D. Aregba-driolet, J. Breil, S. Brull, B. Dubroca, and E. Estibals, Modelling and numerical approximation for the nonconservative bitemperature Euler model, 2017.

S. Atzeni and J. Meyer-ter-vehn, The Physics of Intertial Fusion, 2004.

R. Balescu, Classical Transport, volume 1 of Transport Processes in Plasmas, 1988.

R. Balescu, Classical Transport, volume 2 of Transport Processes in Plasmas, 1988.

D. Balsara and D. Spicer, A Staggered Mesh Algorithm Using High Order Godunov Fluxes to Ensure Solenoidal Magnetic Fields in Magnetohydrodynamic Simulations, Journal of Computational Physics, vol.149, issue.2, pp.270-292, 1999.
DOI : 10.1006/jcph.1998.6153

P. Batten, N. Clarke, C. Lambert, and D. M. Causson, On the Choice of Wavespeeds for the HLLC Riemann Solver, SIAM Journal on Scientific Computing, vol.18, issue.6, pp.1553-1570, 1997.
DOI : 10.1137/S1064827593260140

C. Berthon, F. Coquel, and P. G. Lefloch, Why many theories of shock waves are necessary: kinetic relations for non-conservative systems, Proceedings of the Royal Society of Edinburgh: Section A Mathematics, vol.142, issue.01, pp.1-37, 2012.
DOI : 10.1017/S0308210510001009

C. Berthon, B. Dubroca, and A. Sangam, A Local Entropy Minimum Principle for Deriving Entropy Preserving Schemes, SIAM Journal on Numerical Analysis, vol.50, issue.2, pp.468-491, 2012.
DOI : 10.1137/100814445

URL : https://hal.archives-ouvertes.fr/hal-01280691

C. Berthon, B. Dubroca, and A. Sangam, An entropy preserving relaxation scheme for ten-moments equations with source terms, Communications in Mathematical Sciences, vol.13, issue.8, pp.2119-2154, 2015.
DOI : 10.4310/CMS.2015.v13.n8.a7

URL : https://hal.archives-ouvertes.fr/hal-01255069

A. Bettinger and M. Decroisette, Laser megajoule project and impact on the inertial fusion program, Fusion Engineering and Design, vol.46, issue.2-4, pp.457-460, 1999.
DOI : 10.1016/S0920-3796(99)00037-X

P. L. Bhatnagar, E. P. Gross, and K. Krook, A Model for Collision Processes in Gases. I. Small Amplitude Processes in Charged and Neutral One-Component Systems, Physical Review, vol.22, issue.3, pp.511-524, 1954.
DOI : 10.1121/1.1906652

M. Bilanceri, L. Combe, H. Guillard, and A. Sangam, A 3D finite volume scheme for the simulation of edge plasma in Tokamaks, ESAIM: Proceedings, pp.164-179, 2013.
DOI : 10.1051/proc/201343011

URL : https://hal.archives-ouvertes.fr/hal-01306960

J. Blum, Numerical Simulation and Optimal Control in Plasma Physics, Series in Applied Mathematics. Wiley and Gauthier-Villars, 1989.

A. Bonnement, Modélisation numérique par approximation fluide du plasma de bord des tokamaks (projet ITER), Ecole Doctorale en Sciences Fondamentales et Appliquées, 2012.

A. Bonnement, T. Fajraoui, H. Guillard, M. Martin, B. Nkonga et al., Finite volume method in curvilinear coordinates for hyperbolic conservation laws, ESAIM: Proceedings, pp.163-176, 2011.
DOI : 10.1051/proc/2011019

URL : https://hal.archives-ouvertes.fr/hal-00914822

F. Bouchut, Nonlinear Stability of Finite Volume Methods for hyperbolic Conservation Laws and Well-Balanced Schemes for Sources, Birkhäuser, 2004.

J. U. Brackbill and D. C. Barnes, The Effect of Nonzero ??? ?? B on the numerical solution of the magnetohydrodynamic equations, Journal of Computational Physics, vol.35, issue.3, pp.426-430, 1980.
DOI : 10.1016/0021-9991(80)90079-0

S. I. Braginskii, Transport processes in a plasma, Reviews of Plasma Physics, vol.1, pp.205-311, 1965.

M. Brio and C. C. Wu, An upwind differencing scheme for the equations of ideal magnetohydrodynamics, Journal of Computational Physics, vol.75, issue.2, pp.400-422, 1988.
DOI : 10.1016/0021-9991(88)90120-9

F. Coquel and C. Marmignon, Numerical methods for weakly ionized gas, Astrophysics and Space Science, vol.260, issue.1/2, pp.15-27, 1998.
DOI : 10.1023/A:1001870802972

R. Dautray and J. Watteau, La Fusion Thermonucléaire Inertielle par Laser, Partie 2, les Techniques Expérimentales et Numériques, 1993.

D. De-santis, G. Geraci, and A. Guardone, Node-pair finite volume/finite element schemes for the Euler equation in cylindrical and spherical coordinates, Journal of Computational and Applied Mathematics, vol.236, issue.18, pp.4827-4839, 2012.
DOI : 10.1016/j.cam.2012.02.006

A. Decoster, Fluid equations and transport coefficients of plasmas, Modelling of collisions. Masson, 1997.

A. Dedner, D. Kröner, C. Munz, T. Schnitzer, and M. Wesenberg, Hyperbolic Divergence Cleaning for the MHD Equations, Journal of Computational Physics, vol.175, issue.2, pp.645-673, 2002.
DOI : 10.1006/jcph.2001.6961

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.458.630

B. Einfeldt, C. Munz, P. Roe, and B. Sjögreen, On Godunov-type methods near low densities, Hervé Guillard, and Afeintou Sangam. Bi-temperature Euler Equations Modeling for Fusion Plasma. Research Report RR-9026, pp.273-295, 1991.
DOI : 10.1016/0021-9991(91)90211-3

C. R. Evans and J. F. Hawley, Simulation of magnetohydrodynamic flows - A constrained transport method, The Astrophysical Journal, vol.332, pp.659-677, 1988.
DOI : 10.1086/166684

N. M. Ferraro and S. C. Jardin, Calculations of two-fluid magnetohydrodynamic axisymmetric steady-states, Journal of Computational Physics, vol.228, issue.20, pp.7742-7770, 2009.
DOI : 10.1016/j.jcp.2009.07.015

M. Fey and M. Torrilhon, A Constrained Transport Upwind Scheme for Divergencefree Advection, pp.529-538, 2003.
DOI : 10.1007/978-3-642-55711-8_49

R. Fitzpatrick, Plasma physics: an introduction, 2014.

J. P. Freidberg, Plasma Physics and Fusion, 2007.

D. Furfaro and R. Saurel, A simple HLLC-type Riemann solver for compressible non-equilibrium two-phase flows, Computers & Fluids, vol.111, pp.159-178, 2015.
DOI : 10.1016/j.compfluid.2015.01.016

URL : https://hal.archives-ouvertes.fr/hal-01278892

S. Galera, P. Maire, and J. Breil, A two-dimensional unstructured cell-centered multi-material ALE scheme using VOF interface reconstruction, Journal of Computational Physics, vol.229, issue.16, pp.5755-5787, 2010.
DOI : 10.1016/j.jcp.2010.04.019

URL : https://hal.archives-ouvertes.fr/inria-00453534

E. Godlewski and P. A. Raviart, Numerical Approximation of Hyperbolic System of Conservation Laws, 1996.
DOI : 10.1007/978-1-4612-0713-9

J. P. Goedbloed, R. Keppens, and S. Poedt, Advanced Magnetohydrodynamics: With Applications to Laboratory and Astrophysical Plasmas, 2010.
DOI : 10.1017/CBO9781139195560

J. P. Goedbloed and S. Poedt, Principles of Magnetohydrodynamics: With Applications to Laboratory and Astrophysical Plasmas, 2004.
DOI : 10.1017/CBO9780511616945

V. Grandgirard, M. Brunetti, P. Bertrand, N. Besse, X. Garbet et al., A drift-kinetic Semi-Lagrangian 4D code for ion turbulence simulation, Journal of Computational Physics, vol.217, issue.2, pp.395-423, 2006.
DOI : 10.1016/j.jcp.2006.01.023

URL : https://hal.archives-ouvertes.fr/hal-00594856

H. Guillard and R. Abgrall, Modélisation Numérique des Fluides Compressibles, Series in Applied Mathematics, 2001.

A. Harten, P. D. Lax, and B. Van-leer, On Upstream Differencing and Godunov-Type Schemes for Hyperbolic Conservation Laws, SIAM Review, vol.25, issue.1, p.35, 1983.
DOI : 10.1137/1025002

W. J. Hogan, E. I. Mosses, B. E. Warner, M. S. Soren, and J. M. Soures, The National Ignition Facility, Nuclear Fusion, vol.41, issue.5, pp.565-573, 2001.
DOI : 10.1088/0029-5515/41/5/309

J. D. Huba, NRL plasma formulary, Naval Research Laboratory, 2013.
DOI : 10.21236/ada469421

S. Jin and Z. Xin, The relaxation schemes for systems of conservation laws in arbitrary space dimensions, Communications on Pure and Applied Mathematics, vol.54, issue.3, pp.235-276, 1995.
DOI : 10.1007/978-3-0348-8629-1

B. B. Kadomtsev, Tokamak plasma, a complex physical system, 1993.

A. G. Kulikovskii, N. V. Pogorelov, and A. Y. Semenov, Mathematical Aspects of Numerical Solution of Hyperbolic Systems, 2001.
DOI : 10.1007/978-3-0348-8724-3_10

J. D. Lawson, Some Criteria for a Power Producing Thermonuclear Reactor, Proceedings of the Physical Society. Section B, vol.70, issue.1, p.6, 1957.
DOI : 10.1088/0370-1301/70/1/303

R. J. Leveque, Finite-Volume Methods for Hyperbolic Problems, 2004.
DOI : 10.1017/CBO9780511791253

C. D. Levermore, Moment closure hierarchies for kinetic theories, Journal of Statistical Physics, vol.23, issue.5-6, pp.1021-1065, 1996.
DOI : 10.1007/978-1-4684-0447-0

C. D. Levermore and W. J. Morokoff, The Gaussian Moment Closure for Gas Dynamics, SIAM Journal on Applied Mathematics, vol.59, issue.1, pp.72-96, 1996.
DOI : 10.1137/S0036139996299236

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.52.7696

P. Maire, A high-order cell-centered Lagrangian scheme for compressible fluid flows in two-dimensional cylindrical geometry, Journal of Computational Physics, vol.228, issue.18, pp.6882-6915, 2009.
DOI : 10.1016/j.jcp.2009.06.018

URL : https://hal.archives-ouvertes.fr/inria-00372105

P. Maire, R. Abgrall, J. Breil, and J. Ovadia, A Cell-Centered Lagrangian Scheme for Two-Dimensional Compressible Flow Problems, SIAM Journal on Scientific Computing, vol.29, issue.4, pp.1781-1824, 2007.
DOI : 10.1137/050633019

URL : https://hal.archives-ouvertes.fr/inria-00113542

A. Mignone, P. Tzeferacos, and G. Bado, High-order conservative fonite difference GLM-MHD schemes for cell-centered MHD, Journal of Computational Physics, vol.229, issue.17, pp.5869-5920, 2010.
DOI : 10.1016/j.jcp.2010.04.013

URL : http://arxiv.org/pdf/1001.2832

K. W. Min and D. Y. Lee, Simulation of Kelvin Helmholtz Instability in resistive plasmas, Geophysical Research Letters, vol.91, issue.24, pp.3667-3670, 1996.
DOI : 10.1029/JA091iA03p03042

T. Miyoshi and K. Kusano, A multi-state HLL approximate Riemann solver for ideal magneto-hydrodynamics, Journal of Computational Physics, vol.208, issue.1, pp.314-344, 2005.
DOI : 10.1016/j.jcp.2005.02.017

G. A. Mourou, P. J. Barry, and D. Perry, Ultrahigh???Intensity Lasers: Physics of the Extreme on a Tabletop, Physics Today, vol.76, issue.1, p.22, 1998.
DOI : 10.1103/PhysRevLett.76.3116

C. Munz, P. Omnes, R. Schneider, E. Sonnendrücker, and U. Voß, Divergence Correction Techniques for Maxwell Solvers Based on a Hyperbolic Model, Journal of Computational Physics, vol.161, issue.2, pp.484-511, 2000.
DOI : 10.1006/jcph.2000.6507

K. Nishikawa and M. Wakatani, Plasma Physics, Basic Theory with Fusion Applications . Springer Series on Atoms And Plasmas, 2000.

S. Pfalzner, An Introduction to Inertial Confinement Fusion. Taylor and Francis Group, 2006.
DOI : 10.1201/9781420011845

K. G. Powell, An Approximate Riemann solver for magnetohydrodynamics (that works in more than one dimension), Centrum voor Wiskunde en Informatica (CWI). Amsterdam (NL), 1994.
DOI : 10.1007/978-3-642-60543-7_23

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.211.5157

K. G. Powell, P. L. Roe, T. J. Linde, T. I. Gombosi, and D. L. De-zeew, A Solution-Adaptive Upwind Scheme for Ideal Magnetohydrodynamics, 68] P. Savioni. M2 Plasmas : de l'Espace au Laboratoire : IntroductionàIntroductionà la physique des plasmas, pp.284-309, 1999.
DOI : 10.1006/jcph.1999.6299

R. Sentis, Mathematical Models and Methods for Plasma Physics, 2014.
DOI : 10.1007/978-3-319-03804-9

G. A. Sod, A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws, Journal of Computational Physics, vol.27, issue.1, pp.1-31, 1978.
DOI : 10.1016/0021-9991(78)90023-2

D. P. Stern, Euler Potentials, American Journal of Physics, vol.38, issue.4, pp.494-501, 1970.
DOI : 10.1119/1.1976373

M. Tabak, J. Hammer, M. E. Glinsky, W. L. Kruer, S. C. Wilks et al., Ignition and high gain with ultrapowerful lasers*, Physics of Plasmas, vol.2, issue.5, p.1626, 1994.
DOI : 10.1016/0030-4018(85)90120-8

E. F. Toro, Riemann Solvers and Numerical Methods for Fluids Dynamics, A Practical Introduction, 1999.
DOI : 10.1007/978-3-662-03915-1

E. F. Toro, M. Spruce, and W. Speares, Restoration of the contact surface in the HLL-Riemann solver, Shock Waves, vol.54, issue.1, pp.25-34, 1994.
DOI : 10.1007/BF01414629

G. Tóth, The ?????B=0 Constraint in Shock-Capturing Magnetohydrodynamics Codes, Journal of Computational Physics, vol.161, issue.2, pp.605-652, 2000.
DOI : 10.1006/jcph.2000.6519

B. Van-leer, Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov's method, Journal of Computational Physics, vol.32, issue.1, p.101, 1979.
DOI : 10.1016/0021-9991(79)90145-1

J. and V. Higueros, Godunov-type schemes for hydrodynamic and magnetohydrodynamic modeling, Ecole Doctorale en Sciences Fondamentales et Appliquées, 2014.
URL : https://hal.archives-ouvertes.fr/tel-01120876

C. Viozat, C. Held, K. Mer, and A. Dervieux, On vertex-centered unstructured finite-volume methods for stretched anisotropic triangulations, Computer Methods in Applied Mechanics and Engineering, vol.190, issue.35-36, pp.4733-4766, 2001.
DOI : 10.1016/S0045-7825(00)00345-5

URL : https://hal.archives-ouvertes.fr/inria-00073226

H. Zohm, C. Angioni, E. Fable, G. Federici, G. Gantenbein et al., On the physics guidelines for a tokamak DEMO, Nuclear Fusion, vol.53, issue.7, p.53073019, 2013.
DOI : 10.1088/0029-5515/53/7/073019