Perthame, A fast and stable well-balanced scheme with hydrostatic reconstruction for shallow water flows, SIAM J. Sci. Comput, pp.25-2050, 2004. ,
Kinetic entropy inequality and hydrostatic reconstruction scheme for the Saint-Venant system, Mathematics of Computation, vol.85, issue.302, pp.2815-2837, 2016. ,
DOI : 10.1090/mcom/3099
URL : https://hal.archives-ouvertes.fr/hal-01063577
A Wave Propagation Method for Conservation Laws and Balance Laws with Spatially Varying Flux Functions, SIAM Journal on Scientific Computing, vol.24, issue.3, pp.24-955, 2002. ,
DOI : 10.1137/S106482750139738X
Multidimensional HLLC Riemann solver for unstructured meshes ??? With application to Euler and MHD flows, Journal of Computational Physics, vol.261, pp.172-208, 2014. ,
DOI : 10.1016/j.jcp.2013.12.029
A Staggered Mesh Algorithm Using High Order Godunov Fluxes to Ensure Solenoidal Magnetic Fields in Magnetohydrodynamic Simulations, Journal of Computational Physics, vol.149, issue.2, pp.270-292, 1999. ,
DOI : 10.1006/jcph.1998.6153
A fully well-balanced, positive and entropy-satisfying Godunov-type method for the shallow-water equations, Mathematics of Computation, vol.85, issue.299, pp.1281-1307, 2016. ,
DOI : 10.1090/mcom3045
URL : https://hal.archives-ouvertes.fr/hal-00956799
Efficient well-balanced hydrostatic upwind schemes for shallow-water equations, Journal of Computational Physics, vol.231, issue.15, pp.4993-5015, 2012. ,
DOI : 10.1016/j.jcp.2012.02.031
Nonlinear stability of finite volume methods for hyperbolic conservation laws, and well-balanced schemes for sources, 2004. ,
A NEW MODEL FOR SHALLOW VISCOELASTIC FLUIDS, Mathematical Models and Methods in Applied Sciences, vol.23, issue.08, pp.1479-1526, 2013. ,
DOI : 10.1142/S0218202513500140
URL : https://hal.archives-ouvertes.fr/hal-00628651
A 5-Wave Relaxation Solver for the Shallow Water MHD System, Journal of Scientific Computing, vol.20, issue.1, pp.92-115, 2016. ,
DOI : 10.1007/s10915-015-0130-4
URL : https://hal.archives-ouvertes.fr/hal-01131293
A Subsonic-Well-Balanced Reconstruction Scheme for Shallow Water Flows, SIAM Journal on Numerical Analysis, vol.48, issue.5, pp.1733-1758, 2010. ,
DOI : 10.1137/090758416
URL : https://hal.archives-ouvertes.fr/hal-00693032
A robust well-balanced scheme for multi-layer shallow water equations, Discrete and Continuous Dynamical Systems, pp.739-758, 2010. ,
A Class of Computationally Fast First Order Finite Volume Solvers: PVM Methods, SIAM Journal on Scientific Computing, vol.34, issue.4, pp.2173-2196, 2012. ,
DOI : 10.1137/100795280
WELL-BALANCED NUMERICAL SCHEMES BASED ON A GENERALIZED HYDROSTATIC RECONSTRUCTION TECHNIQUE, Mathematical Models and Methods in Applied Sciences, vol.17, issue.12, pp.2065-2113, 2007. ,
DOI : 10.1142/S021820250700256X
On some fast well-balanced first order solvers for nonconservative systems, Mathematics of Computation, vol.79, issue.271, pp.1427-1472, 2010. ,
DOI : 10.1090/S0025-5718-09-02317-5
GODUNOV-TYPE SCHEMES FOR HYPERBOLIC SYSTEMS WITH PARAMETER-DEPENDENT SOURCE: THE CASE OF EULER SYSTEM WITH FRICTION, Mathematical Models and Methods in Applied Sciences, vol.20, issue.11, pp.2109-2166, 2010. ,
DOI : 10.1142/S021820251000488X
URL : https://hal.archives-ouvertes.fr/hal-00401616
Central-upwind schemes for the system of shallow water equations with horizontal temperature gradients, Numerische Mathematik, vol.1, issue.1, pp.595-639, 2014. ,
DOI : 10.1007/s00211-013-0597-6
Hyperbolic Divergence Cleaning for the MHD Equations, Journal of Computational Physics, vol.175, issue.2, pp.645-673, 2002. ,
DOI : 10.1006/jcph.2001.6961
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.458.630
Hamiltonian and symmetric hyperbolic structures of shallow water magnetohydrodynamics, Physics of Plasmas, vol.9, issue.4, p.1130, 2002. ,
DOI : 10.1063/1.1463415
Hyperbolic theory of the ???shallow water??? magnetohydrodynamics equations, Physics of Plasmas, vol.8, issue.7, p.3293, 2001. ,
DOI : 10.1063/1.1379045
Well-balanced schemes to capture non-explicit steady states: Ripa model, Mathematics of Computation, vol.85, issue.300, pp.1571-1602, 2016. ,
DOI : 10.1090/mcom/3069
A well-balanced scheme to capture non-explicit steady states in the Euler equations with gravity, International Journal for Numerical Methods in Fluids, vol.50, issue.2, pp.104-127, 2016. ,
DOI : 10.1002/fld.4177
Abstract, Communications in Computational Physics, vol.3, issue.02, pp.324-362, 2011. ,
DOI : 10.1016/0021-9991(87)90031-3
Augmented Riemann solvers for the shallow water equations over variable topography with steady states and inundation, Journal of Computational Physics, vol.227, issue.6, pp.3089-3113, 2008. ,
DOI : 10.1016/j.jcp.2007.10.027
Magnetohydrodynamic ???Shallow Water??? Equations for the Solar Tachocline, The Astrophysical Journal, vol.544, issue.1, pp.79-82, 2000. ,
DOI : 10.1086/317291
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
On the well-balance property of Roe's method for nonconservative hyperbolic systems. applications to shallow-water systems, ESAIM: Mathematical Modelling and Numerical Analysis, vol.38, issue.5, pp.821-852, 2004. ,
DOI : 10.1051/m2an:2004041
Application of space???time CE/SE method to shallow water magnetohydrodynamic equations, Journal of Computational and Applied Mathematics, vol.196, issue.1, pp.132-149, 2006. ,
DOI : 10.1016/j.cam.2005.08.014
A constrained transport method for the shallow water MHD equations, in Hyperbolic problems: theory, numerics, applications, 9th International Conference on Hyperbolic Problems, pp.851-860, 2002. ,
A wave propagation algorithm for hyperbolic systems on curved manifolds, Journal of Computational Physics, vol.199, issue.2, pp.199-631, 2004. ,
DOI : 10.1016/j.jcp.2004.03.002
A robust numerical scheme for highly compressible magnetohydrodynamics: Nonlinear stability, implementation and tests, Journal of Computational Physics, vol.230, issue.9, pp.3331-3351, 2011. ,
DOI : 10.1016/j.jcp.2011.01.026
A survey of high order schemes for the shallow water equations, J. Math. Study, vol.47, pp.221-249, 2014. ,
On the Advantage of Well-Balanced Schemes for??Moving-Water Equilibria of the Shallow Water Equations, Journal of Scientific Computing, vol.214, issue.1-3, pp.48-339, 2011. ,
DOI : 10.1007/s10915-010-9377-y
Remarks on rotating shallow-water magnetohydrodynamics, Nonlinear Processes in Geophysics, vol.20, issue.5, pp.893-898, 2013. ,
DOI : 10.5194/npg-20-893-2013
URL : https://hal.archives-ouvertes.fr/hal-01099390
Geostrophic vs magneto-geostrophic adjustment and nonlinear magneto-inertia-gravity waves in rotating shallow water magnetohydrodynamics, Geophysical & Astrophysical Fluid Dynamics, vol.9, issue.5, pp.497-523, 2015. ,
DOI : 10.5194/npg-20-893-2013
URL : https://hal.archives-ouvertes.fr/hal-01205761