G. K. Batchelor, An introduction to Fluid Dynamics, 1970.
DOI : 10.1017/CBO9780511800955

D. J. Benson, An efficient, accurate, simple ale method for nonlinear finite element programs, Computer Methods in Applied Mechanics and Engineering, vol.72, issue.3, pp.305-350, 1989.
DOI : 10.1016/0045-7825(89)90003-0

A. Bernard-champmartin and J. Ghidaglia, Finite volume solvers for multimaterial 3d compressible Euler equations with cylindrical symmetry, International Conference on numerical Methods For Multi-Material Fluid Flows, MULTIMAT

P. Birken and A. Meister, Stability of Preconditioned Finite Volume Schemes at Low Mach Numbers, BIT Numerical Mathematics, vol.45, issue.3, pp.463-480, 2005.
DOI : 10.1007/s10543-005-0009-0

B. Blais, Reconstruction d'interfaces dans les écoulements parfaits et compressibles à multiples matériaux, 2011.

M. Boucker, Modélisation numérique multidimensionnelle d'écoulements diphasiques liquide-gaz en régimes transitoire et permanent : méthodes et applications, Thèse de Doctorat, ENS Cachan, 1998.

J. Braeunig, Sur la simulation d'écoulements multi-matériaux par une méthode eulérienne directe avec capture d'interfaces en dimensions 1, 2 et 3, 2007.

J. Braeunig, An algorithm to control the pressure evolution for the fvcf-nip method for multi-material compressible fluid flows, IJFV, vol.7, pp.101-132, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00531586

J. Braeunig, B. Desjardins, and J. Ghidaglia, A totally Eulerian finite volume solver for multi-material fluid flows, European Journal of Mechanics - B/Fluids, vol.28, issue.4, pp.475-485, 2009.
DOI : 10.1016/j.euromechflu.2009.03.003

URL : https://hal.archives-ouvertes.fr/hal-00527765

J. Braeunig and M. Peybernes, Parallélisation mpi par transposition d'un solveur vf eulérien pour les écoulements hydrodynamiques multi-fluides, 2011.

C. Buet and B. Despres, Asymptotic analysis of fluid models for the coupling of radiation and hydrodynamics, Journal of Quantitative Spectroscopy and Radiative Transfer, vol.85, issue.3-4, pp.385-418, 2004.
DOI : 10.1016/S0022-4073(03)00233-4

C. Buet and B. Despres, Asymptotic preserving and positive schemes for radiation hydrodynamics, Journal of Computational Physics, vol.215, issue.2, pp.717-740, 2006.
DOI : 10.1016/j.jcp.2005.11.011

H. Choi and C. Merkle, The Application of Preconditioning in Viscous Flows, Journal of Computational Physics, vol.105, issue.2, pp.207-223, 1993.
DOI : 10.1006/jcph.1993.1069

P. Colella and P. R. Woodward, The numerical simulation of two-dimensional fluid flow with strong shocks, J. Comput. Phys, vol.54, pp.115-173, 1984.

P. Colella and P. R. Woodward, The Piecewise Parabolic Method (PPM) for gas-dynamical simulations, Journal of Computational Physics, vol.54, issue.1, pp.174-201, 1984.
DOI : 10.1016/0021-9991(84)90143-8

D. Torres, D. Jamet, and J. U. Brackbill, On the theory and computation of surface tension : The elimination of parasitic currents through energy conservation in the second-gradient method, J. Comput. Phys, vol.182, pp.262-276, 2002.

C. M. Dafermos, Polygonal approximations of solutions of the initial value problem for a conservation law, Journal of Mathematical Analysis and Applications, vol.38, issue.1, pp.33-41, 1972.
DOI : 10.1016/0022-247X(72)90114-X

C. M. Dafermos, Hyperbolic conservation laws in continuum physics, 2002.

F. Dauvergne, J. Ghidaglia, F. Pascal, and J. Rovarch, Renormalization of the numerical diffusion for an upwind finite volume method. application to the simulation of Kelvin-Helmholtz instability, Proceedings of the Fifth International Symposium on Finite Volumes for Complex Applications, pp.321-328, 2008.

P. De-gennes, F. Brochard-wyart, and D. Quéré, Capillarity and Wetting Phenomena, Drops, Bubbles, Pearls, Waves, 2004.

S. Dellacherie, Analysis of Godunov type schemes applied to the compressible Euler system at low Mach number, Journal of Computational Physics, vol.229, issue.4, pp.978-1016, 2010.
DOI : 10.1016/j.jcp.2009.09.044

D. Enright, R. P. Fedkiw, J. H. Ferziger, and I. Mitchell, A Hybrid Particle Level Set Method for Improved Interface Capturing, Journal of Computational Physics, vol.183, issue.1, pp.83-116, 2002.
DOI : 10.1006/jcph.2002.7166

M. Tajchman, F. Alouges, and J. Ghidaglia, On the interaction of upwinding and forcing for nonlinear hyperbolic systems of conservation laws

M. M. Francois, S. J. Cummins, E. D. Dendy, D. Kothe, J. M. Sicilian et al., A balanced-force algorithm for continuous and sharp interfacial surface tension models within a volume tracking framework, Journal of Computational Physics, vol.213, issue.1, pp.141-173, 2006.
DOI : 10.1016/j.jcp.2005.08.004

J. Ghidaglia, FLUX SCHEMES FOR SOLVING NONLINEAR SYSTEMS OF CONSERVATION LAWS, Innovative Methods for Numerical Solutions of PDEs. Proceedings of the symposium on progress in numerical solutions of PDEs, pp.232-242, 1998.
DOI : 10.1142/9789812810816_0011

J. Ghidaglia, Numerical computation of 3d two phase flow by finite volumes methods using flux schemes, Proceedings of the Second International Symposium on Finite Volumes for Complex Applications, Hermes, pp.69-94, 1999.

J. Ghidaglia, A. Kumbaro, and G. L. Coq, On the numerical solution to two fluid models via a cell centered finite volume method, European Journal of Mechanics - B/Fluids, vol.20, issue.6, pp.841-867, 2001.
DOI : 10.1016/S0997-7546(01)01150-5

J. Ghidaglia and F. Pascal, The normal flux method at the boundary for multidimensional finite volume approximations in CFD, European Journal of Mechanics - B/Fluids, vol.24, issue.1, pp.1-17, 2005.
DOI : 10.1016/j.euromechflu.2004.05.003

R. A. Gingold and J. J. Monaghan, Smoothed particle hydrodynamics: theory and application to non-spherical stars, Monthly Notices of the Royal Astronomical Society, vol.181, issue.3, pp.375-389, 1977.
DOI : 10.1093/mnras/181.3.375

J. Glimm, J. W. Grove, X. L. Li, W. Oh, and D. H. Sharp, A Critical Analysis of Rayleigh???Taylor Growth Rates, Journal of Computational Physics, vol.169, issue.2, pp.652-677, 2001.
DOI : 10.1006/jcph.2000.6590

J. Glimm, J. W. Grove, X. L. Li, K. Shyue, Y. Zeng et al., Three-Dimensional Front Tracking, SIAM Journal on Scientific Computing, vol.19, issue.3, 1995.
DOI : 10.1137/S1064827595293600

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.57.569

E. Godlewski and P. Raviart, Numerical approximation of hyperbolic systems of conservation laws, 1996.
DOI : 10.1007/978-1-4612-0713-9

S. K. Godunov, A finite difference method for the numerical computation and discontinuous solutions of the equations of fluid dynamics, Math. Sbornik, vol.47, pp.271-306, 1959.

H. Guillard and A. Murrone, On the behaviour of upwind schemes in the low mach number limit : Ii. godunov type schemes. Computers and fluids, pp.655-675, 2004.

H. Guillard and C. Viozat, On the behavior of upwind scheme in the low mach number limit, technical report 3160 , inria, 1999.

H. Guillard and C. Viozat, On the behaviour of upwind schemes in the low mach number limit. Computers and fluids, pp.63-86, 1999.
URL : https://hal.archives-ouvertes.fr/hal-00871725

F. H. Harlow, PIC and its progeny, Computer Physics Communications, vol.48, issue.1, pp.1-11, 1988.
DOI : 10.1016/0010-4655(88)90017-3

F. H. Harlow and J. E. Welch, Numerical Calculation of Time-Dependent Viscous Incompressible Flow of Fluid with Free Surface, Physics of Fluids, vol.8, issue.12, pp.2182-2189, 1965.
DOI : 10.1063/1.1761178

C. W. Hirt, A. A. Amsden, and J. L. Cook, An arbitrary Lagrangian-Eulerian computing method for all flow speeds, Journal of Computational Physics, vol.14, issue.3, pp.227-253, 1974.
DOI : 10.1016/0021-9991(74)90051-5

C. W. Hirt and B. D. Nichols, Volume of fluid (VOF) method for the dynamics of free boundaries, Journal of Computational Physics, vol.39, issue.1, pp.201-225, 1981.
DOI : 10.1016/0021-9991(81)90145-5

H. Holden and N. H. Risebro, Front Tracking for Hyperbolic Conservation Laws, 2002.
DOI : 10.1007/978-3-642-23911-3

URL : http://dx.doi.org/10.1016/s0898-1221(03)90158-1

C. Zemach, J. U. Brackbill, and D. B. Kothe, A continuum method for modeling surface tension, J. Comput. Phys, vol.100, pp.335-354, 1992.

S. Y. Kadioglu and D. A. Knoll, A fully second order implicit/explicit time integration technique for hydrodynamics plus nonlinear heat conduction problems, Journal of Computational Physics, vol.229, issue.9, pp.3237-3249, 2010.
DOI : 10.1016/j.jcp.2009.12.039

S. Y. Kadioglu, D. A. Knoll, R. B. Lowrie, and R. M. Rauezahn, A second order self-consistent IMEX method for radiation hydrodynamics, Journal of Computational Physics, vol.229, issue.22, pp.9313-8332, 2010.
DOI : 10.1016/j.jcp.2010.07.019

M. Kang, R. P. Fedkiw, and X. Liu, A boundary condition capturing method for multiphase incompressible flow, Journal of Scientific Computing, vol.15, issue.3, pp.323-360, 2000.
DOI : 10.1023/A:1011178417620

B. Lafaurie, C. Nardone, R. Scardovelli, S. Zaleski, and G. Zanetti, Modelling Merging and Fragmentation in Multiphase Flows with SURFER, Journal of Computational Physics, vol.113, issue.1, pp.134-147, 1994.
DOI : 10.1006/jcph.1994.1123

B. Van-leer, Towards the ultimate conservative difference scheme. IV. A new approach to numerical convection, Journal of Computational Physics, vol.23, issue.3, pp.276-299, 1977.
DOI : 10.1016/0021-9991(77)90095-X

B. Van-leer, B. Lee, and P. Roe, Characteristic time-stepping or local preconditioning of the Euler equations, 1991.

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

X. Li and C. Gu, An All-Speed Roe-type scheme and its asymptotic analysis of low Mach number behaviour, Journal of Computational Physics, vol.227, issue.10, pp.978-1016, 2010.
DOI : 10.1016/j.jcp.2008.01.037

D. Lorstad, M. M. Francois, W. Shyy, and L. Fuchs, Assessment of volume of fluid and immersed boundary methods for droplet computations, International Journal for Numerical Methods in Fluids, vol.46, issue.2, pp.109-125, 2004.
DOI : 10.1002/fld.746

R. Loubère, J. Braeunig, and J. Ghidaglia, A totally Eulerian finite volume solver for multi-material fluid flows: Enhanced Natural Interface Positioning (ENIP), European Journal of Mechanics - B/Fluids, vol.31, 2011.
DOI : 10.1016/j.euromechflu.2011.07.005

R. Loubère and M. J. Shashkov, A subcell remapping method on staggered polygonal grids for arbitrary-Lagrangian???Eulerian methods, Journal of Computational Physics, vol.209, issue.1, pp.105-138, 2005.
DOI : 10.1016/j.jcp.2005.03.019

R. B. Lowrie and J. D. Edwards, Radiative shock solutions with grey nonequilibrium diffusion, Shock Waves, vol.5, issue.5, pp.129-143, 2008.
DOI : 10.1007/s00193-008-0143-0

R. B. Lowrie and J. E. , The Coupling of Radiation and Hydrodynamics, The Astrophysical Journal, vol.521, issue.1, pp.423-450, 1999.
DOI : 10.1086/307515

M. Meier, G. Yadigaroglu, and B. L. Smith, A novel technique for including surface tension in PLIC-VOF methods, European Journal of Mechanics - B/Fluids, vol.21, issue.1, pp.61-73, 2002.
DOI : 10.1016/S0997-7546(01)01161-X

J. J. Monaghan, Smoothed Particle Hydrodynamics, Annual Review of Astronomy and Astrophysics, vol.30, issue.1, pp.543-574, 1992.
DOI : 10.1146/annurev.aa.30.090192.002551

V. A. Mousseau and D. A. Knoll, Temporal accuracy of the nonequilibrium radiation diffusion equations applied to two-dimensional multimaterial simulations, Nuclear Science and Engineering, vol.154, pp.174-189, 2006.

W. F. Noh and P. Woodward, Slic (simple line interface calculation) Lecture notes in Physics 59, 1976.

S. Osher and R. P. Fedkiw, Level Set Methods and Dynamic Implicit Surfaces, 2002.
DOI : 10.1007/b98879

URL : http://dx.doi.org/10.1016/s0898-1221(03)90179-9

S. Osher and J. A. Sethian, Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations, Journal of Computational Physics, vol.79, issue.1, pp.12-49, 1988.
DOI : 10.1016/0021-9991(88)90002-2

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.413.5254

F. Pascal, Passerelles VFFC-Éléments finis P1D : application aux écoulements à faible Mach, 2000.

F. Pascal, Sur des méthodes d'approximation effectives et d'analyse numérique pour les équations de la mécanique des fluides. Mémoire d'habilitation à diriger des recherches, 2002.

G. C. Pomraning, The Equations of Radiation Hydrodynamics, 1973.

L. Rayleigh, On the Capillary Phenomena of Jets, Proceedings of the Royal Society of London, vol.29, issue.196-199, pp.41-48, 1879.
DOI : 10.1098/rspl.1879.0015

Y. Renardy and M. Renardy, PROST: A Parabolic Reconstruction of Surface Tension for the Volume-of-Fluid Method, Journal of Computational Physics, vol.183, issue.2, pp.400-421, 2002.
DOI : 10.1006/jcph.2002.7190

R. K. Chan, A generalized arbitrary Lagrangian-Eulerian method for incompressible flows with sharp interfaces, Journal of Computational Physics, vol.17, issue.3, pp.311-331, 1975.
DOI : 10.1016/0021-9991(75)90055-8

P. L. Roe, Characteristic-Based Schemes for the Euler Equations, Annual Review of Fluid Mechanics, vol.18, issue.1, p.337, 1986.
DOI : 10.1146/annurev.fl.18.010186.002005

J. Rovarch, Solveurs tridimensionnels pour les écoulements diphasiques avec transferts d'énergie, Thèse de Doctorat, ENS Cachan, 2006.

M. Rudman, VOLUME-TRACKING METHODS FOR INTERFACIAL FLOW CALCULATIONS, International Journal for Numerical Methods in Fluids, vol.93, issue.7, pp.671-691, 1998.
DOI : 10.1002/(SICI)1097-0363(19970415)24:7<671::AID-FLD508>3.0.CO;2-9

Y. Saad and M. H. Schultz, GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems, SIAM Journal on Scientific and Statistical Computing, vol.7, issue.3, pp.856-869, 1986.
DOI : 10.1137/0907058

J. A. Sethian, Level set methods, 1996.

D. Starinshak and S. Karni, A level-set method for multimaterial radiative shock hydrodynamics, International Conference on numerical Methods For Multi-Material Fluid Flows, MULTIMAT, pp.5-9, 2011.

J. C. Strikwerda, Finite differences and partial differential equations, Society for Industrial and Applied Mathematics, 2004.

M. Sussman, A second order coupled level set and volume-of-fluid method for computing growth and collapse of vapor bubbles, Journal of Computational Physics, vol.187, issue.1, pp.110-136, 2003.
DOI : 10.1016/S0021-9991(03)00087-1

M. Sussman and P. Smereka, Axisymmetric free boundary problems, Journal of Fluid Mechanics, vol.341, pp.269-294, 1997.
DOI : 10.1017/S0022112097005570

M. Sussman, P. Smereka, and S. Osher, A Level Set Approach for Computing Solutions to Incompressible Two-Phase Flow, Journal of Computational Physics, vol.114, issue.1, pp.146-159, 1994.
DOI : 10.1006/jcph.1994.1155

E. F. Toro, Riemann Solvers and Numerical Methods for Fluid Dynamics 2nd edition, 1999.
DOI : 10.1007/b79761

S. O. Unverdi and G. Tryggvason, A front-tracking method for viscous, incompressible, multi-fluid flows, Journal of Computational Physics, vol.100, issue.1, pp.25-37, 1992.
DOI : 10.1016/0021-9991(92)90307-K

J. Vonneumann and R. D. Richtmeyer, A Method for the Numerical Calculation of Hydrodynamic Shocks, Journal of Applied Physics, vol.21, issue.3, 1950.
DOI : 10.1063/1.1699639

M. L. Wilkins, Calculation of elastic-plastic flow, Methods in Computational Physics, vol.3, pp.211-262, 1964.

D. Youngs and R. Williams, Turbulent mixing in spherical implosions, International Journal for Numerical Methods in Fluids, vol.99, issue.8, pp.1597-1603, 2008.
DOI : 10.1002/fld.1594

D. L. Youngs, Time-dependant multi-material flow with large fluid distortion. Numerical Methods for Fluid Dynamics, pp.279-285, 1982.

Y. B. Zel-'dovich, Y. P. Raizer, and .. , Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena, p.23, 2002.

.. Évolution-des-courants-parasites, 82 3.4 Perturbation du cas-test de Laplace (1)-suite), 83 3.5 Perturbation du cas-test de Laplace 84 3.6 Perturbation du cas-test de Laplace, p.85

. Géométrie, températures matière et radiative à t = 0.5, p.121

. Tube-À-choc-de-sod, Pression : valeur numérique et valeur exacte, p.125

. Tube-À-choc-de-sod, Densité : valeur numérique et valeur exacte, p.125

. Tube-À-choc-de-sod, Vitesse : valeur numérique et valeur exacte, p.125