[3] E. Audusse, F. Bouchut, M.-O. Bristeau, R. Klein, and B. Perthame, A fast and stable well-balanced scheme with hydrostatic reconstruction for Shallow Water flows, SIAM J. Sci. Comput. 25 (2004), no. 6, 2050–2065.
[4] E. Audusse, F. Bouchut, M.-O. Bristeau, and J. Sainte-Marie, Kinetic entropy inequality and hydrostatic reconstruction scheme for the Saint-Venant system, Math. Comp. 85 (2016), no. 302, 2815–2837. MR 3522971
[5] E. Audusse and M.-O. Bristeau, A well-balanced positivity preserving second-order scheme for Shallow Water flows on unstructured meshes, J. Comput. Phys. 206 (2005), no. 1, 311–333.
[6] ——, Finite-volume solvers for a multilayer Saint-Venant system, Int. J. Appl. Math. Comput. Sci. 17 (2007), no. 3, 311–319.
[7] E. Audusse, M.-O. Bristeau, and A. Decoene, Numerical simulations of 3d free surface flows by a multilayer Saint-Venant model, Internat. J. Numer. Methods Fluids 56 (2008), no. 3, 331–350.
[8] E. Audusse, M.-O. Bristeau, M. Pelanti, and J. Sainte-Marie, Approximation of the hydrostatic Navier-Stokes system for density stratified flows by a multilayer model. Kinetic interpretation and numerical validation., J. Comp. Phys. 230 (2011), 3453–3478.
[9] E. Audusse, M.-O. Bristeau, B. Perthame, and J. Sainte-Marie, A multilayer Saint-Venant system with mass exchanges for Shallow Water flows. Derivation and numerical validation, ESAIM: M2AN 45 (2011), 169–200.
[10] E. Audusse, M.-O. Bristeau, and J. Sainte-Marie, Kinetic entropy for the layer-averaged hydrostatic Navier-Stokes equations, working paper or preprint, September 2017.
[11] A.-J.-C. Barré de Saint-Venant, Théorie du mouvement non permanent des eaux avec applications aux crues des rivières et à l'introduction des marées dans leur lit, C. R. Acad. Sci. Paris 73 (1871), 147–154.
[12] O. Bernard, A.-C. Boulanger, M.-O. Bristeau, and J. Sainte-Marie, A 2d model for hydrodynamics and biology coupling applied to algae growth simulations, ESAIM: Mathematical Modelling and Numerical Analysis 47 (2013), 1387–1412.
[13] F. Berthelin and F. Bouchut, Relaxation to isentropic gas dynamics for a BGK system with single kinetic entropy, Methods Appl. Anal. 9 (2002), no. 2, 313–327. MR 1957492
[14] F. Bouchut, Construction of BGK models with a family of kinetic entropies for a given system of conservation laws, J. Stat. Phys. 95 (1999), 113–170.
[15] ——, Entropy satisfying flux vector splittings and kinetic BGK models, Numer. Math. 94 (2003), 623–672.
[16] ——, An introduction to finite volume methods for hyperbolic conservation laws, ESAIM Proc. 15 (2004), 107–127.
[17] ——, Nonlinear stability of finite volume methods for hyperbolic conservation laws and well-balanced schemes for sources, Birkhäuser, 2004.
[18] F. Bouchut and T. Morales de Luna, An entropy satisfying scheme for two-layer shallow water equations with uncoupled treatment, M2AN Math. Model. Numer. Anal. 42 (2008), 683–698.