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
A very simple well-balanced positive and entropy-satisfying scheme for the shallow-water equations, to appear in Commun, Math. Sci, 2015. ,
Upwind Methods for Hyperbolic Conservation Laws with Source Terms, Comp. & Fluids, pp.1049-1071, 1994. ,
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
Fully well-balanced, positive and simple approximate Riemann solver for shallow water equations, Bulletin of the Brazilian Mathematical Society, New Series, vol.33, issue.4, pp.1-14, 2016. ,
DOI : 10.1007/s00574-016-0126-1
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
Abstract, Communications in Computational Physics, vol.26, issue.02, pp.307-347, 2014. ,
DOI : 10.1016/j.advwatres.2009.12.006
A REDUCED STABILITY CONDITION FOR NONLINEAR RELAXATION TO CONSERVATION LAWS, Journal of Hyperbolic Differential Equations, vol.01, issue.01, pp.149-170, 2004. ,
DOI : 10.1142/S0219891604000020
Non-linear stability of finite volume methods for hyperbolic conservation laws and well-balanced schemes for sources, Frontiers in Mathematics, 2004. ,
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
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
Navier-Stokes equations with several independent pressure laws and explicit predictor-corrector schemes, Numerische Mathematik, vol.36, issue.3, pp.451-478, 2005. ,
DOI : 10.1007/s00211-005-0612-7
URL : https://hal.archives-ouvertes.fr/hal-00112166
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
Relaxation approximation of the Euler equations, Journal of Mathematical Analysis and Applications, vol.348, issue.2, pp.872-893, 2008. ,
DOI : 10.1016/j.jmaa.2008.07.034
Large Time-Step Numerical Scheme for the Seven-Equation Model of Compressible Two-Phase Flows, Proceedings in Mathematics, FVCA 6, pp.225-233, 2011. ,
DOI : 10.1007/978-3-642-20671-9_24
URL : https://hal.archives-ouvertes.fr/hal-01018835
Large Time Step and Asymptotic Preserving Numerical Schemes for the Gas Dynamics Equations with Source Terms, SIAM Journal on Scientific Computing, vol.35, issue.6, pp.2874-2902, 2013. ,
DOI : 10.1137/130908671
URL : https://hal.archives-ouvertes.fr/hal-00718022
Operator-splitting based AP schemes for the 1D and 2D gas dynamics equations with stiff sources, AIMS Series on Applied Mathematics, vol.8, pp.607-614, 2014. ,
Abstract, Communications in Computational Physics, 2016. ,
DOI : 10.1016/j.compfluid.2013.07.019
An all-regime Lagrange-Projection like scheme for 2D homogeneous models for two-phase flows on unstructured meshes, Journal of Computational Physics, vol.335 ,
DOI : 10.1016/j.jcp.2017.01.017
URL : https://hal.archives-ouvertes.fr/hal-01495699
Hyperbolic conservation laws with stiff relaxation terms and entropy, Communications on Pure and Applied Mathematics, vol.44, issue.6, pp.787-830, 1994. ,
DOI : 10.1002/cpa.3160470602
A well-balanced numerical scheme for the approximation of the shallow-water equations with topography: the resonance phenomenon, International Journal on Finite, vol.1, issue.1, pp.1-33, 2004. ,
URL : https://hal.archives-ouvertes.fr/hal-00017378
Entropy-satisfying relaxation method with large time-steps for Euler IBVPs, Mathematics of Computation, vol.79, issue.271, pp.1493-1533, 2010. ,
DOI : 10.1090/S0025-5718-10-02339-2
Some New Godunov and Relaxation Methods for Two-Phase Flow Problems, In Godunov methods, pp.179-188, 1999. ,
DOI : 10.1007/978-1-4615-0663-8_18
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
Numerical approximation of hyperbolic systems of conservation laws, Applied Mathematical Sciences, vol.118, 1996. ,
DOI : 10.1007/978-1-4612-0713-9
A well-balanced flux-vector splitting scheme designed for hyperbolic systems of conservation laws with source terms, Computers & Mathematics with Applications, vol.39, issue.9-10, pp.135-159, 2000. ,
DOI : 10.1016/S0898-1221(00)00093-6
Computing qualitatively correct approximations of balance laws. Exponential-fit, wellbalanced and asymptotic-preserving, SEMA SIMAI Springer Series, 2013. ,
A Well-Balanced Scheme for the Numerical Processing of Source Terms in Hyperbolic Equations, SIAM Journal on Numerical Analysis, vol.33, issue.1, pp.1-16, 1996. ,
DOI : 10.1137/0733001
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. ,
DOI : 10.1051/m2an:2001130
The relaxation schemes for systems of conservation laws in arbitrary space dimensions, Communications on Pure and Applied Mathematics, vol.54, issue.3, pp.235-276, 1995. ,
DOI : 10.1002/cpa.3160480303
A kinetic scheme for the Saint-Venant system with source term, Calcolo, pp.201-231, 2001. ,
On the thermodynamics of rate-type fluids and phase transitions. I. Rate-type fluids, International Journal of Engineering Science, vol.36, issue.9, pp.921-947, 1998. ,
DOI : 10.1016/S0020-7225(98)00005-6
Exactly well-balanced discontinuous Galerkin methods for the shallow water equations with moving water equilibrium, Journal of Computational Physics, vol.257, pp.536-553, 2014. ,
DOI : 10.1016/j.jcp.2013.10.010
High order well-balanced finite volume WENO schemes and discontinuous Galerkin methods for a class of hyperbolic systems with source terms, Journal of Computational Physics, vol.214, issue.2, pp.567-598, 2006. ,
DOI : 10.1016/j.jcp.2005.10.005
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.339-349, 2011. ,
DOI : 10.1007/s10915-010-9377-y
Positivity-preserving high order well-balanced discontinuous Galerkin methods for the shallow water equations, Advances in Water Resources, vol.33, issue.12, pp.1476-1493, 2010. ,
DOI : 10.1016/j.advwatres.2010.08.005
On the Mach-uniformity of the Lagrange--projection scheme, ESAIM: Mathematical Modelling and Numerical Analysis, 2016. ,
DOI : 10.1051/m2an/2016064