C. Bardos-;-f, D. Golse, and . Levermore, Fluid dynamic limits of kinetic equations. I. Formal derivations, Journal of Statistical Physics, vol.16, issue.1-2, pp.323-344, 1991.
DOI : 10.1007/BF01026608

M. Bennoune-;-m, L. Lemou, and . Mieussens, Uniformly stable numerical schemes for the Boltzmann equation preserving the compressible Navier???Stokes asymptotics, Journal of Computational Physics, vol.227, issue.8, pp.3781-3803, 2008.
DOI : 10.1016/j.jcp.2007.11.032

P. L. Bhatnagar, E. P. Gross, and K. Krook, A model for collision processes in gases, Phys. Rev, pp.94-511, 1954.

J. Bourgat, P. Le-tallec, B. Perthame, and Y. Qiu, Coupling Boltzmann and Euler equations without overlapping, Contemp. Math, vol.157, pp.377-398, 1994.
DOI : 10.1090/conm/157/01439

R. Caflish-;-s, G. Jin, and . Russo, Uniformly Accurate Schemes for Hyperbolic Systems with Relaxation, SIAM Journal on Numerical Analysis, vol.34, issue.1, p.246281, 1997.
DOI : 10.1137/S0036142994268090

R. E. Caflisch and L. Pareschi, An implicit Monte Carlo method for rarefied gas dynamics I: The space homogeneous case, J. Computational Physics, vol.154, pp.90-116, 1999.

J. A. Carrillo and G. , Toscani Asymptotic L 1 -decay of solutions of the porous medium equation to self-similarity, Math. J, vol.49, pp.113-142, 2000.

C. Cercignani, The Boltzmann equation and its applications, 1998.
DOI : 10.1007/978-1-4612-1039-9

C. Chainais-hillairet and F. Filbet, Asymptotic behaviour of a finite-volume scheme for the transient drift-diffusion model, IMA Journal of Numerical Analysis, vol.27, issue.4, pp.689-716, 2007.
DOI : 10.1093/imanum/drl045

G. Q. Chen, T. P. Liu, and C. D. Levermore, 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

F. Coquel and B. Perthame, Relaxation of Energy and Approximate Riemann Solvers for General Pressure Laws in Fluid Dynamics, SIAM Journal on Numerical Analysis, vol.35, issue.6, pp.2223-2249, 1998.
DOI : 10.1137/S0036142997318528

F. Coron and B. Perthame, Numerical Passage from Kinetic to Fluid Equations, SIAM Journal on Numerical Analysis, vol.28, issue.1, pp.26-42, 1991.
DOI : 10.1137/0728002

P. Crispel-;-p, M. Degond, and . Vignal, An asymptotically preserving scheme for the two-fluid Euler-Poisson model in the quasi-neutral limit, J. Comput. Phys, pp.223-208234, 2007.

P. Degond-;-f, L. Deluzet, and . Navoret, An asymptotically stable Particle-in-Cell (PIC) scheme for collisionless plasma simulations near quasineutrality, Comptes Rendus Mathematique, vol.343, issue.9, pp.343-613618, 2006.
DOI : 10.1016/j.crma.2006.09.033

P. Degond and S. Jin, A Smooth Transition Model between Kinetic and Diffusion Equations, SIAM Journal on Numerical Analysis, vol.42, issue.6, pp.2671-2687, 2005.
DOI : 10.1137/S0036142903430414

P. Degond-;-s, J. Jin, and . Liu, Mach-number uniform asymptotic-preserving gauge schemes for compressible flows, Bull. Inst. Math. Acad. Sin. (N.S.), vol.2, pp.851-892, 2007.

P. Degond-;-s, L. Jin, and . Mieussens, A smooth transition model between kinetic and hydrodynamic equations, Journal of Computational Physics, vol.209, issue.2, pp.665-694, 2005.
DOI : 10.1016/j.jcp.2005.03.025

F. Filbet and L. Pareschi, A Numerical Method for the Accurate Solution of the Fokker???Planck???Landau Equation in the Nonhomogeneous Case, Journal of Computational Physics, vol.179, issue.1, pp.1-26, 2002.
DOI : 10.1006/jcph.2002.7010

F. Filbet and G. Russo, High order numerical methods for the space non-homogeneous Boltzmann equation, Journal of Computational Physics, vol.186, issue.2, pp.457-480, 2003.
DOI : 10.1016/S0021-9991(03)00065-2

F. Filbet-;-l, G. Pareschi, and . Toscani, Accurate numerical methods for the collisional motion of (heated) granular flows, Journal of Computational Physics, vol.202, issue.1, pp.216-235, 2005.
DOI : 10.1016/j.jcp.2004.06.023

F. Filbet, A finite volume scheme for the Patlak???Keller???Segel chemotaxis model, Numerische Mathematik, vol.146, issue.N 37(4, pp.457-488, 2006.
DOI : 10.1007/s00211-006-0024-3

F. Filbet, An asymptotically stable scheme for diffusive coagulation-fragmentation models, Communications in Mathematical Sciences, vol.6, issue.2, pp.257-280, 2008.
DOI : 10.4310/CMS.2008.v6.n2.a1

URL : https://hal.archives-ouvertes.fr/hal-00167384

F. Filbet, C. W. Shu, E. Gabetta-;-l, G. Pareschi, and . Toscani, Relaxation schemes for nonlinear kinetic equations, work in progress [25], pp.34-2168, 1997.

C. W. Gear, Numerical Initial Value Problems in Ordinary Differential Equations, 1971.

F. Golse, S. Jin, and C. D. Levermore, The Convergence of Numerical Transfer Schemes in Diffusive Regimes I: Discrete-Ordinate Method, SIAM Journal on Numerical Analysis, vol.36, issue.5, pp.36-1333, 1999.
DOI : 10.1137/S0036142997315986

L. Gosse and G. Toscani, An asymptotic-preserving well-balanced scheme for the hyperbolic heat equations, Comptes Rendus Mathematique, vol.334, issue.4, pp.337-342, 2002.
DOI : 10.1016/S1631-073X(02)02257-4

M. Günther, P. Le-tallec, J. Perlat, and J. Struckmeier, Numerical Modeling of Gas Flows in the Transition between Rarefied and Continuum Regimes, Notes Numer. Fluid Mech, vol.66, pp.222-241, 1997.
DOI : 10.1007/978-3-663-10916-7_11

J. Haack, S. Jin, and J. Liu, An all-speed asymptotic-preserving schemes for compressible flows

S. Jin, Efficient Asymptotic-Preserving (AP) Schemes For Some Multiscale Kinetic Equations, SIAM Journal on Scientific Computing, vol.21, issue.2, pp.441-454, 1999.
DOI : 10.1137/S1064827598334599

S. Jin, Runge-Kutta Methods for Hyperbolic Conservation Laws with Stiff Relaxation Terms, Journal of Computational Physics, vol.122, issue.1, pp.51-67, 1995.
DOI : 10.1006/jcph.1995.1196

S. Jin and C. D. Levermore, Numerical Schemes for Hyperbolic Conservation Laws with Stiff Relaxation Terms, Journal of Computational Physics, vol.126, issue.2, pp.449-467, 1996.
DOI : 10.1006/jcph.1996.0149

S. Jin and L. Pareschi, Discretization of the Multiscale Semiconductor Boltzmann Equation by Diffusive Relaxation Schemes, Journal of Computational Physics, vol.161, issue.1, pp.312-330, 2000.
DOI : 10.1006/jcph.2000.6506

S. Jin, L. Pareschi, and G. Toscani, Diffusive Relaxation Schemes for Multiscale Discrete-Velocity Kinetic Equations, SIAM Journal on Numerical Analysis, vol.35, issue.6, pp.2405-2439, 1998.
DOI : 10.1137/S0036142997315962

S. Jin-;-l, G. Pareschi, and . Toscani, Uniformly Accurate Diffusive Relaxation Schemes for Multiscale Transport Equations, SIAM Journal on Numerical Analysis, vol.38, issue.3, pp.913-936, 2000.
DOI : 10.1137/S0036142998347978

A. Klar, An Asymptotic-Induced Scheme for Nonstationary Transport Equations in the Diffusive Limit, SIAM Journal on Numerical Analysis, vol.35, issue.3, 1998.
DOI : 10.1137/S0036142996305558

A. Klar, An Asymptotic Preserving Numerical Scheme for Kinetic Equations in the Low Mach Number Limit, SIAM Journal on Numerical Analysis, vol.36, issue.5, p.15071527, 1999.
DOI : 10.1137/S0036142997321765

A. Klar, H. Neunzert, and J. Struckmeier, Transition from Kinetic theory to macroscopic fluid equations: A problem for domain decomposition and a source for new algorithms, Transport Theory and Statistical Physics, vol.15, issue.1-2, pp.29-93, 2000.
DOI : 10.1023/B:JOSS.0000015179.12689.e4

M. Lemou and L. Mieussens, A New Asymptotic Preserving Scheme Based on Micro-Macro Formulation for Linear Kinetic Equations in the Diffusion Limit, SIAM Journal on Scientific Computing, vol.31, issue.1, pp.31-334, 2008.
DOI : 10.1137/07069479X

URL : https://hal.archives-ouvertes.fr/hal-00348594

L. Pareschi and G. Russo, Time Relaxed Monte Carlo Methods for the Boltzmann Equation, SIAM Journal on Scientific Computing, vol.23, issue.4, pp.1253-1273, 2001.
DOI : 10.1137/S1064827500375916

P. , L. Tallec, and F. Mallinger, Coupling Boltzmann and Navier-Stoke s equations by half fluxes, J. Comput. Phys, vol.136, pp.51-67, 1997.

H. C. Yee, A Class of High-Resolution Explicit and Implicit Shock-Capturing Methods, Von Karman Institute for Fluid Dynamics Lecture Series, 1989.