H. Babovsky, On a simulation scheme for the Boltzmann equation, Mathematical Methods in the Applied Sciences, vol.81, issue.1, pp.223-233, 1986.
DOI : 10.1002/mma.1670080114

C. Bardos, F. Golse, and D. 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

G. A. Bird, Molecular gas dynamics and direct simulation of gas flows, 1994.

M. Bennoune, M. Lemou, and L. 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

URL : https://hal.archives-ouvertes.fr/hal-00348598

J. Burt and I. Boyd, A hybrid particle approach for continuum and rarefied flow simulation, Journal of Computational Physics, vol.228, issue.2, pp.460-475, 2009.
DOI : 10.1016/j.jcp.2008.09.022

S. Brunner, E. Valeo, and J. A. Krommes, scheme with evolving background for transport time scale simulations, Physics of Plasmas, vol.6, issue.12, p.12, 1999.
DOI : 10.1063/1.873738

S. Brunner, E. Valeo, and J. A. Krommes, simulations of nonlocal electron heat transport, Physics of Plasmas, vol.7, issue.7, 2000.
DOI : 10.1063/1.874131

M. , C. Pinto, and F. Charles, Uniform convergence of a linearly transformed particle method for the Vlasov-Poisson system, SIAM J. Numer. Anal, pp.54-137, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01080732

C. Cercignani, The Boltzmann equation and its applications, 1988.
DOI : 10.1007/978-1-4612-1039-9

A. Crestetto, N. Crouseilles, and M. Lemou, Kinetic/fluid micro-macro numerical schemes for Vlasov-Poisson-BGK equation using particles, Kinetic and Related Models, vol.5, issue.4, pp.787-816, 2012.
DOI : 10.3934/krm.2012.5.787

URL : https://hal.archives-ouvertes.fr/hal-00728875

N. Crouseilles and M. Lemou, An asymptotic preserving scheme based on a micro-macro decomposition for Collisional Vlasov equations: diffusion and high-field scaling limits, Kinetic and Related Models, vol.4, issue.2, pp.441-477, 2011.
DOI : 10.3934/krm.2011.4.441

URL : https://hal.archives-ouvertes.fr/hal-00533327

P. Degond, G. Dimarco, and L. Pareschi, The moment-guided Monte Carlo method, International Journal for Numerical Methods in Fluids, vol.5, issue.1, pp.189-213, 2011.
DOI : 10.1002/fld.2345

URL : https://hal.archives-ouvertes.fr/hal-00408891

P. Degond and G. Dimarco, Fluid simulations with localized boltzmann upscaling by direct simulation Monte-Carlo, Journal of Computational Physics, vol.231, issue.6, pp.2414-2437, 2012.
DOI : 10.1016/j.jcp.2011.11.030

URL : https://hal.archives-ouvertes.fr/hal-00933464

P. Degond, S. Jin, and L. 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

URL : https://hal.archives-ouvertes.fr/hal-00362974

G. Dimarco, The moment guided Monte Carlo method for the Boltzmann equation, Kinetic and Related Models, vol.6, issue.2, pp.291-315, 2013.
DOI : 10.3934/krm.2013.6.291

URL : https://hal.archives-ouvertes.fr/hal-00966057

G. Dimarco and L. Pareschi, Hybrid Multiscale Methods II. Kinetic Equations, Multiscale Modeling & Simulation, vol.6, issue.4, pp.1169-1197, 2007.
DOI : 10.1137/070680916

R. Caflisch, C. Wang, G. Dimarco, B. Cohen, and A. , A Hybrid Method for Accelerated Simulation of Coulomb Collisions in a Plasma, Multiscale Modeling & Simulation, vol.7, issue.2, pp.865-887, 2008.
DOI : 10.1137/070704939

G. Dimarco and L. Pareschi, Fluid Solver Independent Hybrid Methods for Multiscale Kinetic Equations, SIAM Journal on Scientific Computing, vol.32, issue.2, pp.603-634, 2010.
DOI : 10.1137/080730585

URL : https://hal.archives-ouvertes.fr/hal-00629581

G. Dimarco and L. Pareschi, Asymptotic preserving implicit-explicit Runge-Kutta methods for non linear kinetic equations, SIAM J. Num. Anal, vol.32, pp.1064-1087, 2013.

G. Dimarco and L. Pareschi, Numerical methods for kinetic equations, Acta Numerica, vol.39, pp.369-520, 2014.
DOI : 10.3934/krm.2011.4.441

URL : https://hal.archives-ouvertes.fr/hal-00986714

F. Filbet and T. Rey, A Hierarchy of Hybrid Numerical Methods for Multiscale Kinetic Equations, SIAM Journal on Scientific Computing, vol.37, issue.3, pp.1218-1247, 2015.
DOI : 10.1137/140958773

URL : https://hal.archives-ouvertes.fr/hal-00951980

D. B. Hash and H. A. Hassan, Assessment of schemes for coupling Monte Carlo and Navier-Stokes solution methods, Journal of Thermophysics and Heat Transfer, vol.10, issue.2, pp.242-249, 1996.
DOI : 10.2514/3.781

T. Homolle and N. Hadjiconstantinou, A low-variance deviational simulation Monte Carlo for the Boltzmann equation, Journal of Computational Physics, vol.226, issue.2, pp.2341-2358, 2007.
DOI : 10.1016/j.jcp.2007.07.006

T. Homolle and N. Hadjiconstantinou, Low-variance deviational simulation Monte Carlo, Physics of Fluids, vol.19, issue.4, p.41701, 2007.
DOI : 10.1063/1.2717721

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

Q. Li, J. Lu, and W. Sun, Diffusion approximations and domain decomposition method of linear transport equations: Asymptotics and numerics, Journal of Computational Physics, vol.292, pp.141-167, 2015.
DOI : 10.1016/j.jcp.2015.03.014

Q. Li, J. Lu, and W. Su, Half-space Kinetic Equations with General Boundary Conditions, to appear in Math, Comp, 2016.

M. Lemou, Relaxed micro???macro schemes for kinetic equations, Comptes Rendus Mathematique, vol.348, issue.7-8, pp.455-460, 2010.
DOI : 10.1016/j.crma.2010.02.017

URL : https://hal.archives-ouvertes.fr/hal-00521523

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

P. Letallec and F. Mallinger, Coupling Boltzmann and Navier???Stokes Equations by Half Fluxes, Journal of Computational Physics, vol.136, issue.1, pp.51-67, 1997.
DOI : 10.1006/jcph.1997.5729

R. J. Leveque, Numerical methods for conservation laws, Lecture in Mathematics, 1992.

S. Liu, Monte Carlo strategies in scientific computing, 2004.
DOI : 10.1007/978-0-387-76371-2

K. Nanbu, Direct simulation scheme derived from the Boltzmann equation, J. Phys. Soc. Japan, pp.49-2042, 1980.

G. A. Radtke, J. M. Peraud, and N. Hadjiconstantinou, On efficient simulations of multiscale kinetic transport, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.45, issue.1, pp.371-2012182, 2013.
DOI : 10.1063/1.354111

S. Tiwari, A. Klar, and S. Hardt, A particle???particle hybrid method for kinetic and continuum equations, Journal of Computational Physics, vol.228, issue.18, pp.7109-7124, 2009.
DOI : 10.1016/j.jcp.2009.06.019

B. Yan, A hybrid method with deviational particles for spatial inhomogeneous plasma, Journal of Computational Physics, vol.309, pp.18-36, 2016.
DOI : 10.1016/j.jcp.2015.12.050

B. Yan and R. Caflisch, A Monte Carlo method with negative particles for Coulomb collisions, Journal of Computational Physics, vol.298, pp.711-740, 2015.
DOI : 10.1016/j.jcp.2015.06.021

. Acknowledgments, This work was supported by the french ANR project MOON- RISE ANR-14-CE23-0007-01, Crouseilles and M. Lemou are supported by the Enabling Research EUROFusion project CfP-WP14-ER-01/IPP-03