Entrainment and motion of coarse particles in a shallow water stream down a steep slope, Journal of Fluid Mechanics, vol.69, pp.83-114, 2008. ,
DOI : 10.1016/S0022-1694(97)00123-6
Sediment transport modelling : Relaxation schemes for Saint-Venant ??? Exner and three layer models, EDP Sciences ESAIM:Proc, pp.80-94, 2012. ,
DOI : 10.1051/proc/201238005
URL : https://hal.archives-ouvertes.fr/hal-00796049
A simple well-balanced and positive numerical scheme for the shallow-water system, Communications in Mathematical Sciences, vol.13, issue.5, pp.1317-1332, 2015. ,
DOI : 10.4310/CMS.2015.v13.n5.a11
URL : https://hal.archives-ouvertes.fr/hal-01083364
Parallelization of a relaxation scheme modelling the bedload transport of sediments in shallow water flow, EDP Sciences ESAIM: Proc, pp.80-94, 2013. ,
DOI : 10.1051/proc/201343005
URL : https://hal.archives-ouvertes.fr/hal-00840200
Solution of the Sediment Transport Equations Using a Finite Volume Method Based on Sign Matrix, SIAM Journal on Scientific Computing, vol.31, issue.4, pp.2866-2889, 2009. ,
DOI : 10.1137/080727634
Abstract, Advances in Applied Mathematics and Mechanics, vol.473, issue.04, pp.470-492, 2011. ,
DOI : 10.4208/aamm.10-m1056
Nonlinear stability of finite volume methods for hyperbolic conservation laws and well-balanced schemes for sources, Frontiers in Mathematics, 2004. ,
Minimisation principles for the evolution of a soft sea bed interacting with a shallow sea, International Journal of Computational Fluid Dynamics, vol.110, issue.1, pp.163-172, 2012. ,
DOI : 10.1029/JC094iC01p00951
Well-balanced high-order centred schemes for non-conservative hyperbolic systems. Applications to shallow water equations with fixed and mobile bed, Advances in Water Resources, vol.32, issue.6, pp.834-844, 2009. ,
DOI : 10.1016/j.advwatres.2009.02.006
Coupled and Decoupled Numerical Modeling of Flow and Morphological Evolution in Alluvial Rivers, Journal of Hydraulic Engineering, vol.128, issue.3, pp.306-321, 2002. ,
DOI : 10.1061/(ASCE)0733-9429(2002)128:3(306)
Sediment transport models in Shallow Water equations and numerical approach by high order finite volume methods, Computers & Fluids, vol.37, issue.3, pp.299-316, 2008. ,
DOI : 10.1016/j.compfluid.2007.07.017
Exner equation: A continuum approximation of a discrete granular system, Water Resources Research, vol.23, issue.3, 2009. ,
DOI : 10.1016/S0301-9322(96)00080-8
Bedload transport in shallow water models: Why splitting (may) fail, how hyperbolicity (can) help, Advances in Water Resources, vol.34, issue.8, pp.980-989, 2011. ,
DOI : 10.1016/j.advwatres.2011.05.002
URL : https://hal.archives-ouvertes.fr/hal-00536267
Simulation du ruissellement d'eau de pluie sur des surfaces agricoles, 2010. ,
URL : https://hal.archives-ouvertes.fr/tel-00531377
Relaxation approximation to bed-load sediment transport, Journal of Computational and Applied Mathematics, vol.213, issue.2, pp.521-546, 2008. ,
DOI : 10.1016/j.cam.2007.02.003
Über die wechselwirkung zwischen wasser und geschiebe in flüssen, Akad. Wiss. Wien Math. Naturwiss . Klasse, vol.134, issue.2a, pp.165-204, 1925. ,
On an Intermediate Field Capturing Riemann Solver Based on a Parabolic Viscosity Matrix for the Two-Layer Shallow Water System, Journal of Scientific Computing, vol.102, issue.2, pp.117-140, 2011. ,
DOI : 10.1007/s10915-011-9465-7
On the influence of the thickness of the sediment moving layer in the definition of the bedload transport formula in Exner systems, Computers & Fluids, vol.91, pp.87-106, 2014. ,
DOI : 10.1016/j.compfluid.2013.11.031
Formal deduction of the saintvenant-exner model including arbitrarily sloping sediment beds and associated energy, 2016. ,
Solveurs simples positifs et entropiques pour les syst??mes hyperboliques avec terme source, Comptes Rendus Mathematique, vol.334, issue.8, pp.713-716, 2002. ,
DOI : 10.1016/S1631-073X(02)02307-5
Positive and Entropy Stable Godunov-type Schemes for Gas Dynamics and MHD Equations in Lagrangian or Eulerian Coordinates, Numerische Mathematik, vol.94, issue.4, pp.673-713, 2003. ,
DOI : 10.1007/s00211-002-0430-0
Free surface flows over mobile bed: mathematical analysis and numerical modeling of coupled and decoupled approaches, Commun. Appl. Ind. Math, vol.2, issue.1, 2011. ,
On the range of validity of the Exner-based models for mobile-bed river flow simulations, Journal of Hydraulic Research, vol.32, issue.10, 2013. ,
DOI : 10.1080/00221686.2008.9521846
Derivation of Viscous Saint-Venant System for Laminar Shallow Water, Discrete Cont. Dyn. Syst. Ser. B, vol.1, issue.1, 2001. ,
URL : https://hal.archives-ouvertes.fr/hal-00691701
Sediment transport by waves and currents. SERC London Cent, Mar. Technol, p.29, 1981. ,
Staggered scheme for the Exner???shallow water equations, Computational Geosciences, vol.133, issue.1, 2015. ,
DOI : 10.1007/s10596-015-9533-4
On upstream differencing and Godunov-type schemes for hyperbolic conservation laws, SIAM Review, vol.25, issue.1, pp.53-61, 1983. ,
Numerical approaches for 1D morphodynamic modelling, Coastal Engineering, vol.52, issue.8, pp.691-707, 2005. ,
DOI : 10.1016/j.coastaleng.2005.04.004
Formulations for numerically approximating hyperbolic systems governing sediment transport, Journal of Scientific Computing, vol.19, issue.1/3, pp.225-252, 2003. ,
DOI : 10.1023/A:1025304008907
A 2D weakly-coupled and efficient numerical model for transient shallow flow and movable bed, Advances in Water Resources, vol.71, pp.93-109, 2014. ,
DOI : 10.1016/j.advwatres.2014.05.014
Finite Volume Methods for Hyperbolic Problems, 2002. ,
DOI : 10.1017/CBO9780511791253
An Exner-based coupled model for two-dimensional transient flow over erodible bed, Journal of Computational Physics, vol.229, issue.23, pp.8704-8732, 2010. ,
DOI : 10.1016/j.jcp.2010.08.006
An experimental investigation of bed degradation in an open channel, Boston Society of Civil Engineers, 1951. ,
A new bound for polynomials when all roots are real. The Mathematical Gazette, pp.520-526, 2011. ,
A generalized Exner equation for sediment mass balance, Journal of Geophysical Research: Earth Surface, vol.89, issue.2a, 2005. ,
DOI : 10.1029/2004JF000274
Modélisation et simulation de la propagation de l'onde de rupture de barrage, 1995. ,
Numerical methods for nonconservative hyperbolic systems: a theoretical framework., SIAM Journal on Numerical Analysis, vol.44, issue.1, pp.300-321, 2006. ,
DOI : 10.1137/050628052
1D Sediment Transport Morphodynamics with applications to Rivers and Turbidity Currents, 2004. ,
A multi-purpose, intra-wave, shallow water hydro-morphodynamic solver, Advances in Water Resources, vol.38, pp.13-26, 2012. ,
DOI : 10.1016/j.advwatres.2011.12.003
Generalized Roe schemes for 1D two-phase, free-surface flows over a mobile bed, Journal of Computational Physics, vol.227, issue.24, pp.10058-10077, 2008. ,
DOI : 10.1016/j.jcp.2008.08.007
Finite volumes for 2D shallow-water flow with bed-load transport on unstructured grids, Journal of Hydraulic Research, vol.3, issue.8, pp.154-163, 2012. ,
DOI : 10.1016/0378-3839(87)90037-8
HLLC scheme with novel wave-speed estimators appropriate for two-dimensional shallow-water flow on erodible bed, International Journal for Numerical Methods in Fluids, vol.4, issue.9, pp.1019-1036, 2011. ,
DOI : 10.1002/fld.2300
Laboratory study of aggradation in alluvial channels, Journal of Hydrology, vol.49, issue.1-2, pp.87-106, 1981. ,
DOI : 10.1016/0022-1694(81)90207-9
Sediment Transport, Part I: Bed Load Transport, Journal of Hydraulic Engineering, vol.110, issue.10, pp.1431-1456, 1984. ,
DOI : 10.1061/(ASCE)0733-9429(1984)110:10(1431)
AN ENERGETICALLY CONSISTENT VISCOUS SEDIMENTATION MODEL, Mathematical Models and Methods in Applied Sciences, vol.19, issue.03, pp.477-499, 2009. ,
DOI : 10.1142/S0218202509003504