
year = {1997},
volume = {33},
pages = {2759--2767},
number = {12},
month = Dec,
abstract = {Water infiltration into the unsaturated zone is potentially affected
by air compression ahead of the wetting front. Analytical infiltration
equations accounting for air compression, air counterflow, and flow
hysteresis in a porous medium were derived on the basis of the Green
and Ampt [1911] assumptions. Air compression ahead of the wetting
front was predicted using the perfect gas law. The capillary pressure
at the wetting front was found to vary between the dynamic water-bubbling
value and the dynamic air-bubbling value of the material. These equations,
accounting also for the effects of macropores near the soil surface,
turned out to be simpler than the traditional Kostiakov [1932] and
the Philip [1957a, b, c, d] equations. The equation parameters are
physically meaningful and can be readily obtained from field measurements
of the natural sturated hydraulic conductivity and soil water retention
or pressure infiltrometer data. Experimental testing showed that
the equations are reasonably accurate.},
file = {Wang97.pdf:Wang97.pdf:PDF},
keywords = {Green-Ampt; Philip; Kostiakov;},
owner = {olivier},
timestamp = {2010.04.25}
}
@ARTICLE{Warrick07,
author = {Warrick, A.~W. and Lazarovitch, N. and Furman, A. and Zerihun, D.},
title = {Explicit {I}nfiltration {F}unction for {F}urrows},
journal = {Journal of {I}rrigation and {D}rainage {E}ngineering},
year = {2007},
volume = {133},
pages = {307--313},
number = {4},
month = Aug,
abstract = {Abstract: This study addresses inﬁltration from furrows or narrow
channels. The basic approach is to develop the two-dimensional inﬁltration
as a combination of the corresponding one-dimensional vertical and
an edge effect. The idea is borrowed from previous applications for
inﬁltration from disc and strip sources. The assumption is tested
directly with numerical experiments using four representative soils
and three furrow shapes ͑triangular, rectangular, and parabolic͒.
The edge effect is the difference between the cumulative inﬁltration
per unit of adjusted wetting perimeter and the corresponding one-dimensional
inﬁltration. A general conclusion is that the edge effect is linearly
related to time. In addition, it was observed that the two empirical
parameters in the function used to relate the edge effect with time
have narrow ranges and are related to soil hydraulic parameters,
furrow shape, the boundary and initial conditions and additional
geometric factors. The approach leads to a physically based inﬁltration
function for irrigation furrows ͑or narrow channels͒ without the
need to perform a fully two-dimensional simulation. Also, a simpliﬁed
expression was found for the limiting steady-state case, which is
analogous to Wooding’s equation for inﬁltration from a shallow pond.},
file = {Warrick07.pdf:Warrick07.pdf:PDF},
keywords = {Furrow irrigation; Inﬁltration; Two-dimensional models; Mathematical
models; Analytical techniques},
owner = {olivier},
timestamp = {2010.04.23}
}
@ARTICLE{Warrick05,
author = {Warrick, A. W. and Zerihun, D. and Sanchez, C. A. and Furman, A.},
title = {Infiltration under {V}ariable {P}onding {D}epths of {W}ater},
journal = {Journal of Irrigation and Drainage Engineering},
year = {2005},
volume = {131},
pages = {358--363},
number = {4},
month = Aug,
abstract = {Abstract: Cumulative inﬁltration was computed as a function of time-varying
ponded water depths using a Green and Ampt analysis. The input water
depths were ﬁeld-measured values from two irrigation events on Superstition
sand, one from a basin and one from a border. For both types of irrigation,
the computed cumulative inﬁltration at a given measuring station
was nearly the same whether using a variable head input or a constant
͑average͒ head during the time of opportunity. As an example, at
the ﬁrst measurement station for the
basin event, the ponded depth went from a 0 to 9 cm depth over the
2–12 min. from the time water was introduced into the basin; this
was followed by a decrease to a depth of 4 cm at 60 min. The computed
inﬁltration using the depth hydrograph was 14.3 cm compared to 14.1
cm when using an average depth. A smaller value of 13.7 cm is found
using the appropriate time of opportunity with a ﬁeld averaged depth
and a considerably smaller value of 12.4 cm was found when a zero-depth
boundary is considered. Basin and border uniformities were also computed
based on variable and different constant depths and the results were
found to be reasonably robust whether inﬁltration is computed using
a variable or an appropriate constant ponded depth.},
doi = {10.1061/͑ASCE͒0733-9437͑2005͒131:4͑358͒},
file = {Warrick05.pdf:Warrick05.pdf:PDF},
keywords = {Soil water; Inﬁltration rate; Border irrigation; Surface irrigation},
owner = {olivier},
timestamp = {2010.04.23}
}
@ARTICLE{Wedernikow45,
author = {Wedernikow, V. V.},
title = {Conditions at the front of a translation wave disturbing a steady
motion of a real fluid},
journal = {Comptes Rendus (Doklady) de l'{A}cad\'emie des {S}ciences de l'{URSS}},
year = {1945},
volume = {XLVIII},
pages = {239-242},
number = {4},
file = {Wedernikow45.pdf:Wedernikow45.pdf:PDF},
owner = {olivier},
timestamp = {2010.02.12}
}
@PHDTHESIS{Weill07,
author = {Weill, S.},
title = {Mod{\'e}lisation des {\'e}changes surface/subsurface {\`a} l'{\'e}chelle
de la parcelle par une approche darc{\'e}enne multidomaine},
school = {{\'e}cole des Mines de Paris},
year = {2007},
month = nov,
abstract = {This study deals with physically based distributed modelling of surface/subsurface
interactions. A new modelling approach, called Darcy multidomain
approach, is presented. Richards and diffusive wave equations are
used to describe respectively infiltration and runoff processes.
Diffusive wave equation is turned into a nonlinear diffusion equation,
that looks like Richards one. Overland flow is then assimilated as
a flow in porous medium that has particular properties. A porous
layer, called runoff layer, is introduced in the computational domain.
The whole surface/subsurface dynamics is then described in a Darcy
continuum by a single nonlinear Darcy equation with domain dependent
parameters. It allows to impose an hydraulic continuity between surface
and subsurface waters. The model is evaluated from classical test
cases of the literature. A sensibility analysis and a detailed study
of Hortonian runoff are then presented. Finally, the plot scale experiment
realised by IRD in Thies, Senegal is reproduced. Results are satisfying
and show that the developed modelling approach allow to reproduce
the strongly coupled dynamics of small scale hydrological systems.},
file = {Weill07.pdf:Weill07.pdf:PDF},
keywords = {overland flow; infiltration; surface/subsurface interactions; integrated
modelling},
owner = {olivier},
timestamp = {2008.05.04}
}
@MASTERSTHESIS{Weill04,
author = {Weill, S.},
title = {Mod{\'e}lisation hydrodynamique du cycle de l'eau de pluie sur un
sol inclin{\'e}},
school = {Paris VI},
year = {2004},
month = mar # {-} # sep,
file = {Weill04.pdf:Weill04.pdf:PDF},
owner = {olivier},
timestamp = {2008.05.04}
}
@ARTICLE{Weill09,
author = {Weill, S.and Mouche, E. and Patin, J.},
title = {A generalized Richards equation for surface/subsurface flow modelling},
journal = {Journal of Hydrology},
year = {2009},
volume = {366},
pages = {9--20},
abstract = {An approach for modelling surface/subsurface ﬂow and transport in
a fully integrated way is presented. The diffusive wave approximation
used to model runoff is formulated as a nonlinear Darcy law and coupled
with the Richards equation for variably saturated ﬂow. The water
dynamics in the three physical domains, land surface, vadose zone
and saturated zone, is described through a single Richards type equation
with domain-dependent parameters. This approach naturally provides
pressure and ﬂuxes continuity along land surface. An advective–diffusive
transport equation is incorporated in the model in order to follow
and identify pre-event and event water. This multi-domain Richards
equation is solved with a mixed hybrid ﬁnite element formulation.
The time discretization is implicit and the nonlinear equations are
solved within a sequential iterative Picard scheme. This model can
describe both inﬁltration excess or saturation excess runoff. In
order to assess this modelling approach, several classical validation,
veriﬁcation and application test cases are presented. For overland
ﬂow solely, the model is compared to an analytical solution and to
commonly used hydrological models. The integrated model is then validated
with a sandbox laboratory experiment. Finally, the dynamic response
of a saturated contributing area at the toe of a 3D virtual hillslope
is simulated to illustrate the applicability of the model to 3D situations.},
file = {Weill09.pdf:Weill09.pdf:PDF},
keywords = {Surface/subsurface interactions; Integrated modelling; Saturation
excess runoff; Inﬁltration excess runoff; Numerical simulation},
owner = {olivier},
timestamp = {2010.05.03}
}
@ARTICLE{Wen06,
author = {Xin Wen},
title = {A steady state capturing and preserving method for computing hyperbolic
systems with geometrical source terms having concentrations},
journal = {Journal of Computational Physics},
year = {2006},
volume = {219},
pages = {322 - 390},
number = {1},
abstract = {We propose a simple well-balanced method named the slope selecting
method which is efficient in both steady state capturing and preserving
for hyperbolic system with geometrical source terms having concentrations.
Physical problems under consideration include the shallow water equations
with discontinuous topography, and the quasi-one-dimensional nozzle
flows with discontinuous cross-sectional area. This method is an
extension from the interface type method developed in [S. Jin, X.
Wen, An efficient method for computing hyperbolic systems with geometrical
source terms having concentrations, J. Comput. Math. 22 (2004) 230-249].
The slope selecting method keeps two merits of the previous method.
It can be applied when the homogeneous system solver is available
and has efficient steady state capturing property. Compared with
the previous method, the slope selecting method has two improvements.
One is this method also has satisfactory steady state preserving
property. The other is this method can be applied to any conservative
scheme for the homogeneous system. Numerical examples provide strong
evidence on the effectiveness of this slope selecting method for
various unsteady, steady and quasi-steady state solutions calculations
as well as the flexibility of this method of being applicable to
any conservative scheme for the homogeneous system.},
doi = {DOI: 10.1016/j.jcp.2006.03.019},
file = {Wen06.pdf:Wen06.pdf:PDF},
issn = {0021-9991},
keywords = {Shallow water equations; Nozzle flow equations; Discontinuous topography;
Well-balanced scheme; Surface gradient method; Shock capturing},
owner = {olivier},
timestamp = {2010.06.27},
url = {http://www.sciencedirect.com/science/article/B6WHY-4JX38Y3-1/2/5eace51257ebca73235c1d8b7ec77a45}
}
@ARTICLE{Wheater89,
author = {Wheater, H.~S. and Bell, N.~C. and Johnston, P.~M.},
title = {Evaluation of overland flow models using laboratory catchment data.
III: Comparison of conceptual models},
journal = {Hydrological sciences journal},
year = {1989},
volume = {34},
pages = {319-337},
number = {3},
abstract = {In the previous paper of this series (Bell et al., 1989), data from
96 experiments on a marine-plywood plane were used to investigate
the performance of numerical models of overland flow based on the
kinematic wave approximation. These models incorporated laminar and
turbulent friction relationships, based on Darcy-Weisbach, Manning
and Colebrook-White formulations, and four parameters were required
to account for the effect of raindrop impact on effective roughness.
In this paper a simpler kinematic formulation based on the Manning
turbulent flow relationship (with two parameter values to allow for
raindrop impact) is tested, and although physically less realistic,
is shown to give comparable fits to the experimental data and to
be more readily amenable to automatic optimization. The conceptualization
of overland flow is extended further, to consider linear and non-linear
reservoir cascades. The simplified kinematic wave model is shown
to be superior in fit, in consistency of optimized model parameters
and in split-sample tests, and has the advantage of physically interprétable
parameters, but this improvement in performance is achieved at significantly
greater computational cost.},
file = {Wheater89.pdf:Wheater89.pdf:PDF},
keywords = {Drainage basins ; Runoff ; Experimental studies ; Kinematics},
owner = {olivier},
timestamp = {2009.07.19}
}
@ARTICLE{Whisler70,
author = {Whisler, Frank D. and Bouwer, Herman},
title = {Comparison of methods for calculating vertical drainage and infiltration
for soils},
journal = {Journal of Hydrology},
year = {1970},
volume = {10},
pages = {1 - 19},
number = {1},
abstract = {The Youngs, Gardner, Ligon, and numerical analysis techniques for
calculating the amounts of one-dimensional, vertical drainage from
soil are discussed and compared with each other and with observed
data, where possible. The same was done with the Green and Ampt,
Philip, and numerical analysis methods for calculating the amounts
of infiltration into soil profiles. Numerical analysis gave the best
agreement with the observations, but required considerable input
data and the calculation procedure was not simple. The Youngs drainage
equation and the Green and Ampt infiltration equation were the easiest
to use and gave reasonably accurate results, which are probably sufficient
for most field problems.},
doi = {DOI: 10.1016/0022-1694(70)90051-X},
file = {Whisler70.pdf:Whisler70.pdf:PDF},
issn = {0022-1694},
keywords = {infiltration; Green-Ampt; Philip; Youngs},
owner = {olivier},
timestamp = {2010.06.06},
url = {http://www.sciencedirect.com/science/article/B6V6C-487F8MK-2B/2/6b8a2a67768aa7033566cb6b06c01ec6}
}
@ARTICLE{Whitaker86,
author = {Whitaker, Stephen},
title = {Flow in Porous Media I: A Theorical Derivation of Darcy's Law},
journal = {Transport in Porous Media},
year = {1986},
volume = {1},
pages = {3--25},
abstract = {Stokes flow through a rigid porous medium is analyzed in terms of
the method of volume averaging. The traditional averaging procedure
leads to an equation of motion and a continuity equation expressed
in terms of the volume-averaged pressure and velocity. The equation
of motion contains integrals involving spatial deviations of the
pressure and velocity, the Brinkman correction, and other lower-order
terms. The analysis clearly indicates why the Brinkman correction
should not be used to accommodate a no slip condition at an interface
between a porous medium and a bounding solid surface, The presence
of spatial deviations of the pressure and velocity in the volume-averaged
equations of motion gives rise to a closure problem, and representations
for the spatial deviations are derived that lead to Darcy's law.
The theoretical development is not restricted to either homogeneous
or spatially periodic porous media; however, the problem of abrupt
changes in the structure of a porous medium is not considered.},
file = {Whitaker86.pdf:Whitaker86.pdf:PDF},
keywords = {volume averaging; Brinkman; correction; closure},
owner = {olivier},
timestamp = {2010.06.06}
}
@BOOK{Whitham74,
title = {Linear and {N}onlinear {W}aves.},
year = {1974},
editor = {Wiley},
author = {Whitham, G.},
file = {Whitham74.pdf:Whitham74.pdf:PDF},
owner = {olivier},
timestamp = {2009.08.03}
}
@ARTICLE{Whitham55,
author = {Whitham, G.B.},
title = {The effects of hydraulic resistance in the dam-break problem},
journal = {Proc. Roy. Soc. of London, Ser. A.},
year = {1955},
volume = {227},
pages = {399--407},
file = {Whitham55.pdf:Whitham55.pdf:PDF},
keywords = {dam-break; friction; analyrical solution},
owner = {olivier},
timestamp = {2011.04.23}
}
@PHDTHESIS{Wibmer04,
author = {Wibmer, Michael},
title = {One-dimensional Simulation of Arterial Blood Flow with Applications},
school = {eingereicht an der Technischen Universitat Wien -- Fakultat fur Technische
Naturwissenschaften und Informatik},
year = {2004},
month = Jan,
abstract = {This thesis is concerned with the one-dimensional approximation of
human arterial blood flow and addresses some topics in modeling,
the application of finite volume schemes to the governing equations
and applications such as the study of the effects of vascular prothesis
on the pressure waves and the simulation of an ergometer test including
the comparison to measured data. It is divided into four parts.
First, the derivation of the governing equations starting from the
integral balances of mass and momentum is presented. different formulations
of the governing equations expressed in different pairs of variables
such as cross-sectional area A(x,t) and volume flow Q(x,t) (denoted
as (A,Q) equations) or cross-sectional area A(x,t) and (mean-)velocity
v(x,t) (denoted as (A,v) equations), are considered. The model procedure
allows space varying vessel properties such as slightly tapering
or local changes of elasticity properties of vessels walls in the
case of a vascular prothesis, e.g. stent arteries. Finally, models
for the vessel wall, bifurcation and Windkessel terminal elements
are discussed.
In the second part of this thesis some theoretical aspects are presented.
Because vessel walls are moving and can exhibit geometrical and mechanical
non-uniformities, the (A,Q) equations are originally not given in
conservation form. Possible conservative formulations are presented
and related to the (A,v) equations. The benefits of each formulation
are discussed. Within physiological flow conditions the governing
equations are of strictly hyperbolic type and anlyse whether the
corresponding characteristic fields are linear degenerate or genuinely
nonlinear. Motivated from the numerical viewpoint the solution to
the Riemann problem is given and the Riemann problem in case of non-uniform
vessel properties is considered. Bifurcations, Windkessel elements
and measured data lead to different types of boundary conditions.
It is analysed whether the possible boundary data are correct in
the sense that they do not lead to a prescribtion of the outgoing
characteristics.
The third part of this thesis addresses the numerical solution of
the (A,Q) and (A,v) equations by finite volume schemes. In the past,
the numerical treatment of the governing equations was either based
on finite difference or finite element schemes. The weakly linear
behavior of the governing equations within physiological flow conditions
allows the development of an efficient approximate Riemann solver.
Combined with the F-Wave algorithm developed in [8] it is shown that
the resulting method is superior in terms of efficiency compared
to the Lax-Wendroff method. Furthermore we present the numerical
treatment of the boundary conditions based on the extrapolation of
the Riemann Invariants. This allows bifurcations to be treated numerically
independently of the flow direction. The numerical algorithm for
the solution of an arterial tree can easily be parallelized. The
formal definition of this parallel algorithm is presented. Finally
the benefits of an object oriented implementation of an arterial
tree simulator is addressed.
The fourth part of this thesis deals with applicaions of the developed
model. First, some simple experments with well known results show
that the F-Wave algorithm leads to satisfactory results. The standard
simulation of an arterial network consisting of 55 arteries is presented.
The parallel algorithm decreases the total execution time for one
heart beat at about 30%. The next application is based on the work
of Formaggia, Nobile and Quarteroni [19] and addreses the local stiffening
of an artery in case of a vascular prothesis. The work of [19] is
extended so that the complicated wave reflections at the elasticity
interfaces are accurately resolved. These results are applied to
the simulation of the effects of a stented femoralis artery on the
pressure wave forms throghout the human body. Finally we consider
a model describing the baroreceptor control loop of the human body
developed by Moller, Popovic, Thiele in [43], called the MPT-model.
We extend the MPT model so that the arterial pressure is calculated
from the one-dimensional approximation of arterial blood flow. The
simulation of an ergometer test is performed by the solution of the
MPT model and the extended MPT model and find good agreements to
measured data.},
file = {Wibmer04.pdf:Wibmer04.pdf:PDF},
keywords = {arterial tree; blood flow; bifurcation of arteries; artery; boundary
condition; finite-difference scheme; finite-volume scheme; object
oriented software; vascular prothesis; stent; F-wave},
owner = {olivier},
timestamp = {2010.11.28}
}
@PHDTHESIS{Wiggert62,
author = {Wiggert, James M.},
title = {The development of disturbances in supercritical flows},
school = {The university of Michigan industry program of the college of engineering},
year = {1962},
file = {Wiggert62.pdf:Wiggert62.pdf:PDF},
keywords = {disturbances; supercritical flows; instability investigations; physical
experiments; basics for computer method; method of characteristics;
roll waves; open channel; Chezy; Vedernikov; Craya; Manning},
owner = {olivier},
timestamp = {2011.03.03}
}
@ARTICLE{Willemet11,
author = {Willemet, Marie and Lacroix, Val\'erie and Marchandise, Emilie},
title = {Inlet boundary conditions for blood flow simulations in truncated
arterial networks},
journal = {Journal of Biomechanics},
year = {2011},
volume = {44},
pages = {897--903},
number = {5},
abstract = {In the context of patient-specific cardiovascular applications, hemodynamics
models (going from 3D to 0D) are often limited to a part of the arterial
tree. This restriction implies the set up of artificial interfaces
with the remaining parts of the cardiovascular system. In particular,
the inlet boundary condition is crucial: it supplies the impulsion
to the system and receives the reflected backward waves created by
the distal network. Some aspects of this boundary condition need
to be properly defined such as the treatment of backward waves (reflected
or absorbed) and the value of the imposed hemodynamic wave (total
or forward component). Most authors prescribe as inlet boundary condition
(BC) the total measured variable (pressure, velocity or flow rate)
in a reflective way. We show that with this type of inlet boundary
condition, the model does not produce physiological waveforms. We
suggest instead to prescribe only the forward component of the prescribed
variable in an absorbing way. In this way, the computed reflected
waves superpose with the prescribed forward waves to produce the
total wave at the inlet. In this work, different inlet boundary conditions
are implemented and compared for a 1D blood flow model. We test our
boundary conditions on a truncated arterial model presented in the
literature as well as on a patient-specific lower-limb model of a
femoral bypass. We show that with this new boundary condition, a
much better fitting is observed on the shape and intensity of the
simulated pressure and velocity waves.},
doi = {DOI: 10.1016/j.jbiomech.2010.11.036},
file = {Willemet11.pdf:Willemet11.pdf:PDF},
issn = {0021-9290},
keywords = {Blood flow; finite volume; inlet boundary condition; 1D models; wave
separation; lower-limb model; bypass graft},
owner = {olivier},
timestamp = {2011.03.10},
url = {http://www.sciencedirect.com/science/article/B6T82-51V8Y64-1/2/eb86e3d4873bd8ec019a622d0c33ca36}
}
@ARTICLE{Womersley55,
author = {Womersley, J.R.},
title = {On the oscillatory motion of a viscous liquid in thin-walled elastic
tube: I.},
journal = {Philos. Mag.},
year = {1955},
volume = {46},
pages = {199--221},
owner = {olivier},
timestamp = {2011.03.15}
}
@ARTICLE{Wong06,
author = {Wong, T.~S.~W. and Lim, C.~K.},
title = {Effect of loss model on evaluation of {M}anning roughness coefficient
of experimental concrete catchment},
journal = {Journal of Hydrology},
year = {2006},
volume = {331},
pages = {205--218},
abstract = {To simulate a runoff hydrograph from a concrete catchment that is
subject to natural rainfall, the use of computer model is essential.
To develop such a model, the modeller is required to specify the
rainfall data, the physical characteristics of the catchment, the
Manning roughness coefficient (Manning n) of the concrete surface,
and the loss model. To evaluate the Manning n for simulating runoff
hydrographs, it is common to use the hydrograph fitting technique.
With this technique, the simulated hydrographs are actually dependent
on the loss model. Hence, the Manning n that is being evaluated is
also dependent on the loss model. In view of this, the effect of
loss model on the Manning n has been examined. Based on the rainfall
and runoff data on a 25 m2 experimental concrete catchment comprising
two overland planes and one rectangular channel, the examination
shows that: (1) During the initial portion of the events, as the
concrete was dry, the actual loss was higher than those assigned
in the four loss models (the proportional, the initial and proportional,
the upperbound, and the initial and upperbound). Hence, the evaluation
of Manning n should omit this portion and only consider the subsequent
wet portion of the events. (2) Based on the wet portions of the events,
the effect of loss model on the optimum Manning n is small. (3) For
the four loss models, the overall optimum Manning n for concrete
are 0.013-0.015. These values are within the recommended Manning
n for steady, uniform flow in concrete channel. Hence, the Manning
n for steady, uniform flow is applicable to runoff simulation in
which the flow is unsteady and non-uniform. (4) A comparison of the
simulated hydrographs by the upperbound loss models and the proportional
loss models shows that the upperbound loss models produce simulated
hydrographs that are closer to the observed. (5) By adding one parameter
to account for the initial loss in the loss.},
doi = {10.1016/j.jhydrol.2006.05.009},
file = {Wong06.pdf:Wong06.pdf:PDF},
keywords = {catchment; concrete; hydrograph; kinematic wave; open channel flow;
rainfall loss; roughness coefficient; runoff},
owner = {olivier},
timestamp = {2008.05.04}
}
@ARTICLE{Wooding66,
author = {Wooding, R.A.},
title = {A hydraulic model for the catchment-stream problem: III. Comparison
with runoff observations},
journal = {Journal of Hydrology},
year = {1966},
volume = {4},
pages = {21--37},
abstract = {The catchment-stream model is fitted to three natural catchments by
suitable choice of the parameters vo (rainfall intensity scale, an
initial, arbitrary, choice), ts (catchment equilibrium time), [lambda]
(ratio of stream equilibrium time to ts and Qs (scale of the discharge
hydrograph). Although the geometry of natural catchments is far more
complicated than that of the model, the agreement between computed
and actual discharge hydrographs is quite good. The optimum value
of [lambda] is usually about 0.5. Although Qs should be equal, by
definition, to the product of vo by the catchment area, it is usually
found to be somewhat less. When stream rating curves are available,
the scale of stream stage, Hs, can be estimated. The model parameters
L (catchment length), D (stream length) and [alpha] and A (parameters
which combine slope and roughness effects for catchment and stream
respectively) can then be found. Thus stage measurements are of particular
importance. Infiltration is assumed to take place over the catchment
sheet-flow areas mainly while rain is falling. Thereafter infiltration
continues in streambeds, decreasing with time as the smaller ephemeral
streams become dry. Some discharge hydrographs also appear to contain
contributions from interflow. It is concluded that the theoretical
model could be improved if a better geometrical description of the
stream network could be found. At present the model incorporates
many of the smaller streams in the #catchment##phase#, and a concentrating
effect, which can modify the rising front of the discharge hydrograph,
is not included.},
doi = {DOI: 10.1016/0022-1694(66)90065-5},
file = {Wooding66.pdf:Wooding66.pdf:PDF},
issn = {0022-1694},
owner = {olivier},
timestamp = {2010.06.18},
url = {http://www.sciencedirect.com/science/article/B6V6C-487DC0R-8D/2/d27c4229ff2a93f4cd26fdbe5a21a078}
}
@ARTICLE{Wooding65,
author = {Wooding, R.A.},
title = {A hydraulic model for the catchment-stream problem: I. Kinematic-wave
theory},
journal = {Journal of Hydrology},
year = {1965},
volume = {3},
pages = {254--267},
number = {3-4},
abstract = {Linear mathematical models describing stream or river outflow due
to storm runoff do not explain several important observed features,
such as the change in shape of the discharge hydrograph and the non-linear
variation of peak discharge rate with variation of rainfall intensity.
In the present paper, analytical solutions for a hydraulic model
are obtained by the method of characteristics, firstly, for flow
over a plane V-shaped catchment under a constant uniformly-distributed
rainfall of finite duration, and secondly, for the stream outflow
arising from the catchment discharge. The advantage of this simplified
two-component model lies in the fact that only four parameters are
involved; these comprise two dimensionless indices in the power-law
equations of motion assumed for catchment and stream flow, a scale
of (i) rainfall intensity or (ii) total rainfall or (iii) rainfall
duration and a dimensionless parameter which represents a ratio of
suitably-defined time constants for stream and catchment respectively.
The calculated stream hydrograph - for either stage or discharge
rate - is found to be a smooth curve which contains up to six discontinuities
in curvature, the locations of these discontinuities, and hence the
shape of the function, depending upon the values of the parameters
noted above. It is noted that the rising part of the curve depends
initially only upon the integral of the catchment outflow. In this
region various segments of the curve exhibit power-law behavior,
but this is, in fact, a consequence of assuming power-law depth-discharge
relationships. For a similar reason, the falling part of the curve
exhibits a power-law decay. This paper is the first in a series of
three. Part II discusses model solutions for a steady rainfall of
finite duration, which could be relevant to work with sprinkled plots.
In Part III, the model is applied to three natural catchments. Additional
problems arising from infiltration are discussed in Parts II and
III.},
doi = {DOI: 10.1016/0022-1694(65)90084-3},
file = {Wooding65.pdf:Wooding65.pdf:PDF},
issn = {0022-1694},
keywords = {V; catchment flow; analyrical solution},
owner = {olivier},
timestamp = {2010.06.18},
url = {http://www.sciencedirect.com/science/article/B6V6C-48763GP-2K/2/b09e7bfac50da8167103e5382d1b9ff8}
}
@ARTICLE{Wooding65b,
author = {Wooding, R.A.},
title = {A hydraulic model for the catchment-stream problem: II. Numerical
solutions},
journal = {Journal of Hydrology},
year = {1965},
volume = {3},
pages = {268--282},
number = {3-4},
abstract = {With the aid of kinematic-wave theory described in Part I for flow
over a catchment and along a stream, the predicted form of stream
hydrograph is calculated numerically, assuming that the rainfall
is of constant intensity and of finite duration. The influence of
the parameter [lambda], a measure of the ratio of stream #response##time#
to catchment #response##time#, becomes significant for [lambda] =
0(1); the general effect of large [lambda] is to delay the arrival
time of a flood peak and to reduce its amplitude. For [lambda] small,
the catchment discharge function is a good guide to the form of the
stream hydrograph. With finite infiltration, the duration of catchment
discharge is finite.},
doi = {DOI: 10.1016/0022-1694(65)90085-5},
file = {Wooding65b.pdf:Wooding65b.pdf:PDF},
issn = {0022-1694},
keywords = {V-shaped; hydrograph; infiltration; rain},
owner = {olivier},
timestamp = {2010.06.18},
url = {http://www.sciencedirect.com/science/article/B6V6C-48763GP-2M/2/5358f190e17aa6cbf6fd298c6e79ce77}
}
@ARTICLE{Woodward84,
author = {Woodward, Paul and Colella, Phillip},
title = {The Numerical Simulation of Two-Dimensional Fluid Flow with Strong
Shocks},
journal = {Journal of Computational Physics},
year = {1984},
volume = {54},
pages = {115--173},
abstract = {Results of an extensive comparison of numerical methods for simulating
hydrodynamics are presented and discussed. This study focuses on
the simulation of fluid flows with strong shocks in two dimensions.
By “strong shocks,” we here refer to shocks in which there is substantial
entropy production. For the case of shocks in air, we therefore refer
to Mach numbers of three and greater. For flows containing such strong
shocks we find that a careful treatment of flow discontinuities is
of greatest importance in obtaining accurate numerical results. Three
approaches to treating discontinuities in the flow are discussed-artificial
viscosity, blending of low- and high-order-accurate fluxes, and the
use of nonlinear solutions to Riemann’s problem. The advantages and
disadvantages of each approach are discussed and illustrated by computed
results for three test problems. In this comparison we have focused
our attention entirely upon the performance of schemes for differencing
the hydrodynamic equations. We have regarded the nature of the grid
upon which such differencing schemes are applied as an independent
issue outside the scope of this work. Therefore we have restricted
our study to the case of uniform, square computational zones in Cartesian
coordinates. For difference schemes simplicity we have further restricted
our attention to two-dimensional which are built out of symmetrized
products of one-dimensional difference operators.},
file = {Woodward84.pdf:Woodward84.pdf:PDF},
keywords = {artificial viscosity; linear hybridization; Godunov's approach; MUSCL},
owner = {olivier},
timestamp = {2011.02.23}
}
@ARTICLE{Woolhiser67,
author = {Woolhiser, D.A. and Liggett, J. A.},
title = {Unsteady, One-Dimensional Flow ober a Plane - the Rising Hydrograph},
journal = {Water Resources Research},
year = {1967},
volume = {3},
pages = {753--771},
number = {3},
file = {Woolhiser67.pdf:Woolhiser67.pdf:PDF},
keywords = {rain; hydrograph},
owner = {olivier},
timestamp = {2010.05.12}
}
@ARTICLE{WortmannVierthaler95,
author = {Wortmann-Vierthaler, M. and Moussiopoulos, N.},
title = {Numerical tests of a refined flux corrected transport advection scheme},
journal = {Environmental Software},
year = {1995},
volume = {10},
pages = {157 - 175},
number = {3},
abstract = {In the last years several high resolution schemes for solving the
advection equation have been developed. One group of these second
order, oscillation free, explicit scalar difference schemes are the
Flux Corrected Transport (FCT) algorithms. Within these algorithms
the flux is computed as a weighted combination of fluxes from a monotonic
low order scheme and a higher order scheme. In the construction of
FCT algorithms there are three components of interest: the low order
scheme, the flux-limiting algorithm and the high order scheme. In
this paper the often used Lax Wendroff high order scheme is replaced
by the Adams Bashforth scheme. Results of different well known two
dimensional tests are shown. Also two new three dimensional test
problems with nonzero topography, which are closer to meteorological
applications, are introduced and applied to the proposed scheme and
to several other advection schemes.},
doi = {DOI: 10.1016/0266-9838(95)00014-C},
file = {WortmannVierthaler95.pdf:WortmannVierthaler95.pdf:PDF},
issn = {0266-9838},
keywords = {Advection scheme; high resolution schemes; flux corrected transport;
Adams Bashforth scheme; numerical tests},
owner = {olivier},
timestamp = {2010.06.03},
url = {http://www.sciencedirect.com/science/article/B6VSW-40T9MJ8-7/2/a3c5c492b2a6d5224fd8ae8a6c337a7c}
}
@ARTICLE{Wu89,
author = {Wu, Shigui and Lee, George C.},
title = {Theoretical and computational investigations of nonlinear wave propagations
in arteries (I) -- A theoretical model of nonlinear pulse wave propagations},
journal = {Science in China (Series B)},
year = {1989},
volume = {32},
pages = {711--728},
number = {6},
month = Jun,
abstract = {In this paper, a new theoretical model of nonlinear wave propagations
in arteries with surrounding tissues was put forward. The equations
of motion for the blood vessels and their peripheral tissues as a
system have been derived. These equations were expressed in terms
of the stresses of the vessel wall and fluid, and the geometry of
the blood vessel. They can be used to solve numerically the problems
for the propagations of nonlinear pulse waves in arteries together
with the momentum and continuity equations of incompressible-viscous
flow, as well as the constitutive equations of fluid and vessel wall.
The numerical solutions can involve pressure, velocities and flowrate
of the blood flow, as well as displacements, velocities and stresses
of the vessel wall. These physical variables of propagations of pulse
waves in arteries are all of significance physiologically and clinically.},
file = {Wu89.pdf:Wu89.pdf:PDF},
keywords = {nonlinear waves; theoretical model; blood flow; arterial walls; surrounding
tissue; motion equations; constitutive equations},
owner = {olivier},
timestamp = {2011.03.03}
}
@ARTICLE{Xing06,
author = {Xing, Y. and Shu, C.-W.},
title = {A new approach of high order well-balanced finite volume {WENO} schemes
and discontinuous {G}alerkin methods for a class of hyperbolic systems
with source terms},
journal = {Communications in Computational Physics},
year = {2006},
volume = {1},
pages = {100--134},
number = {1},
month = feb,
file = {Xing06.pdf:Xing06.pdf:PDF},
keywords = {hyperbolic balance laws; WENO finite volume scheme; discontinuous
Galerkin method; high order accuracy; source term; conservation laws;
shallow water equation; elastic wave equation; chemosensitive movement;
nozzle flow; two phase flow},
owner = {olivier},
timestamp = {2008.05.01}
}
@ARTICLE{Xing05,
author = {Xing, Yulong and Shu, C.-W.},
title = {High order finite difference {WENO} schemes with the exact conservation
property for the shallow water equations},
journal = {Journal of Computational Physics},
year = {2005},
volume = {208},
pages = {206-227},
abstract = {Shallow water equations with nonﬂat bottom have steady state solutions
in which the ﬂux gradients are nonzero but exactly balanced by the
source term. It is a challenge to design genuinely high order accurate
numerical schemes which preserve exactly these steady state solutions.
In this paper we design high order ﬁnite diﬀerence WENO schemes to
this system with such exact conservation property (C-property) and
at the same time maintaining genuine high order accuracy. Extensive
one and two dimensional simulations are performed to verify high
order accuracy, the exact C-property, and good resolution for smooth
and discontinuous solutions.},
file = {Xing05.pdf:Xing05.pdf:PDF},
keywords = {Shallow water equation; WENO scheme; High order accuracy; Source term;
Conservation laws; C-property},
owner = {olivier},
timestamp = {2010.01.26}
}
@ARTICLE{Xiu07,
author = {Xiu, Dongbin and Sherwin, Spencer J.},
title = {Parametric uncertainty analysis of pulse wave propagation in a model
of a human arterial network},
journal = {Journal of Computational Physics},
year = {2007},
volume = {226},
pages = {1385--1407},
abstract = {Reduced models of human arterial networks are an eﬃcient approach
to analyze quantitative macroscopic features of human arterial ﬂows.
The justiﬁcation for such models typically arise due to the signiﬁcantly
long wavelength associated with the system in comparison to the lengths
of arteries in the networks. Although these types of models have
been employed extensively and many issues associated with their implementations
have been widely researched, the issue of data uncertainty has received
comparatively little attention. Similar to many biological systems,
a large amount of uncertainty exists in the value of the parameters
associated with the models. Clearly reliable assessment of the system
behaviour cannot be made unless the eﬀect of such data uncertainty
is quantiﬁed. In this paper we present a study of parametric data
uncertainty in reduced modelling of human arterial networks which
is governed by a hyperbolic system. The uncertain parameters are
modelled as random variables and the governing equations for the
arterial network therefore become stochastic. This type stochastic
hyperbolic systems have not been previously systematically studied
due to the diﬃculties introduced by the uncertainty such as a potential
change in the mathematical character of the system and imposing boundary
conditions. We demonstrate how the application of a high-order stochastic
collocation method based on the generalized polynomial chaos expansion,
combined with a discontinuous Galerkin spectral/hp element discretization
in physical space, can successfully simulate this type of hyperbolic
system subject to uncertain inputs with bounds. Building upon a numerical
study of propagation of uncertainty and sensitivity in a simpliﬁed
model with a single bifurcation, a systematical parameter sensitivity
analysis is conducted on the wave dynamics in a multiple bifurcating
human arterial network. Using the physical understanding of the dynamics
of pulse waves in these types of networks we are able to provide
an insight into the results of the stochastic simulations, thereby
demonstrating the eﬀects of uncertainty in physiologically accurate
human arterial networks.},
file = {Xiu07.pdf:Xiu07.pdf:PDF},
keywords = {methematical biology; hemodynamics; arterial network; stochastic modelling;
uncertainty analysis; high-order methods; blood flow},
owner = {olivier},
timestamp = {2011.03.15}
}
@ARTICLE{Xu02,
author = {Xu, Kun},
title = {A well-balanced gas-kinetic scheme for the shallow-water equations
with source terms},
journal = {Journal of Computational Physics},
year = {2002},
volume = {178},
pages = {533-562},
abstract = {This paper is about the extension of the gas-kinetic BGK scheme to
the shallow-water equations with source terms. In the current study,
the particle velocity change due to the gravitational force and variable
river bottom is implemented explicitly in the ﬂux evaluation. The
current scheme is a well-balanced method, which presents accurate
and robust results in both steady and unsteady ﬂow simulations.},
file = {Xu02.pdf:Xu02.pdf:PDF},
keywords = {shallow water equations;source terms;gas-kinetic scheme;gravitational
force},
owner = {olivier},
timestamp = {2009.07.24}
}
@ARTICLE{Yamada88,
author = {Yamada, T. and Kobayashi, M.},
title = {Kinematic wave characteristics and new equations of unsaturated infiltration},
journal = {Journal of Hydrology},
year = {1988},
volume = {102},
pages = {257 - 266},
number = {1-4},
abstract = {Several characteristics of the physical mechanism for the vertical
infiltration of water into a soil layer are described. In this investigation,
it is shown that the vertical infiltration of soil moisture has kinematic
wave properties similar to flood waves in rivers. According to the
theory, the vertical moisture profile moves downward faster than
tracers or fluid particles. This is confirmed by comparison with
the results of field observation. Next we investigate the effects
of hysteresis on infiltration and propose new equations of infiltration
expressing the hysteretic behavior. By numerical calculation, it
is shown that the soil moisture profiles do not differ significantly
whether the hysteresis is considered or not, but the profiles of
capillary potential are affected by the hysteresis. Furthermore,
we found that the capillary potential advances faster vertically
than soil moisture.},
doi = {DOI: 10.1016/0022-1694(88)90101-1},
file = {Yamada88.pdf:Yamada88.pdf:PDF},
issn = {0022-1694},
keywords = {infiltration; Richards; Darcy; transport},
owner = {olivier},
timestamp = {2010.06.03},
url = {http://www.sciencedirect.com/science/article/B6V6C-487FDKT-1PJ/2/0233c08acff5a0ea285d4ad82af1c503}
}
@ARTICLE{Yan07,
author = {Yan, Min and Kahawita, Rene},
title = {Simulating the evolution of non-point source pollutants in a shallow
water environment},
journal = {Chemosphere},
year = {2007},
volume = {67},
pages = {879--885},
abstract = {Non-point source pollution originating from surface applied chemicals
in either liquid or solid form as part of agricultural activities,
appears in the surface runoff caused by rainfall. The infiltration
and transport of these pollutants has a significant impact on subsurface
and riverine water quality. The present paper describes the development
of a unified 2-D mathematical model incorporating individual models
for infiltration, adsorption, solubility rate, advection and diffusion,
which significantly improve the current practice on mathematical
modeling of pollutant evolution in shallow water. The governing equations
have been solved numerically using cubic spline integration. Experiments
were conducted at the Hydrodynamics Laboratory of the Ecole Polytechnique
de Montreal to validate the mathematical model. Good correspondence
between the computed results and experimental data has been obtained.
The model may
be used to predict the ultimate fate of surface applied chemicals
by evaluating the proportions that are dissolved, infiltrated into
the subsurface or are washed off.},
file = {Yan07.pdf:Yan07.pdf:PDF},
keywords = {transport; solubility rate; dissolution; adsorption; infiltration;
mathematical model; Manning; Green-Ampt; Horton; pollutant transport},
owner = {olivier},
timestamp = {2010.11.24}
}
@ARTICLE{Yang11,
author = {Yang, Chao and Cai, Xiao-Chuan},
title = {Parallel multilevel methods for implicit solution of shallow water
equations with nonsmooth topography on the cubed-sphere},
journal = {Journal of Computational Physics},
year = {2011},
volume = {230},
pages = {2523--2539},
abstract = {High resolution and scalable parallel algorithms for the shallow water
equations on the sphere are very important for modeling the global
climate. In this paper, we introduce and study some highly scalable
multilevel domain decomposition methods for the fully implicit solution
of the nonlinear shallow water equations discretized with a second-order
well-balanced ﬁnite volume method on the cubed-sphere. With the fully
implicit approach, the time step size is no longer limited by the
stability condition, and with the multilevel preconditioners, good
scalabilities are obtained on computers with a large number of processors.
The investigation focuses on the use of semismooth inexact Newton
method for the case with nonsmooth topography and the use of two-
and three-level overlapping Schwarz methods with different order
of discretizations for the preconditioning of the Jacobian systems.
We test the proposed algorithm for several benchmark cases and show
numerically that this approach converges well with smooth and nonsmooth
bottom topography, and scales perfectly in terms of the strong scalability
and reasonably well in terms of the weak scalability on machines
with thousands and tens of thousands of processors.},
doi = {10.1016/j.jcp.2010.12.027},
file = {Yang11.pdf:Yang11.pdf:PDF},
keywords = {shallow water equations; fully implicit method; Newton-Krylov-Schwarz;
multilevel domain decomposition method; cubed-sphere mesh; parallel
processing; strong and weak scalability},
owner = {olivier},
timestamp = {2011.02.23}
}
@ARTICLE{Yang92,
author = {Yang, H.Q. and Przekwas, A.J.},
title = {A comparative study of advanced shock-capturing shcemes applied to
Burgers' equation},
journal = {Journal of Computational Physics},
year = {1992},
volume = {102},
pages = {139 - 159},
number = {1},
abstract = {In recent years, a number of new shock-capturing finite difference
schemes, often called high resolution schemes, have been proposed.
We have considered several variations of the TVD and FCT schemes
and geometrical approaches such as MUSCL, ENO, and PPM. Included
is an organized overview and classification of the schemes. Only
essential features are described, and numerical implementation is
discussed. Much of the mathematical theory is omitted, but a key
source reference list is provided. In this paper we present a comparative
study of these schemes applied to the Burgers' equation. The objective
is to assess their performance for problems involving formation and
propagation of shocks, shock collisions, and expansion of discontinuities.},
doi = {DOI: 10.1016/S0021-9991(05)80012-9},
file = {Yang92.pdf:Yang92.pdf:PDF},
issn = {0021-9991},
keywords = {MUSCL; ENO; PPM; minmod; superbee; Burgers},
owner = {olivier},
timestamp = {2010.06.03},
url = {http://www.sciencedirect.com/science/article/B6WHY-4GWT78Y-D/2/91c6dce0b2413e126a872c6a094574f3}
}
@ARTICLE{Yen02,
author = {Yen, B.~C.},
title = {Open channel flow resistance},
journal = {Journal of Hydraulic Engineering},
year = {2002},
volume = {128},
pages = {20--39},
number = {1},
month = jan,
doi = {10.1061/(ASCE)0733-9429(2002)128:1(20)},
file = {Yen02.pdf:Yen02.pdf:PDF},
keywords = {open channel flow; flow resistance; alluvial channels; open channels},
owner = {olivier},
timestamp = {2008.05.03}
}
@ARTICLE{Yildirim09,
author = {Yildirim, G\¨urol},
title = {Computer-based analysis of explicit approximations to the implicit
Colebrook-White equation in turbulent flow friction factor calculation},
journal = {Advances in Engineering Software},
year = {2009},
volume = {40},
pages = {1183--1190},
abstract = {The implicit Colebrook–White equation has been widely used to estimate
the friction factor for turbulent ﬂuid-ﬂow in rough-pipes. In this
paper, the state-of-the-art review for the most currently available
explicit alternatives to the Colebrook–White equation, is presented.
An extensive comparison test was established on the 20 Â 500 grid,
for a wide range of relative roughness (e/D) and Reynolds number
(R) values (1 * 10-6 < e/D < 5 * 10-2; 4 * 10^3 < R < 10^8), covering
a large portion of turbulent ﬂow zone in Moody’s diagram. Based on
the comprehensive error analysis, the magnitude points in which the
maximum absolute and the maximum relative error are occurred at the
pair of e/D and R values, are observed. A limiting case of the most
of these approximations provided friction factor estimates that are
characterized by a mean absolute error of 5 * 10-4, a maximum absolute
error of 4 * 10-3 whereas, a mean relative error of 1.3% and a maximum
relative error of 5.8%, over the entire range of e/D and R values,
respectively. For practical purposes, the complete results for the
maximum and the mean relative errors versus the 20 sets of e/D value,
are also indicated in two comparative ﬁgures. The examination results
for error properties of these approximations gives one an opportunity
to practically evaluate the most accurate formula among of all the
previous explicit models; and showing in this way its great ﬂexibility
for estimating turbulent ﬂow friction factor. Comparative analysis
for the mean relative error proﬁle revealed, the classiﬁcation for
the best-ﬁtted six equations examined was in a good agreement with
those of the best model selection criterion claimed in the recent
literature, for all performed simulations.},
doi = {10.1016/j.advengsoft.2009.04.004},
file = {Yildirim09.pdf:Yildirim09.pdf:PDF},
keywords = {fluid mechanics; turbulent flow; C-W friction factor; Moody's diagram;
closed form solution; explicit scheme; analysis; excel spreadsheet;
Techdig 2.0 software},
owner = {olivier},
timestamp = {2011.02.23}
}
@ARTICLE{Yomosa87,
author = {Yomosa, Siego},
title = {Solitary Waves in Large Blood Vessels},
journal = {Journal of the Physical Society of Japan},
year = {1987},
volume = {56},
pages = {506--520},
number = {2},
month = Feb,
abstract = {In order to elucidate the dynamical features of the pulsatile blood
flow in large arteries, we propose a soliton theory for a simplified
and idealized model-system of the blood motion in large blood vessels.
The theory is performed for an infinitely long, straight, circular,
homogeneous thin-walled elastic tube filled with an ideal fluid.
It is shown the pulse waves of pressure and flow propagating through
the arteries can be described as solitary waves excited by cardiac
ejections of blood and the features of the pulse wave such as "peaking"
and "steepening" are interpreted in the viewpoint of soliton. The
clinical importance of the "lowest blood pressure" and the "pulse-pressure",
which corresponds to the amplitude of pressure pule-wave, is physically
explained by the formula obtained from our theory.},
file = {Yomosa87.pdf:Yomosa87.pdf:PDF},
keywords = {blood flow; large arteries; blood vessel},
owner = {olivier},
timestamp = {2011.03.02}
}
@ARTICLE{Yoon71,
author = {Yoon, Y.N. and Wenzel, H.G.},
title = {Mechanics of Sheet Flow under Simulated Rainfall},
journal = {Proc. of ASCE, J. of Hydraul. Div.},
year = {1971},
volume = {97 (HY9)},
pages = {1367--1386},
owner = {olivier},
timestamp = {2010.05.10}
}
@ARTICLE{Youngs88,
author = {Youngs, E.G.},
title = {Soil physics and hydrology},
journal = {Journal of Hydrology},
year = {1988},
volume = {100},
pages = {411 - 431},
number = {1-3},
abstract = {Soil physics provides the physical basis for calculating soil-water
flow in hydrological models, particularly that through the region
of unsaturated soil that acts as a buffer between the atmosphere
and the groundwater zone. The development of the continuum theory
of soil-water movement is outlined and its success in describing
soil-water behaviour in infiltration and drainage processes discussed.
In particular, assumptions in the theory are examined, together with
the use of the simplifying Green and Ampt approximate analysis. For
multidimensional infiltration, steady-state flows obtained assuming
a step-function relationship between hydraulic conductivity and soil-water
pressure, as implied in the Green and Ampt analysis, and those obtained
assuming an exponential relationship, are both found to agree satisfactorily
with experiment. Scaling of soil-water behaviour based on similar
media theory and also seepage analysis of groundwater flow are introduced.
Complicating physical factors, such as soil heterogeneity, swelling
and shrinking, and aggregation, that occur in field situations and
often make classical theory too simplistic, are considered.},
doi = {DOI: 10.1016/0022-1694(88)90194-1},
file = {Youngs88.pdf:Youngs88.pdf:PDF},
issn = {0022-1694},
keywords = {Green-Ampt; Darcy; Forchheimer; Richards},
owner = {olivier},
timestamp = {2010.06.06},
url = {http://www.sciencedirect.com/science/article/B6V6C-487D3JX-5K/2/be67616d9bfbe22b73ea2a8b84b42244}
}
@ARTICLE{Yu64,
author = {Yu, Y.~S. and Mc{N}own, John~S.},
title = {Runoff from impervious surfaces},
journal = {Journal of Hydraulic Research},
year = {1964},
volume = {2},
pages = {3--24},
number = {1},
file = {Yu64.pdf:Yu64.pdf:PDF},
owner = {Fred. DARBOUX},
review = {En fran\c{c}ais et en anglais (!)},
timestamp = {2008.07.24}
}
@ARTICLE{Yu97,
author = {Yu, Zhongbo},
title = {Application of vector and parallel supercomputers to ground-water
flow modeling},
journal = {Computers \& Geosciences},
year = {1997},
volume = {23},
pages = {917--927},
number = {9},
abstract = {A new generation of high-performance computers oers geoscientists
new and exciting tools for computationally-intensive scientific problems.
This paper presents preliminary results on optimizing the performance
for ground-water ¯ow models on a Cray supercomputer. The traditional
method of solving a tridiagonal matrix system, that of forward solution
and backsubstitution (FB), is intrinsically data dependent, in that
the equations at a given grid node depend on values from adjacent
grid nodes. This feature effectively prohibits vectorizing and parallelizing
the method for solution on vector and parallel processors. An alternative
method of solution, that of reduction and backsubstitution (RB),
has no data dependence and was implemented in Fortran for vector
and parallel processors to solve a tridiagonal matrix system in a
ground-water flow model. The vectorized code has an overall execution
rate of 110 MFLOPs on a Cray Y-MP that is five to sixteen times faster
than the scalar code. Implementing the code in vector-parallel mode
using eight undedicated processors on a Cray Y-MP results in an overall
additional speedup of 2.8 times in wall clock time for a two-dimensional
flow problem and 2.2 times for a three-dimensional flow problem.
In comparison with the FB code, the RB code requires 26% less CPU
time and 66% less wall-clock time on the same flow problem. Demonstrative
application of the model is included for two- and three-dimensional
flow problems.},
file = {Yu97.pdf:Yu97.pdf:PDF},
keywords = {finite difference method; Darcy's law; Amdahl's law; Theis},
owner = {olivier},
timestamp = {2010.06.13}
}
@ARTICLE{Zagzoule91,
author = {Zagzoule, M. and Khalid-Naciri, J. and Mauss, J.},
title = {Unsteady wall shear stress in a distensible tube},
journal = {J. Biomechanics},
year = {1991},
volume = {24},
pages = {435--439},
number = {6},
abstract = {An asymptotic expression of the wall shear stress (WSS) in an elastic
tube is deduced for small values of the Womersley parameter. In the
case of a rigid tube this asymptotic expression is shown to compare
better with the exact solution than Poiseuille's or Lambossy's approximations.
Its integration in a one-dimensional model of the internal carotid
artery blood flow predicts more marked systolic and less marked diastolic
WSS than those predicted by the commonly used Poisseuille's approximation.},
file = {Zagzoule91.pdf:Zagzoule91.pdf:PDF},
owner = {olivier},
timestamp = {2011.03.02}
}
@ARTICLE{Zagzoule86,
author = {Zagzoule, Mokhtar and Marc-Vergnes, Jean-Pierre},
title = {A global mathematical model of the cerebral circulation in man},
journal = {J. Biomechanics},
year = {1986},
volume = {19},
pages = {1015--1022},
number = {12},
abstract = {A mathematical model of the cerebral circulation has been formulated.
It was based on non-linear equations of pulsatile fluid flow in distensible
conduits and applied to a network simulating the entire cerebral
vasculature, from the carotid and vertebral arteries to the sinuses
and the jugular veins. The quasi-linear hyperbolic system of equations
was numerically solved using the two-step Lax-Wendroff scheme. The
model's results were in good agreement with pressure and flow data
recorded in humans during rest. The model was also applied to the
study of autoregulation during arterial hypotension. A close relationship
between cerebral blood flow (CBF) and capillary pressure was obtained.
At arterial pressure of 80 mmHg, the vasodilation of the pial arteries
was unable to maintain CBF at its control value. At the lower limit
of autoregulation (60 mmHg), CBF was maintained with a 25 % increase
of zero transmural pressure diameter of nearly the whole arterial
network.},
file = {Zagzoule86.pdf:Zagzoule86.pdf:PDF},
keywords = {blood flow; cerebral network; cerebral blood flow; hemodynamic},
owner = {olivier},
timestamp = {2011.03.02}
}
@ARTICLE{Zanuttigh02,
author = {Zanuttigh, Barbara and Lamberti, Alberto},
title = {Roll waves simulation using shallow water equations and {W}eighted
{A}verage {F}lux method},
journal = {Journal of hydraulic research},
year = {2002},
volume = {40},
pages = {610-622},
abstract = {The weighted average ﬂux method is used to represent trough 1-D shallow
water equations the development of natural roll waves in rectangular
channels. The method is reformulated in such a way that all source
terms are incorporated into the local Riemann problem by means of
a useful transformation of the equations, maintaining second-order
accuracy of the solution. A code based on this method has been developed
and results of numerical applications to a Venturi channel and to
the attenuation of waves are presented to check for well known situations
how accurately the source terms are evaluated. The code is applied
to reproduce Brock’s experiments on roll waves performed in a rectangular
laboratory channel. The numerical solution accurately represents
roll waves evolution due to uniform ﬂow instability as well as wave
intensity increase due to instability and wave coalescence. A sensitivity
analysis of the numerical solution to changes of computational parameters
is performed, in order to explain the discrepancies among computed
and experimental values.},
file = {Zanuttigh02.pdf:Zanuttigh02.pdf:PDF},
owner = {olivier},
timestamp = {2010.01.26}
}
@ARTICLE{Zerihun08,
author = {Zerihun, D. and Furman, A. and Sanchez, C.~A. and Warrick, A. W.},
title = {Development of {S}implified {S}olutions for {M}odeling {R}ecession
in {B}asins},
journal = {Journal of Irrigation and Drainage Engineering},
year = {2008},
volume = {134},
pages = {327--340},
number = {3},
month = Jun,
abstract = {Abstract: In irrigation basins the decrease in the gradient of the
water-surface elevation following inﬂow cutoff often leads to reduced
rate of convergence, increased computational time, and reduced robustness
of the numerical solutions of the recession phase. As the water surface
levels off, the underlying physical problem simpliﬁes, thus allowing
the use of highly accurate yet simple alternate solutions to the
full-numerical solution of the zero-inertia equations. For level
basins, the simpliﬁcation involves treating the stream as a static
pool, in which water level only falls in response to inﬁltration.
Graded basins may require partitioning the stream into a ﬂowing and
static pool, before water-surface eventually levels off over the
entire stream length. Implementation of these solutions enhances
computational efﬁciency and robustness of surface irrigation models
without a concomitant loss of accuracy. This paper discusses numerical
problems related to the recession phase computation in basins and
proposes simpliﬁed and robust, yet highly accurate solutions. A comparison
of the recession trajectories and ﬁnal inﬁltration proﬁles predicted
by the full-numerical solution of the zero-inertia equations, obtained
by using double-precision ﬂoating-point arithmetic, and the simpliﬁed
alternate solutions, which is robust enough to be implemented over
a range of hardware–software capabilities, show that the two approaches
yield essentially identical results. Finally, the general validity
of the proposed solutions is tested by comparing predictions of recession
trajectories and inﬁltration proﬁles with those obtained using a
surface irrigation hydraulic model, SRFR.},
file = {Zerihun08.pdf:Zerihun08.pdf:PDF},
keywords = {Basin; Irrigation; Recession; models},
owner = {olivier},
timestamp = {2010.04.23}
}
@ARTICLE{Zehirun05,
author = {Zerihun, D. and Furman, A. and Warrick, A. W. and Sanchez, C.~A.},
title = {Coupled {S}urface-{S}ubsurface {S}olute {T}ransport {M}odel for {I}rrigation
{B}orders and {B}asins. {I}. {M}odel {D}evelopment},
journal = {Journal of Irrigation and Drainage Engineering},
year = {2005},
volume = {131},
pages = {396--406},
number = {5},
month = Oct,
abstract = {Abstract: Surface fertigation is widely practiced in irrigated crop
production systems. Lack of design and management tools limits the
effectiveness of surface fertigation practices. The availability
of a process-based coupled surface–subsurface hydraulic and solute
transport model can lead to improved surface fertigation management.
This paper presents the development of a coupled surface- subsurface
solute transport model. A hydraulic model described in a previous
paper by the writers provided the hydrodynamic basis for the solute
transport model presented here. A numerical solution of the area
averaged advection–dispersion equation, based on the split-operator
approach, forms the surface solute transport component of the coupled
model. The subsurface transport process is simulated using HYDRUS-1D,
which also solves the one-dimensional advection–dispersion equation.
A driver program is used for the internal coupling of the surface
and subsurface transport models. Solute ﬂuxes calculated using the
surface transport model are used as upper boundary conditions for
the subsurface model. Evaluation of the model is presented in a companion
paper.},
doi = {10.1061/͑ASCE͒0733-9437͑2005͒131:5͑396͒},
file = {Zehirun05.pdf:Zehirun05.pdf:PDF},
keywords = {Surface irrigation; Coupling; Models; Unsaturated ﬂow; Solutes; Salinity},
owner = {olivier},
timestamp = {2010.04.23}
}
@ARTICLE{Zerihun05c,
author = {Zerihun, D. and Furman, A. and Warrick, A. W. and Sanchez, C. A.},
title = {Coupled {S}urface-{S}ubsurface {F}low {M}odel for {I}mproved {B}asin
{I}rrigation {M}anagement},
journal = {Journal of Irrigation and Drainage Engineering},
year = {2005},
volume = {131},
pages = {111--128},
number = {2},
month = Apr,
abstract = {Abstract: The availability of a process-based coupled surface-subsurface
model can lead to improved surface irrigation/fertigation management
practices. In this study, a one-dimensional zero-inertia model is
coupled with a one-dimensional unsaturated zone water-ﬂow
model: HYDRUS-1D. A driver program is used to effect internal iterative
coupling of the surface and subsurface ﬂow models. Flow depths calculated
using the surface-ﬂow model are used as Dirichlet boundary conditions
for the subsurface-ﬂow model, and inﬁltration amounts calculated
by the subsurface model are in turn used in surface-ﬂow mass balance
calculations. The model was tested by using ﬁeld data collected at
the University of Arizona, Yuma Mesa, research farm. The maximum
mean absolute difference between ﬁeld-observed and model-predicted
advance is 2 min. Applications of the coupled model in improved irrigation
management are highlighted. In addition, the signiﬁcance of the effects
of soil moisture redistribution on irrigation water availability
to crops and the capability of the coupled model in tracking those
changes in soil water status over time are discussed using examples.},
doi = {10.1061/͑ASCE͒0733-9437͑2005͒131:2͑111͒},
file = {Zerihun05c.pdf:Zerihun05c.pdf:PDF},
keywords = {Surface irrigation; Irrigation practices; Coupling; Hydrologic models;
Unsaturated ﬂow},
owner = {olivier},
timestamp = {2010.04.23}
}
@ARTICLE{Zehirun05b,
author = {Zerihun, D. and Sanchez, C. A. and Furman, A. and Warrick, A. W.},
title = {Coupled {S}urface-{S}ubsurface {S}olute {T}ransport {M}odel for {I}rrigation
{B}orders and {B}asins. {II}. {M}odel {E}valuation},
journal = {Journal of Irrigation and Drainage Engineering},
year = {2005},
volume = {131},
pages = {407--419},
number = {5},
month = Oct,
abstract = {Abstract: The development of a coupled surface–subsurface solute transport
model for surface fertigation management is presented in a companion
paper ͑Part I͒. This paper discusses an evaluation of the coupled
model. The numerical solution for pure advection of solute in the
surface stream was evaluated using test problems with steep concentration
gradients. The result shows that the model can simulate advection
without numerical diffusion and oscillations, an important problem
in the solution of the advection–dispersion equation in advection
dominated solute transport. In addition, a close match was obtained
between the numerical solution of the one-dimensional advection–dispersion
equation and a simpliﬁed analytical solution. A comparison of ﬁeld
data and model output show that the overall mean relative residual
between ﬁeld observed and model predicted solute breakthrough curves
in the surface stream is 16.0%. Excluding only two outlier ͑in the
graded basin data͒ reduces the over all mean relative residual between
ﬁeld observed and model predicted breakthrough curves to 5.2%. Finally,
potential applications of the model in surface fertigation and salinity
management are highlighted.},
doi = {10.1061/͑ASCE͒0733-9437͑2005͒131:5͑407͒},
file = {Zehirun05b.pdf:Zehirun05b.pdf:PDF},
keywords = {Surface irrigation; Coupling; Models; Unsaturated ﬂow; Solutes; Salinity},
owner = {olivier},
timestamp = {2010.04.23}
}
@ARTICLE{Zhan04,
author = {Zhan, Tony L. T. and Ng, Charles W. W.},
title = {Analytical {A}nalysis of {R}ainfall {I}nfiltration {M}echanism in
{U}nsatured {S}oils},
journal = {International Journal of Geomechanics},
year = {2004},
volume = {4},
pages = {273--284},
number = {4},
month = Dec,
abstract = {Abstract: To improve the understanding of the inﬂuence of hydraulic
properties and rainfall conditions on rainfall inﬁltration mechanism
and hence on the pore-water pressure distributions in single and
two-layer unsaturated soil systems, an analytical parametric study
has been carried out. Parameters considered in this study include
saturated permeability (ks), desaturation coefﬁcient (alpha), water
storage capacity theta_s-theta_r, and antecedent and subsequent rainfall
inﬁltration rate (qA and qB). Moreover, the inﬂuence of soil proﬁle
heterogeneity is also investigated. The calculated results demonstrate
that the inﬁltration process and pore-water pressure response are
primarily controlled by both q alpha / ks and ks /alpha. Generally
the larger the value of q alpha / ks , the greater the reduction
of negative pore-water pressure in shallow soil layer. The larger
the ratio of ks /alpha, the faster is the advancement of wetting
front. Among the three hydraulic parameters, the effects of alpha
and ks on pore-water pressure response are much more signiﬁcant than
that of ͑theta_s − theta_r. However, the relative importance of ks
and alpha depends on the initial negative pore-water pressure range
in the ground. In addition, the inﬂuence of antecedent inﬁltration
rate (qA) on pore-water pressure response appears to be much more
signiﬁcant than that of subsequent inﬁltration rate (qB).},
doi = {10.1061/(ASCE)1532-3641(2004)4:4(273)},
file = {Zhan04.pdf:Zhan04.pdf:PDF},
keywords = {Inﬁltration; Unsaturated soils; Analytical techniques; Rainfall; Pore
water pressure},
owner = {olivier},
timestamp = {2010.04.23}
}
@TECHREPORT{Zhang90,
author = {Zhang, Weihua},
title = {Numerical simulation of the hydrodynamics of overland flow with spatial
variation in its physical characteristics},
institution = {University of {W}ashington {D}epartment of {C}ivil and {E}nvironmental
{E}ngineering},
year = {1990},
number = {123},
month = Aug,
file = {Zhang90.pdf:Zhang90.pdf:PDF},
owner = {olivier},
timestamp = {2010.04.01}
}
@ARTICLE{Zhang89,
author = {Zhang, W. and Cundy, T.~W.},
title = {Modeling of two-dimensional overland flow},
journal = {Water Resources Research},
year = {1989},
volume = {25},
pages = {2019--2035},
number = {9},
month = sep,
abstract = {A two-dimensional hydrodynamic and numerical model for overland flow
is developed in this paper. The model allows spatial variations in
hillslope physical characteristics, including surface roughness,
infiltration, and microtopography. The accuracy of the model is tested
by comparison with characteristic-based solutions and experimental
data. The results of these tests indicate that the model is accurate
and has good stability and convergence properties. The application
of the model to two-dimensional overland flow on hillslopes is demonstrated
by applying it to surfaces with spatially variable roughness, infiltration,
and microtopography. These simulations show that microtopography
is the dominant factor causing spatial variation in overland flow
depth, velocity, and direction.},
file = {Zhang89.pdf:Zhang89.pdf:PDF},
owner = {olivier},
timestamp = {2009.01.11}
}
@ARTICLE{Zhou02,
author = {Zhou, J.~G. and Causon, D.~M. and Ingram, D.~M. and Mingham, C.~G.},
title = {Numerical solutions of the shallow water equations with discontinuous
bed topography},
journal = {International Journal for Numerical Methods in Fluids},
year = {2002},
volume = {38},
pages = {769-788},
file = {Zhou02.pdf:Zhou02.pdf:PDF},
keywords = {bed discontinuity; surface gradient method; shallow water equations;
data reconstruction; high resolution method; Godunov method},
owner = {olivier},
timestamp = {2009.07.28}
}
@ARTICLE{Zhou01,
author = {Zhou, J.~G. and Causon, D.~M. and Mingham, C.~G. and Ingram, D.~M.},
title = {The surface gradient method for treatment of source terms in the
shallow-water equations},
journal = {Journal of Computational Physics},
year = {2001},
volume = {168},
pages = {1--25},
abstract = {A novel scheme has been developed for data reconstruction within a
Godunov type method for solving the shallow-water equations with
source terms. In contrast to conventional data reconstruction methods
based on conservative variables, the water surface level is chosen
as the basis for data reconstruction. This provides accurate values
of the conservative variables at cell interfaces so that the fluxes
can be accurately calculated with a Riemann solver. The main advantages
are: (1) a simple centered discretization is used for the source
terms; (2) the scheme is no more complicated than the conventional
method for the homogeneous terms; (3) small perturbations in the
water surface elevation can be accurately predicted; and (4) the
method is generally suitable for both steady and unsteady shallow-water
problems. The accuracy of the scheme has been verified by recourse
to both steady and unsteady flow problems. Excellent agreement has
been obtained between the numerical predictions and analytical solutions.
The results indicate that the new scheme is accurate, simple, efficient,
and robust.},
doi = {10.1006/jcph.2000.6670},
file = {Zhou01.pdf:Zhou01.pdf:PDF},
keywords = {source terms; shallow-water equations; data reconstruction; high-resolution
method; Godunov method; MUSCL scheme},
owner = {olivier},
timestamp = {2008.05.04}
}
@ARTICLE{Zlotnik07,
author = {Zlotnik, Vitaly A. and Wang, Tiejun and Nieber, John L. and Simunek,
Jirka},
title = {Verification of numerical solutions of the Richards equation using
a traveling wave solution},
journal = {Advances in Water Resources},
year = {2007},
volume = {30},
pages = {1973--1980},
abstract = {Eﬀorts to ﬁnd solutions that can be used for veriﬁcation of numerical
techniques for solving the Richards equation have generated a wealth
of approximate and exact analytical solutions. Coeﬃcients of this
equation involve two highly non-linear functions related to the soil
water potential, the unsaturated hydraulic conductivity, and the
soil water content. The known exact solutions for realistic ﬂow geometries
are commonly limited to simpliﬁed descriptions of unsaturated hydraulic
properties, while the approximate solutions involve various simpliﬁcations
that require additional veriﬁcation. We present a technique, referred
to as the ‘‘launch pad’’ technique, which is based on the traveling
wave solution to generate an exact solution of the boundary value
problem for the Richards equation. The technique that is applicable
to any descriptor of unsaturated hydraulic properties is illustrated
on an application involving the inﬁltration of water into soils with
properties described by Brooks–Corey and van Genuchten models. Examples
of veriﬁcation are presented for HYDRUS-1D, a popular numerical computer
code for solving the Richards equation.},
file = {Zlotnik07.pdf:Zlotnik07.pdf:PDF},
keywords = {equation; soil descriptors; traveling wave; numerical solution; code
verification; analytical solution},
owner = {olivier},
timestamp = {2010.06.06}
}
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