D. Aregba-driollet and R. Natalini, Discrete Kinetic Schemes for Multidimensional Systems of Conservation Laws, SIAM Journal on Numerical Analysis, vol.37, issue.6, pp.1973-2004, 2000.
DOI : 10.1137/S0036142998343075
URL : https://hal.archives-ouvertes.fr/hal-00959531

J. Bey and G. Wittum, Downwind numbering: robust multigrid for convection-diffusion problems, Applied Numerical Mathematics, vol.23, issue.1, pp.177-192, 1997.
DOI : 10.1016/S0168-9274(96)00067-0

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.
DOI : 10.1023/A:1004525427365

S. Chen and G. D. Doolen, LATTICE BOLTZMANN METHOD FOR FLUID FLOWS, Annual Review of Fluid Mechanics, vol.30, issue.1, pp.329-364, 1998.
DOI : 10.1146/annurev.fluid.30.1.329

F. Coquel, Q. L. Nguyen, M. Postel, and Q. H. Tran, Large Time Step Positivity-Preserving Method for Multiphase Flows, pp.849-856, 2008.
DOI : 10.1007/978-3-540-75712-2_88

D. Coulette, E. Franck, P. Helluy, M. Mehrenberger, and L. Navoret, Palindromic discontinuous Galerkin method for kinetic equations with stiff relaxation. arXiv preprint arXiv, pp.1612-09422, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01422922

B. Graille, Approximation of mono-dimensional hyperbolic systems: A lattice Boltzmann scheme as a relaxation method, Journal of Computational Physics, vol.266, pp.74-88, 2014.
DOI : 10.1016/j.jcp.2014.02.017
URL : https://hal.archives-ouvertes.fr/hal-00919835

E. Hairer, C. Lubich, and G. Wanner, Geometric numerical integration: structure-preserving algorithms for ordinary differential equations, 2006.

W. Kahan and R. C. Li, Composition constants for raising the orders of unconventional schemes for ordinary differential equations, Mathematics of Computation, vol.66, issue.219, pp.1089-1099, 1997.
DOI : 10.1090/S0025-5718-97-00873-9

R. I. Mclachlan and G. R. Quispel, Splitting methods, Acta Numerica, vol.11, pp.341-434, 2002.

X. Shi, J. Lin, and Z. Yu, Discontinuous Galerkin spectral element lattice Boltzmann method on triangular element, International Journal for Numerical Methods in Fluids, vol.165, issue.11, pp.1249-1261, 2003.
DOI : 10.1002/fld.594

M. Suzuki, Fractal decomposition of exponential operators with applications to many-body theories and Monte Carlo simulations, Physics Letters A, vol.146, issue.6, pp.319-323, 1990.
DOI : 10.1016/0375-9601(90)90962-N