,
83 4.4.2 Convection term -WENO interpolation and Riemann Solver, vol.88 ,
,
, , p.94
, , p.96
A numerical method for solving incompressible viscous flow problems, Journal of computational physics, vol.2, issue.1, pp.12-26, 1967. ,
Sur l'approximation de la solution deséquationsdeséquations de navier-stokes par la méthode des pas fractionnaires (ii). Archive for Rational Mechanics and Analysis, vol.33, pp.377-385, 1969. ,
Local adaptive mesh refinement for shock hydrodynamics, Journal of computational Physics, vol.82, issue.1, pp.64-84, 1989. ,
An adaptively-refined, Cartesian cell-based scheme for the Euler and Navier-Stokes equations, vol.106754, 1994. ,
An adaptive mesh projection method for viscous incompressible flow, SIAM Journal on Scientific Computing, vol.18, issue.4, pp.996-1013, 1997. ,
Fully threaded tree algorithms for adaptive refinement fluid dynamics simulations, Journal of Computational Physics, vol.143, issue.2, pp.519-543, 1998. ,
Gerris: a tree-based adaptive solver for the incompressible euler equations in complex geometries, Journal of Computational Physics, vol.190, issue.2, pp.572-600, 2003. ,
URL : https://hal.archives-ouvertes.fr/hal-01445436
Numerical methods for conservation laws, Lectures in Mathematics ETH Zürich, 1992. ,
Why nonconservative schemes converge to wrong solutions: error analysis, Mathematics of computation, vol.62, issue.206, pp.497-530, 1994. ,
Systems of conservation laws, Communications on Pure and Applied mathematics, vol.13, issue.2, pp.217-237, 1960. ,
A difference method for numerical calculation of discontinuous solutions of the equations of hydrodynamics, Matematicheskii Sbornik, vol.89, issue.3, pp.271-306, 1959. ,
Numerical approximation of hyperbolic systems of conservation laws, vol.118, 2013. ,
On the partial difference equations of mathematical physics, IBM journal of Research and Development, vol.11, issue.2, pp.215-234, 1967. ,
Total-variation-diminishing time discretizations, SIAM Journal on Scientific and Statistical Computing, vol.9, issue.6, pp.1073-1084, 1988. ,
Efficient implementation of essentially non-oscillatory shockcapturing schemes, ii, Upwind and High-Resolution Schemes, pp.328-374, 1989. ,
, Total variation diminishing runge-kutta schemes. Mathematics of computation of the, vol.67, pp.73-85, 1998.
Weighted essentially non-oscillatory schemes, Journal of computational physics, vol.115, issue.1, pp.200-212, 1994. ,
A second-order projection method for the incompressible navier-stokes equations, Journal of Computational Physics, vol.85, issue.2, pp.257-283, 1989. ,
A multidimensional second order godunov scheme for conservation laws, J. Comput. Phys, vol.87, pp.171-200, 1990. ,
Multidimensional explicit difference schemes for hyperbolic conservation laws, Proc. of the sixth int'l. symposium on Computing methods in applied sciences and engineering, pp.493-497, 1983. ,
Uniformly high order accurate essentially non-oscillatory schemes, iii, Upwind and high-resolution schemes, pp.218-290, 1987. ,
Efficient implementation of weighted eno schemes, Journal of computational physics, vol.126, issue.1, pp.202-228, 1996. ,
Approximate riemann solvers, parameter vectors, and difference schemes, Journal of computational physics, vol.43, issue.2, pp.357-372, 1981. ,
Towards the ultimate conservative difference scheme. v. a second-order sequel to godunov's method, Journal of computational Physics, vol.32, issue.1, pp.101-136, 1979. ,
High resolution schemes for hyperbolic conservation laws, Journal of computational physics, vol.49, issue.3, pp.357-393, 1983. ,
The piecewise parabolic method (ppm) for gas-dynamical simulations, Journal of computational physics, vol.54, issue.1, pp.174-201, 1984. ,
Efficient implementation of essentially non-oscillatory shockcapturing schemes, Journal of computational physics, vol.77, issue.2, pp.439-471, 1988. ,
A technique of treating negative weights in weno schemes, Journal of Computational Physics, vol.175, issue.1, pp.108-127, 2002. ,
Non-oscillatory central differencing for hyperbolic conservation laws, Journal of computational physics, vol.87, issue.2, pp.408-463, 1990. ,
Central weno schemes for hyperbolic systems of conservation laws, ESAIM: Mathematical Modelling and Numerical Analysis, vol.33, issue.3, pp.547-571, 1999. ,
On the construction, comparison, and local characteristic decomposition for high-order central weno schemes, Journal of Computational Physics, vol.183, issue.1, pp.187-209, 2002. ,
The runge-kutta discontinuous galerkin method for conservation laws v: multidimensional systems, Journal of Computational Physics, vol.141, issue.2, pp.199-224, 1998. ,
Runge-kutta discontinuous galerkin methods for convection-dominated problems, Journal of scientific computing, vol.16, issue.3, pp.173-261, 2001. ,
Eno and weno schemes with the exact conservation property for one-dimensional shallow water equations, Journal of Computational Physics, vol.179, issue.2, pp.593-621, 2002. ,
High order finite difference weno schemes with the exact conservation property for the shallow water equations, Journal of Computational Physics, vol.208, issue.1, pp.206-227, 2005. ,
A new approach of high order well-balanced finite volume weno schemes and discontinuous galerkin methods for a class of hyperbolic systems with source terms, Comput. Phys, vol.1, issue.1, pp.100-134, 2006. ,
High-order well-balanced finite volume weno schemes for shallow water equation with moving water, Journal of Computational Physics, vol.226, issue.1, pp.29-58, 2007. ,
Multiresolution approximations and wavelet orthonormal bases of l 2 . Transactions of the American mathematical society, vol.315, pp.69-87, 1989. ,
Multifrequency channel decompositions of images and wavelet models, IEEE Transactions on Acoustics, Speech, and Signal Processing, vol.37, issue.12, pp.2091-2110, 1989. ,
A theory for multiresolution signal decomposition: the wavelet representation, IEEE transactions on pattern analysis and machine intelligence, vol.11, pp.674-693, 1989. ,
Wavelets and operators, vol.1, 1992. ,
Orthonormal bases of compactly supported wavelets, Communications on pure and applied mathematics, vol.41, issue.7, pp.909-996, 1988. ,
Ten lectures on wavelets, vol.61, 1992. ,
The lifting scheme: A construction of second generation wavelets, SIAM journal on mathematical analysis, vol.29, issue.2, pp.511-546, 1998. ,
Numerical solution of convection-diffusion problems, 1996. ,
Multi-level adaptive solutions to boundary-value problems. Mathematics of computation, vol.31, pp.333-390, 1977. ,
Conjugate gradient-like algorithms for solving nonsymmetric linear systems, Mathematics of Computation, vol.44, issue.170, pp.417-424, 1985. ,
Comparison of second-and fourth-order discretizations for multigrid poisson solvers, Journal of Computational Physics, vol.132, issue.2, pp.226-232, 1997. ,
Multigrid methods for elliptic problems: A review, Monthly Weather Review, vol.114, issue.5, pp.943-959, 1986. ,
Integral and functional equations, The Numerical Treatment of Differential Equations, pp.467-535, 1960. ,
A fourth-order accurate local refinement method for poisson's equation, Journal of Computational Physics, vol.209, issue.1, pp.1-18, 2005. ,
A fourth-order accurate finite-volume method with structured adaptive mesh refinement for solving the advection-diffusion equation, SIAM Journal on Scientific Computing, vol.34, issue.2, pp.179-201, 2012. ,
Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface. The physics of fluids, vol.8, pp.2182-2189, 1965. ,
The method of nets for nonstationary navier-stokes equations, Trudy Matematicheskogo Instituta imeni VA Steklova, vol.92, pp.93-99, 1966. ,
Application of a fractional-step method to incompressible navierstokes equations, Journal of computational physics, vol.59, issue.2, pp.308-323, 1985. ,
Mechanism of the production of small eddies from large ones, Proc. R. Soc. Lond. A, vol.158, pp.499-521, 1937. ,
An accurate adaptive solver for surface-tension-driven interfacial flows, Journal of Computational Physics, vol.228, issue.16, pp.5838-5866, 2009. ,
URL : https://hal.archives-ouvertes.fr/hal-01445445
Theorie du mouvement non permanent des eaux, avec application aux crues des rivieres et a l'introduction de marees dans leurs lits, Comptes rendus des seances de l'Academie des Sciences, vol.36, pp.174-154, 1871. ,
Balancing source terms and flux gradients in high-resolution godunov methods: the quasi-steady wave-propagation algorithm, Journal of computational physics, vol.146, issue.1, pp.346-365, 1998. ,
A steady-state capturing method for hyperbolic systems with geometrical source terms, ESAIM: Mathematical Modelling and Numerical Analysis, vol.35, issue.4, pp.631-645, 2001. ,
Central-upwind schemes for the saint-venant system, ESAIM: Mathematical Modelling and Numerical Analysis, vol.36, issue.3, pp.397-425, 2002. ,
Some approximate godunov schemes to compute shallow-water equations with topography, Computers & Fluids, vol.32, issue.4, pp.479-513, 2003. ,
A fast and stable well-balanced scheme with hydrostatic reconstruction for shallow water flows, SIAM Journal on Scientific Computing, vol.25, issue.6, pp.2050-2065, 2004. ,
A kinetic scheme for the saint-venant system with a source term, Calcolo, vol.38, issue.4, pp.201-231, 2001. ,
URL : https://hal.archives-ouvertes.fr/hal-00922664
Quadtree-adaptive tsunami modelling, Ocean Dynamics, vol.61, issue.9, pp.1261-1285, 2011. ,
URL : https://hal.archives-ouvertes.fr/hal-01445423
High-order finite volume weno schemes for the shallow water equations with dry states, Advances in Water Resources, vol.34, issue.8, pp.1026-1038, 2011. ,