N. Andrianov, Performance of numerical methods on the non-unique solution to the Riemann problem for the shallow water equations, International Journal for Numerical Methods in Fluids, vol.146, issue.8-9, pp.825-831, 2005.
DOI : 10.1002/fld.846

E. Audusse, F. Bouchut, M. Bristeau, R. Klein, and B. Perthame, 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.
DOI : 10.1137/S1064827503431090

D. S. Bale, R. J. Leveque, S. Mitran, and J. A. Rossmanith, A Wave Propagation Method for Conservation Laws and Balance Laws with Spatially Varying Flux Functions, SIAM Journal on Scientific Computing, vol.24, issue.3, 2002.
DOI : 10.1137/S106482750139738X

C. Berthon and C. Chalons, A fully well-balanced, positive and entropy-satisfying Godunov-type method for the shallow-water equations, Mathematics of Computation, vol.85, issue.299, p.956799, 2014.
DOI : 10.1090/mcom3045

URL : https://hal.archives-ouvertes.fr/hal-00956799

C. Berthon and F. Foucher, 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

F. Bouchut, Nonlinear stability of finite volume methods for hyperbolic conservation laws and well-balanced schemes for sources, Frontiers in Mathematics, 2004.

F. Bouchut and T. Morales, 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

M. Castro, J. Macias, and C. Pares, -scheme for a class of systems of coupled conservation laws with source term. Application to a two-layer 1-D shallow water system, ESAIM: Mathematical Modelling and Numerical Analysis, vol.35, issue.1, pp.107-127, 2001.
DOI : 10.1051/m2an:2001108

URL : https://hal.archives-ouvertes.fr/hal-00908624

M. J. Castro, A. Pardo, C. Pares, and E. F. Toro, 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

C. Chalons, F. Coquel, E. Godlewski, P. Raviart, and N. Seguin, 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, p.20, 2010.
DOI : 10.1142/S021820251000488X

URL : https://hal.archives-ouvertes.fr/hal-00401616

A. Chinnayya, A. Leroux, and N. Seguin, A well-balanced numerical scheme for the approximation of the shallow-water equations with topography: the resonance phenomenon, International Journal on Finite Volumes, vol.1, pp.1-33, 2004.
URL : https://hal.archives-ouvertes.fr/hal-00017378

G. Gallice, 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

G. Gallice, 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

T. Gallouët, J. Hérard, and N. Seguin, Some approximate Godunov schemes to compute shallow-water equations with topography, Computers and Fluids, pp.479-513, 2003.

A. Harten, P. Lax, and B. Van-leer, On upstream differencing and Godunov-type schemes for hyperbolic conservation laws, SIAM Review, vol.25, issue.1, pp.53-61, 1983.

R. Leveque, 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.
DOI : 10.1006/jcph.1998.6058

T. Morales-de-luna, M. J. Castro-diaz, and C. Pares, Reliability of first order numerical schemes for solving shallow water system over abrupt topography, Applied Mathematics and Computation, vol.219, issue.17, pp.9012-9032, 2013.
DOI : 10.1016/j.amc.2013.03.033

B. Perthame and C. Simeoni, A kinetic scheme for the Saint-Venant system with source term, Calcolo, pp.201-231, 2001.