R. Abgrall and F. Lafon, ENO schemes on unstructured meshes, 1993.
URL : https://hal.archives-ouvertes.fr/inria-00074573

R. Abgrall and J. Montagné, Généralisation du schéma d'Osher pour le calcul d'´ ecoulements de mélanges de gazàgaz`gazà concentrations variables et de gaz réels, La recherche aérospatiale, 1989.

]. K. Amram, ´ Etude numérique des instabilités dans les couches de mélange compressibles, Thèse de doctorat, ´ Ecole polytechnique, 1995.

D. V. Anosov and V. I. Arnold, Dynamical systems I. Birkhuser, 1992.

M. Arora and P. L. Roe, A Well-Behaved TVD Limiter for High-Resolution Calculations of Unsteady Flow, Journal of Computational Physics, vol.132, issue.1, pp.3-11, 1997.
DOI : 10.1006/jcph.1996.5514

A. Beccantini and H. Pailì-ere, Upwind flux splitting schemes for the 1D Euler equation: application to shock tube and blast wave model problem, 1997.

C. Berthon, ContributionàContribution`Contributionà l'analyse numérique deséquationsdeséquations de Navier- Stokes compressiblesàcompressibles`compressiblesà deux entropies spécifiques. ApplicationàApplication`Applicationà la turbulence compressible, Thèse de doctorat, 1998.

F. Bezard, Approximation numérique deprobì emes d'interfaces en mécanique des fluides, Thèse de doctorat, ´ Ecole polytechnique, 1998.

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

F. Bouchut and F. James, ´ Equations de transport unidimensionnellesàunidimensionnelles`unidimensionnellesà coefficients discontinus. Comptes Rendus de l'Académie des Sciences, pp.1097-1102, 1995.

F. Bouchut and F. James, One-dimensional transport equations with discontinuous coefficients, Nonlinear Analysis: Theory, Methods & Applications, vol.32, issue.7, pp.891-933, 1998.
DOI : 10.1016/S0362-546X(97)00536-1
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.48.1728

D. Chargy, R. Abgrall, L. Fezoui, and B. Larrouturou, Comparisons of several upwind schemes for multi-component one-dimensional inviscid flows, 1990.
URL : https://hal.archives-ouvertes.fr/inria-00075305

I. Chern, J. Glimm, O. Mcbryan, B. Plohr, and S. Yaniv, Front tracking for gas dynamics, Journal of Computational Physics, vol.62, issue.1, pp.83-110, 1986.
DOI : 10.1016/0021-9991(86)90101-4

A. J. Chorin, Random choice solution of hyperbolic systems, Journal of Computational Physics, vol.22, issue.4, pp.517-533, 1976.
DOI : 10.1016/0021-9991(76)90047-4

P. Colella, Glimm???s Method for Gas Dynamics, SIAM Journal on Scientific and Statistical Computing, vol.3, issue.1, pp.76-110, 1982.
DOI : 10.1137/0903007

F. Coquel and P. G. Lefloch, Convergence of finite difference schemes for conservation laws in several space dimensions: the corrected antidiffusive flux approach, Mathematics of Computation, vol.57, issue.195, pp.169-210, 1991.
DOI : 10.1090/S0025-5718-1991-1079010-2

F. Coquel and P. G. Lefloch, Convergence of Finite Difference Schemes for Conservation Laws in Several Space Dimensions: A General Theory, SIAM Journal on Numerical Analysis, vol.30, issue.3, pp.675-700, 1993.
DOI : 10.1137/0730033

J. Croisille, ContributionàContribution`Contributionà l'´ etude théorique etàet`età l'approximation par ´ eléments finis du système hyperbolique de la dynamique des gaz multidimensionnelle et multiespèce, Thèse de doctorat, 1990.

G. Dal-maso, P. G. Lefloch, and F. Murat, Definition and weak stability of nonconservative products, Journal de mathématiques pures et appliquées, pp.483-548, 1995.

F. and D. Vuyst, Schémas non-conservatifs et schémas cinétiques pour la simulation numérique d'´ ecoulements hypersoniques non visqueux en déséquilibre thermochimique, Thèse de doctorat, 1994.

B. Després, Construction, analyse et discrétisation d'un modèle de dynamique des fluides compressibles multi-constituants, 1997.

B. Després, In??galit?? entropique pour un solveur conservatif du syst??me de la dynamique des gaz en coordonn??es de Lagrange, Comptes Rendus de l'Académie des Sciences, pp.1301-1306, 1997.
DOI : 10.1016/S0764-4442(99)80417-0

B. Després, Inégalités entropiques pour un solveur de type Lagrange + convection deséquationsdeséquations de l'hydrodynamique, 1997.

B. Després, Invariance properties of lagrangian systems of conservation laws, approximate Riemann solvers and the entropy condition, 2000.

B. Després and F. Lagoutì-ere, Un schéma non linéaire anti-dissipatif pour l'´ equation d'advection linéaire. Comptes Rendus de l'Académie des Sciences, pp.939-944, 1999.

G. Duvaut, Mécanique des milieux continus [34] L. ´ Etiemble et Ch. Méresse. Schéma Lagrange + projection 1D et 2D en géométrie plane, cylindrique et sphérique, 1990.

R. Fedkiw, T. Aslam, B. Merriman, and S. Osher, A Non-oscillatory Eulerian Approach to Interfaces in Multimaterial Flows (the Ghost Fluid Method), Journal of Computational Physics, vol.152, issue.2, pp.457-492, 1999.
DOI : 10.1006/jcph.1999.6236

R. P. Fedkiw, T. Aslam, B. Merriman, and S. Osher, A Non-oscillatory Eulerian Approach to Interfaces in Multimaterial Flows (the Ghost Fluid Method), Journal of Computational Physics, vol.152, issue.2
DOI : 10.1006/jcph.1999.6236

E. Giusti, Minimal surfaces and functions of bounded variations, Birkhäuser, 1984.
DOI : 10.1007/978-1-4684-9486-0

J. Glimm, Solutions in the large for nonlinear hyperbolic systems of equations, Communications on Pure and Applied Mathematics, vol.12, issue.4, pp.697-715, 1965.
DOI : 10.1002/cpa.3160180408

J. Glimm, E. Isaacson, D. Marchesin, and O. Mcbryan, Front tracking for hyperbolic systems, Advances in Applied Mathematics, vol.2, issue.1, pp.91-119, 1981.
DOI : 10.1016/0196-8858(81)90040-3

E. Godlewski and P. Raviart, Hyperbolic systems of conservation laws. Ellipses, 1991.
URL : https://hal.archives-ouvertes.fr/hal-00113734

E. Godlewski and P. Raviart, Numerical approximation of hyperbolic systems of conservation laws, 1995.
DOI : 10.1007/978-1-4612-0713-9

D. Gueyffier, J. Li, R. Scardovelli, and S. Zaleski, Volume-of-Fluid Interface Tracking with Smoothed Surface Stress Methods for Three-Dimensional Flows, Journal of Computational Physics, vol.152, issue.2, pp.423-456, 1999.
DOI : 10.1006/jcph.1998.6168

A. Harten, High resolution schemes for hyperbolic conservation laws, Journal of Computational Physics, vol.49, issue.3, pp.357-393, 1983.
DOI : 10.1016/0021-9991(83)90136-5

A. Harten, On a Class of High Resolution Total-Variation-Stable Finite-Difference Schemes, SIAM Journal on Numerical Analysis, vol.21, issue.1, pp.1-23, 1984.
DOI : 10.1137/0721001

A. Harten and J. M. Hyman, Self adjusting grid methods for one-dimensional hyperbolic conservation laws, Journal of Computational Physics, vol.50, issue.2, pp.235-269, 1983.
DOI : 10.1016/0021-9991(83)90066-9

A. Harten and S. Osher, Uniformly High-Order Accurate Nonoscillatory Schemes. I, SIAM Journal on Numerical Analysis, vol.24, issue.2, pp.279-309, 1987.
DOI : 10.1137/0724022

T. Hou and P. G. Lefloch, Why nonconservative schemes converge to wrong solutions: error analysis, Mathematics of Computation, vol.62, issue.206, pp.497-530, 1994.
DOI : 10.1090/S0025-5718-1994-1201068-0

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

S. Karni, Multicomponent Flow Calculations by a Consistent Primitive Algorithm, Journal of Computational Physics, vol.112, issue.1, pp.31-43, 1993.
DOI : 10.1006/jcph.1994.1080
URL : http://deepblue.lib.umich.edu/bitstream/2027.42/31590/1/0000519.pdf

S. Karni, Hybrid Multifluid Algorithms, SIAM Journal on Scientific Computing, vol.17, issue.5, pp.1019-1039, 1996.
DOI : 10.1137/S106482759528003X

S. Kokh and G. Allaire, Numerical Simulation of 2-D Two-Phase Flows with Interface, Godunov methods : theory and applications, 2000.
DOI : 10.1007/978-1-4615-0663-8_51

S. Kruzkov, FIRST ORDER QUASILINEAR EQUATIONS IN SEVERAL INDEPENDENT VARIABLES, Mathematics of the USSR-Sbornik, vol.10, issue.2, pp.217-243, 1970.
DOI : 10.1070/SM1970v010n02ABEH002156

B. Larrouturou, How to preserve the mass fractions positivity when computing compressible multi-component flows, Journal of Computational Physics, vol.95, issue.1, pp.59-84, 1991.
DOI : 10.1016/0021-9991(91)90253-H
URL : https://hal.archives-ouvertes.fr/inria-00075479

B. Larrouturou and L. Fezoui, On the equations of muti-component perfect or real gas inviscid flow, Lecture notes in mathematics, nonlinear hyperbolic problems, 1988.

P. D. Lax, Hyperbolic systems of conservation laws II, Communications on Pure and Applied Mathematics, vol.3, issue.4, pp.537-566, 1957.
DOI : 10.1002/cpa.3160100406

P. D. Lax and B. Wendroff, Systems of conservation laws, LeFloch. Entropy weak solutions to nonlinear hyperbolic systems under nonconservative form. Communication in partial differential equations, pp.217-237669, 1960.
DOI : 10.1002/cpa.3160130205

P. G. Lefloch, Shock waves for nonlinear hyperbolic systems in nonconservative form. IMA preprint series, 1989.

P. G. Lefloch and J. Liu, Generalized monotone schemes, discrete paths of extrema, and discrete entropy conditions, Mathematics of Computation, vol.68, issue.227, pp.1025-1055, 1999.
DOI : 10.1090/S0025-5718-99-01062-5

P. G. Lefloch and T. Liu, Existence theory for nonlinear hyperbolic systems in nonconservative form, Forum mathematicum, vol.5, pp.261-280, 1993.

R. J. Leveque, Numerical methods for consevation laws, Birkhuser, 1992.

P. Lions and P. E. Souganidis, Convergence of MUSCL and filtered schemes for scalar conservation laws and Hamilton-Jacobi equations, Numerische Mathematik, vol.69, issue.4, pp.441-470, 1995.
DOI : 10.1007/s002110050102

X. Liu, R. P. Fedkiw, and S. Osher, A quasi-conservative approach to the multiphase Euler equations without spurious pressure oscillations, Computational and Applied Mathematics, vol.11, 1998.

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

K. W. Morton and P. K. Sweby, A comparison of flux limited difference methods and characteristic galerkin methods for shock modelling, Journal of Computational Physics, vol.73, issue.1, pp.203-230, 1987.
DOI : 10.1016/0021-9991(87)90114-8

I. Müller and T. Ruggeri, Rational extended thermodynamics, 1998.
DOI : 10.1007/978-1-4612-2210-1

C. D. Munz, On Godunov-Type Schemes for Lagrangian Gas Dynamics, SIAM Journal on Numerical Analysis, vol.31, issue.1, pp.17-42, 1994.
DOI : 10.1137/0731002

W. F. Noh, Artificial viscosity (Q) and artificial heat flux (H) errors for spherically divergent shocks, 1983.
DOI : 10.2172/5773058

M. Olazabal, Modélisation numérique deprobì emes de stabilité linéarisée Application auxéquationsauxéquations de la dynamique des gaz et de la MHD idéale, Thèse de doctorat, 1998.

S. Osher, Convergence of generalized muscl schemes, SIAM Journal of Numerical Analysis, vol.29, pp.947-961, 1985.

S. Osher and S. Chakravarthy, High Resolution Schemes and the Entropy Condition, SIAM Journal on Numerical Analysis, vol.21, issue.5, pp.955-984, 1984.
DOI : 10.1137/0721060

P. L. Roe, Approximate Riemann solvers, parameter vectors, and difference schemes, Journal of Computational Physics, vol.43, issue.2, pp.357-372, 1981.
DOI : 10.1016/0021-9991(81)90128-5
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.457.5978

P. L. Roe, Some contribution to the modelling of discontinuous flows, Lectures in Applied Mathematics, vol.22, pp.163-193, 1985.

L. Sainsaulieu, Traveling Waves Solution of Convection???Diffusion Systems Whose Convection Terms are Weakly Nonconservative: Application to the Modeling of Two-Phase Fluid Flows, SIAM Journal on Applied Mathematics, vol.55, issue.6, pp.1552-1576, 1995.
DOI : 10.1137/S0036139994268292

R. Saurel and R. Abgrall, A Simple Method for Compressible Multifluid Flows, SIAM Journal on Scientific Computing, vol.21, issue.3, 1997.
DOI : 10.1137/S1064827597323749

R. Saurel and R. Abgrall, A Multiphase Godunov Method for Compressible Multifluid and Multiphase Flows, Journal of Computational Physics, vol.150, issue.2, 1999.
DOI : 10.1006/jcph.1999.6187

B. Scheurer, Quelques méthodes pour la simulation numérique de la fusion par confinement inertiel, Chocs, vol.22, pp.18-30, 1999.

D. Serre, Systèmes de lois de conservation I. Diderot, 1996.

C. Shu, Essentially non-oscillatory and weighted essentially non-oscillatory schemes for hyperbolic conservation laws, 1997.
DOI : 10.1016/0021-9991(90)90120-P

C. Shu and S. Osher, Efficient implementation of essentially non-oscillatory shock-capturing schemes, Journal of Computational Physics, vol.77, issue.2, pp.439-471, 1988.
DOI : 10.1016/0021-9991(88)90177-5

C. Shu and S. 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

H. B. Stewart and B. Wendroff, Two-phase flow : models and methods, Journal of Computational Physics, 1984.

P. K. Sweby, High Resolution Schemes Using Flux Limiters for Hyperbolic Conservation Laws, SIAM Journal on Numerical Analysis, vol.21, issue.5, pp.995-1011, 1984.
DOI : 10.1137/0721062

M. E. Taylor, Partial differential equations I, 1997.

E. F. Toro, Riemann solvers and numerical methods for fluid dynamics. A practical introduction, 1997.

B. Van-leer, Towards the ultimate conservative difference scheme. II. Monotonicity and conservation combined in a second-order scheme, Journal of Computational Physics, vol.14, issue.4, pp.361-376, 1974.
DOI : 10.1016/0021-9991(74)90019-9

J. Vila, High-order schemes and entropy condition for nonlinear hyperbolic systems of conservation laws, Mathematics of Computation, vol.50, issue.181, pp.53-73, 1988.
DOI : 10.1090/S0025-5718-1988-0917818-1

H. S. Zang and R. M. So, A flux-coordinate-splitting technique for flows with shocks and contact discontinuities, Computers & Fluids, vol.20, issue.4, pp.421-442, 1991.
DOI : 10.1016/0045-7930(91)90083-T