]. D. Balsara, Divergence-Free Adaptive Mesh Refinement for Magnetohydrodynamics, Journal of Computational Physics, vol.174, issue.2, pp.614-648, 2001.
DOI : 10.1006/jcph.2001.6917

D. S. Balsara, Second???Order???accurate Schemes for Magnetohydrodynamics with Divergence???free Reconstruction, The Astrophysical Journal Supplement Series, vol.151, issue.1, pp.149-184, 2004.
DOI : 10.1086/381377

D. S. Balsara, Divergence-free reconstruction of magnetic fields and WENO schemes for magnetohydrodynamics, Journal of Computational Physics, vol.228, issue.14, pp.5040-5056, 2009.
DOI : 10.1016/j.jcp.2009.03.038

D. S. Balsara, C. Altmann, C. D. Munz, and M. Dumbser, A sub-cell based indicator for troubled zones in RKDG schemes and a novel class of hybrid RKDG+HWENO schemes, Journal of Computational Physics, vol.226, issue.1, pp.586-620, 2007.
DOI : 10.1016/j.jcp.2007.04.032

D. S. Balsara, T. Rumpf, M. Dumbser, and C. D. Munz, Efficient, high accuracy ADER-WENO schemes for hydrodynamics and divergence-free magnetohydrodynamics, Journal of Computational Physics, vol.228, issue.7, pp.2480-2516, 2009.
DOI : 10.1016/j.jcp.2008.12.003

D. S. Balsara and C. W. Shu, Monotonicity Preserving Weighted Essentially Non-oscillatory Schemes with Increasingly High Order of Accuracy, Journal of Computational Physics, vol.160, issue.2, pp.405-452, 2000.
DOI : 10.1006/jcph.2000.6443

D. S. Balsara and D. S. 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

F. Bezard and B. Després, An Entropic Solver for Ideal Lagrangian Magnetohydrodynamics, Journal of Computational Physics, vol.154, issue.1, pp.65-89, 1999.
DOI : 10.1006/jcph.1999.6300

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. Consultants Bureau, 1965.

E. Buresi, J. Coutant, R. Dautray, M. Decroisette, B. Duborgel et al., Laser program development at CEL-V: overview of recent experimental results, Laser and Particle Beams, vol.21, issue.3-4, pp.531-544, 1986.
DOI : 10.1103/PhysRevLett.52.823

S. A. Chin, Forward and non-forward symplectic integrators in solving classical dynamics problems, International Journal of Computer Mathematics, vol.73, issue.6, pp.729-747, 2007.
DOI : 10.1016/S0377-0427(01)00492-7

B. Cockburn, S. Hou, and C. W. Shu, TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws IV: the multidimensional case, Math. Comp, vol.54, pp.545-581, 1990.

B. Cockburn, S. Y. Lin, and C. W. Shu, TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws III: One-dimensional systems, Journal of Computational Physics, vol.84, issue.1, pp.90-113, 1989.
DOI : 10.1016/0021-9991(89)90183-6

B. Cockburn and C. W. Shu, TVB Runge-Kutta local projection discontinuous Galerkin finite element method for scalar conservation laws II: general framework, Math. Comp, vol.52, pp.411-435, 1989.

B. Cockburn and C. W. Shu, The Runge-Kutta local projection $P^1$-discontinuous-Galerkin finite element method for scalar conservation laws, ESAIM: Mathematical Modelling and Numerical Analysis, vol.25, issue.3, pp.337-361, 1991.
DOI : 10.1051/m2an/1991250303371

B. Cockburn and C. W. Shu, The Runge???Kutta Discontinuous Galerkin Method for Conservation Laws V, Journal of Computational Physics, vol.141, issue.2, pp.199-224, 1998.
DOI : 10.1006/jcph.1998.5892

B. Cockburn, C. W. Shu, C. Johnson, E. Tadmor, and C. W. Shu, Essentially non-oscillatory and weighted essentially non-oscillatory schemes for hyperbolic conservation laws, Advanced Numerical Approximation of Nonlinear Hyperbolic Equations, pp.325-432, 1998.

A. W. Cook, Artificial fluid properties for large-eddy simulation of compressible turbulent mixing, Physics of Fluids, vol.19, issue.5, 2007.
DOI : 10.1063/1.2728937

A. W. Cook and W. H. Cabot, Hyperviscosity for shock-turbulence interactions, Journal of Computational Physics, vol.203, issue.2, pp.379-385, 2005.
DOI : 10.1016/j.jcp.2004.09.011

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

F. Coquel and C. Marmignon, A Roe-type linearization for the Euler equations for weakly ionized gases, Hermes Sci. Publ, 1999.

R. B. Dahlburg and J. M. Picone, Evolution of the Orszag???Tang vortex system in a compressible medium. I. Initial average subsonic flow, Physics of Fluids B: Plasma Physics, vol.1, issue.11, pp.2153-2171, 1989.
DOI : 10.1063/1.859081

R. B. Dahlburg and J. M. Picone, Evolution of the Orszag-Tang vortex system in a compressible medium. II. Supersonic flow, Phys. Fluids B, vol.3, pp.29-44, 1991.

W. Dai and P. R. Woodward, On the Divergence???free Condition and Conservation Laws in Numerical Simulations for Supersonic Magnetohydrodynamical Flows, The Astrophysical Journal, vol.494, issue.1, pp.317-335, 1998.
DOI : 10.1086/305176

R. Dautray and J. Watteau, La fusion thermonucléaire inertielle par laser : l'interaction laser-matì ere, Eyrolles, vol.2, 1993.

A. Decoster, Fluid equations and transport coefficient of plasmas, Modelling of collisions, pp.1-137, 1997.

A. Dedner, F. Kemm, D. Kröner, C. Munz, T. Schnitzer et al., Hyperbolic Divergence Cleaning for the MHD Equations, Journal of Computational Physics, vol.175, issue.2, pp.317-335, 2002.
DOI : 10.1006/jcph.2001.6961

B. Després, Lois de conservations eulériennes, lagrangiennes et méthodes numériques, 2010.
DOI : 10.1007/978-3-642-11657-5

F. Duboc, Extension de schémas de GodunovàGodunovà la MHD orthogonale résistive bi-température et termes de champs magnétiques auto-générés, 2002.

F. Duboc, C. Enaux, S. Jaouen, H. Jourdren, and M. Wolff, High-order dimensionally split Lagrange-remap schemes for compressible hydrodynamics, Comptes Rendus Mathematique, vol.348, issue.1-2, pp.105-110, 2010.
DOI : 10.1016/j.crma.2009.12.008

M. Dumbser, D. S. Balsara, E. F. Toro, and C. D. Munz, A unified framework for the construction of one-step finite volume and discontinuous Galerkin schemes on unstructured meshes, Journal of Computational Physics, vol.227, issue.18, pp.8209-8253, 2008.
DOI : 10.1016/j.jcp.2008.05.025

M. Dumbser and C. D. Munz, Building Blocks for Arbitrary High Order Discontinuous Galerkin Schemes, Journal of Scientific Computing, vol.204, issue.1-4, pp.215-230, 2006.
DOI : 10.1007/s10915-005-9025-0

C. R. Evans and J. F. Hawley, Simulation of magnetohydrodynamic flows - A constrained transport method, The Astrophysical Journal, vol.332, pp.659-667, 1988.
DOI : 10.1086/166684

E. Forest and R. D. Ruth, Fourth-order symplectic integration, Physica D: Nonlinear Phenomena, vol.43, issue.1, pp.105-117, 1990.
DOI : 10.1016/0167-2789(90)90019-L

K. O. Friedrichs and P. D. Lax, Systems of conservation equations with a convex extension, Proc. Nat. Acad. Sci. USA, pp.1686-1688, 1971.

G. A. Gerolymos, D. Sénéchal, and I. Vallet, Very-high-order weno schemes, Journal of Computational Physics, vol.228, issue.23, pp.8481-8524, 2009.
DOI : 10.1016/j.jcp.2009.07.039

N. Godel, S. Schomann, T. Warburton, and M. Clemens, GPU Accelerated Adams–Bashforth Multirate Discontinuous Galerkin FEM Simulation of High-Frequency Electromagnetic Fields, IEEE Transactions on Magnetics, vol.46, issue.8, pp.2735-2738, 2010.
DOI : 10.1109/TMAG.2010.2043655

S. K. Godunov, A finite difference method for the numerical computation of discontinuous solutions of the equations of fluid dynamics, Mat. Sb, vol.47, pp.271-290, 1959.

A. Harten, B. Engquist, S. Osher, and S. Chakravarthy, Uniformly high order accurate essentially non-oscillatory schemes, III, Journal of Computational Physics, vol.71, issue.2, pp.231-303, 1987.
DOI : 10.1016/0021-9991(87)90031-3

A. Hata, K. Mima, A. Sunahara, H. Nagatomo, and A. Nishiguchi, Dynamics of Self-Generated Magnetic Fields in Stagnation Phase and their Effects on Hot Spark Formation, Plasma and Fusion Research, vol.1, issue.20, pp.1-6, 2006.
DOI : 10.1585/pfr.1.020

N. E. Haugen, Hydrodynamic and hydromagnetic energy spectra from large eddy simulations, Physics of Fluids, vol.18, issue.7, 2006.
DOI : 10.1063/1.2222399

F. Hermeline, A Finite Volume Method for the Approximation of Diffusion Operators on Distorted Meshes, Journal of Computational Physics, vol.160, issue.2, pp.481-499, 2000.
DOI : 10.1006/jcph.2000.6466

O. Heuzé, S. Jaouen, and H. Jourdren, Dissipative issue of high-order shock capturing schemes with non-convex equations of state, Journal of Computational Physics, vol.228, issue.3, pp.833-860, 2009.
DOI : 10.1016/j.jcp.2008.10.005

C. Hu and C. W. Shu, Weighted Essentially Non-oscillatory Schemes on Triangular Meshes, Journal of Computational Physics, vol.150, issue.1, pp.97-127, 1999.
DOI : 10.1006/jcph.1998.6165

S. Jaouen, Solveur entropique d'ordré elevé pour leséquationsleséquations de l'hydrodynamiquè a deux températures, 1997.

S. Jaouen, A purely Lagrangian method for computing linearly-perturbed flows in spherical geometry, Journal of Computational Physics, vol.225, issue.1, pp.464-490, 2007.
DOI : 10.1016/j.jcp.2006.12.008

G. S. Jiang, D. Levy, C. T. Lin, S. Osher, and E. Tadmor, High-resolution non-oscillatory central schemes with non-staggered grids for hyperbolic conservation laws, J. Comp. Phys, vol.160, pp.241-282, 2000.

G. S. Jiang and C. W. Shu, Efficient Implementation of Weighted ENO Schemes, Journal of Computational Physics, vol.126, issue.1, pp.202-228, 1996.
DOI : 10.1006/jcph.1996.0130

G. S. Jiang and C. C. Wu, A High-Order WENO Finite Difference Scheme for the Equations of Ideal Magnetohydrodynamics, Journal of Computational Physics, vol.150, issue.2, pp.561-594, 1999.
DOI : 10.1006/jcph.1999.6207

R. E. Kidder, Laser-driven compression of hollow shells: power requirements and stability limitations, Nuclear Fusion, vol.16, issue.1, pp.3-14, 1976.
DOI : 10.1088/0029-5515/16/1/001

D. Levy, G. Puppo, and G. Russo, Central WENO schemes for hyperbolic systems of conservation laws, ESAIM: Mathematical Modelling and Numerical Analysis, vol.33, issue.3, pp.547-571, 1999.
DOI : 10.1051/m2an:1999152

D. Levy, G. Puppo, and G. Russo, A Fourth-Order Central WENO Scheme for Multidimensional Hyperbolic Systems of Conservation Laws, SIAM Journal on Scientific Computing, vol.24, issue.2, pp.480-506, 2002.
DOI : 10.1137/S1064827501385852

F. Li and C. W. Shu, Locally Divergence-Free Discontinuous Galerkin Methods for MHD Equations, Journal of Scientific Computing, vol.14, issue.1-3, pp.413-442, 2005.
DOI : 10.1007/s10915-004-4146-4

S. Li, High order central scheme on overlapping cells for magneto-hydrodynamic flows with and without constrained transport method, Journal of Computational Physics, vol.227, issue.15, pp.7368-7393, 2008.
DOI : 10.1016/j.jcp.2008.04.022

X. D. Liu, S. Osher, and T. Chan, Weighted Essentially Non-oscillatory Schemes, Journal of Computational Physics, vol.115, issue.1, pp.200-212, 1994.
DOI : 10.1006/jcph.1994.1187

E. Livne, L. Dessart, A. Burrows, and C. A. Meakin, A Two???dimensional Magnetohydrodynamics Scheme for General Unstructured Grids, The Astrophysical Journal Supplement Series, vol.170, issue.1, pp.187-202, 2007.
DOI : 10.1086/513701
URL : https://hal.archives-ouvertes.fr/hal-00370684

R. I. Mclachlan and P. Atela, The accuracy of symplectic integrators, Nonlinearity, vol.5, issue.2, pp.541-562, 1992.
DOI : 10.1088/0951-7715/5/2/011

F. H. Mcmahon, The Livermore Fortran kernels: a computer test of the numerical performance range, Lawrence Berkeley Nat. Lab, 1986.

R. Menikoff and B. J. Plohr, The Riemann problem for fluid flow of real materials, Reviews of Modern Physics, vol.61, issue.1, p.75, 1989.
DOI : 10.1103/RevModPhys.61.75

K. Mima, T. Tajima, and J. Leboeuf, Magnetic Field Generation by the Rayleigh-Taylor Instability, Physical Review Letters, vol.41, issue.25, pp.411715-1719, 1978.
DOI : 10.1103/PhysRevLett.41.1715

C. D. 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, 1999.
DOI : 10.1006/jcph.2000.6507

H. Nessyahu and E. Tadmor, Non-oscillatory central differencing for hyperbolic conservation laws, Journal of Computational Physics, vol.87, issue.2, pp.408-463, 1990.
DOI : 10.1016/0021-9991(90)90260-8

W. F. Noh, Errors for calculations of strong shocks using an artificial viscosity and an artificial heat flux, Journal of Computational Physics, vol.72, issue.1, pp.78-120, 1987.
DOI : 10.1016/0021-9991(87)90074-X

E. Novak and K. Ritter, Simple cubature formulas with high polynomial exactness. Constructive Approximation, pp.499-522, 1999.

A. Orszag and C. M. Tang, Small-scale structure of two-dimensional magnetohydrodynamic turbulence, Journal of Fluid Mechanics, vol.17, issue.01, pp.129-143, 1979.
DOI : 10.1007/BF01474610

P. Picard, Reduction and exact solutions of the ideal magnetohydrodynamics equations, 2005.

P. Picard, Some spherical solutions of ideal magnetohydrodynamic equations, J. of Nonlinear Mathemat . Phys, vol.14, pp.583-584, 2007.

K. G. Powell, An approximate Riemann solver for MHD (that works in more than one dimension), ICASE Report, pp.94-118, 1994.

D. Ryu and T. W. Jones, Numerical magetohydrodynamics in astrophysics: Algorithm and tests for one-dimensional flow`, The Astrophysical Journal, vol.442, pp.228-258, 1995.
DOI : 10.1086/175437

Y. Saad, Iterative methods for sparse linear systems, Society for Industrial and Applied Mathematics, 2003.
DOI : 10.1137/1.9780898718003

C. W. Shu and S. J. Osher, Efficient implementation of essentially non-oscillatory shock-capturing schemes, II, Journal of Computational Physics, vol.83, issue.1, pp.32-78, 1989.
DOI : 10.1016/0021-9991(89)90222-2

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

G. Strang, On the Construction and Comparison of Difference Schemes, SIAM Journal on Numerical Analysis, vol.5, issue.3, p.506, 1968.
DOI : 10.1137/0705041

H. Z. Tang and K. Xu, A High-Order Gas-Kinetic Method for Multidimensional Ideal Magnetohydrodynamics, Journal of Computational Physics, vol.165, issue.1, pp.69-88, 2000.
DOI : 10.1006/jcph.2000.6597

A. Taube, M. Dumbser, D. S. Balsara, and C. D. Munz, Arbitrary High-Order Discontinuous Galerkin Schemes for the Magnetohydrodynamic Equations, Journal of Scientific Computing, vol.193, issue.2, pp.441-464, 2007.
DOI : 10.1007/s10915-006-9101-0

M. Temporal, S. Jaouen, L. Masse, and B. Canaud, Hydrodynamic instabilities in ablative tamped flows, Physics of Plasmas, vol.13, issue.12, 2006.
DOI : 10.1063/1.2397041

R. P. Tewarson, Sparse matrices, 1973.

V. A. Titarev and E. F. Toro, ADER: arbitrary high-order Godunov approach, Journal of Scientific Computing, vol.17, issue.1/4, pp.609-618, 2002.
DOI : 10.1023/A:1015126814947

V. A. Titarev and E. F. Toro, Solution of the generalised Riemann problem for advection-reaction equations, Proc. Roy. Soc. Lond, vol.458, pp.271-281, 2002.

V. A. Titarev and E. F. Toro, ADER schemes for scalar hyperbolic conservation laws in three dimensions, J. Comp. Phys, vol.202, pp.196-215, 2005.

V. A. Titarev and E. F. Toro, ADER schemes for three-dimensional non-linear hyperbolic systems, Journal of Computational Physics, vol.204, issue.2, pp.715-736, 2005.
DOI : 10.1016/j.jcp.2004.10.028

E. F. Toro, R. C. Millington, and L. A. Nejad, Primitive upwind numerical methods for hyperbolic partial differential equations, Sixteenth international conference on numerical methods, lecture notes in physics, pp.421-426, 1998.
DOI : 10.1007/BFb0106618

E. F. Toro, R. C. Millington, and L. A. Nejad, Towards Very High Order Godunov Schemes, Godunov methods: theory and applications, pp.907-940, 2001.
DOI : 10.1007/978-1-4615-0663-8_87

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

H. A. Van and . Vorst, Iterative Krylov Methods for Large Linear systems, 2003.

M. Vinokur, A rigorous derivation of the MHD equations based only on Faraday's and Ampère's laws. Presentation at LANL MHD workshop, 1996.

T. Warburton and G. E. Karniadakis, A Discontinuous Galerkin Method for the Viscous MHD Equations, Journal of Computational Physics, vol.152, issue.2, pp.608-641, 1999.
DOI : 10.1006/jcph.1999.6248

M. Wolff, S. Jaouen, and L. Imbert-gérard, Conservative numerical methods for a two-temperature resistive MHD model with self-generated magnetic field term, ESAIM Proceedings, 2011.
DOI : 10.1051/proc/2011021

M. Wolff, S. Jaouen, and H. Jourdren, High-order dimensionally split Lagrange-remap schemes for ideal magnetohydrodynamics, Discrete and Continuous Dynamical Systems Series S: proceedings of Numerical Models for Controlled Fusion (NMCF'09), 2009.

H. C. Yee, N. D. Sandham, and M. J. Djomehri, Low-Dissipative High-Order Shock-Capturing Methods Using Characteristic-Based Filters, Journal of Computational Physics, vol.150, issue.1, pp.199-238, 1999.
DOI : 10.1006/jcph.1998.6177

H. Yoshida, Construction of higher order symplectic integrators, Physics Letters A, vol.150, issue.5-7, pp.262-267, 1990.
DOI : 10.1016/0375-9601(90)90092-3

S. Zhang and C. W. Shu, A New Smoothness Indicator for the WENO Schemes and Its Effect on the Convergence to Steady State Solutions, Journal of Scientific Computing, vol.54, issue.1-2, pp.273-305, 2007.
DOI : 10.1007/s10915-006-9111-y

U. Ziegler, A central-constrained transport scheme for ideal magnetohydrodynamics, Journal of Computational Physics, vol.196, issue.2, pp.393-416, 2004.
DOI : 10.1016/j.jcp.2003.11.003