M. Bachmann, S. Müller, P. Helluy, and H. Mathis, A simple model 165 for cavitation with non-condensable gases, Hyperbolic Problems: Theory, Numerics and Applications, pp.289-296, 2012.

F. Bouchut, Construction of BGK models with a family of kinetic entropies for a given system of conservation laws, Journal of Statistical Physics, vol.95, issue.1-2, pp.113-170, 1999.

D. Coulette and E. Franck,

, High-order implicit palindromic discontinuous galerkin method for kinetic-relaxation approximation, Computers & Fluids, vol.190, pp.485-502, 2019.

C. Courtès, D. Coulette, E. Franck, and L. Navoret, Vectorial kinetic relaxation model with central velocity. application to implicit relaxations schemes, 2018.

F. Drui, E. Franck, P. Helluy, and L. Navoret, An analysis of over-175 relaxation in a kinetic approximation of systems of conservation laws, Comptes Rendus Mécanique, vol.347, issue.3, pp.259-269, 2019.

F. Dubois, Equivalent partial differential equations of a lattice boltzmann scheme, Computers & Mathematics with Applications, vol.55, issue.7, pp.1441-1449, 2008.
URL : https://hal.archives-ouvertes.fr/hal-01809947

A. Harten, D. Peter, B. Lax, and . Van-leer, On upstream differencing and godunov-type 180 schemes for hyperbolic conservation laws, SIAM review, vol.25, issue.1, pp.35-61, 1983.

P. Helluy and H. Mathis, Pressure laws and fast legendre transform, Mathematical Models and Methods in Applied Sciences, vol.21, issue.04, pp.745-775, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00424061

S. Jin and Z. Xin, The relaxation schemes for systems of conservation laws in arbitrary space dimensions, Communications on Pure and Applied Mathematics, vol.48, issue.3, pp.235-276, 1995.

H. Otomo, M. Bruce, F. Boghosian, and . Dubois, Two complementary latticeboltzmann-based analyses for nonlinear systems, Physica A: Statistical Mechanics and its Applications, vol.486, pp.1000-1011, 2017.