R. Abgrall and S. Karni, Computations of Compressible Multifluids, Journal of Computational Physics, vol.169, issue.2, pp.594-623, 2001.
DOI : 10.1006/jcph.2000.6685

R. Abgrall, Approximation duprobì eme de Riemann vraiment multidimensionnel deséquationsdeséquations d'Euler par une méthode de type Roe. I. La linéarisation, C. R. Acad

R. Abgrall, Approximation duprobì eme de Riemann vraiment multidimensionnel deséquationsdeséquations d'Euler par une méthode de type Roe. II. Solution duprobì eme de Riemann approché, C. R. Acad. Sci. Paris Sér. I Math, vol.319, issue.6, pp.625-629, 1994.

R. Abgrall and A. Harten, Multiresolution representation in unstrutured meshes

R. Abgrall and M. Mezine, Construction of second order accurate monotone and stable residual distribution schemes for unsteady flow problems, Journal of Computational Physics, vol.188, issue.1, pp.16-55, 2003.
DOI : 10.1016/S0021-9991(03)00084-6

M. Asch, J. Gac, and P. Helluy, An adjoint method for geoacoustic inversions, 2nd Conference on Inverse Problems, Control and Shape Optimization, 2002.

T. Barberon, Modélisation mathématique et numérique de la cavitation dans lesécoulements lesécoulements multiphasiques compressibles, 2002.

T. Barberon and H. , Finite volume simulation of cavitating flows. Computers and Fluids, 2004.
URL : https://hal.archives-ouvertes.fr/inria-00071762

T. Barberon, P. Helluy, and S. Rouy, Practical computation of axisymmetrical multifluid flows, International Journal of Finite Volumes, vol.1, issue.1, pp.1-34, 2003.
URL : https://hal.archives-ouvertes.fr/hal-00139598

T. Barberon and P. Helluy, Finite volume simulations of cavitating flows In Finite volumes for complex applications, III (Porquerolles, Lab. Anal. Topol. Probab. CNRS, pp.441-448, 2002.

M. Ben-artzi and J. Falcovitz, An Upwind Second-Order Scheme for Compressible Duct Flows, SIAM Journal on Scientific and Statistical Computing, vol.7, issue.3, pp.744-768, 1986.
DOI : 10.1137/0907051

C. Berthon and B. Nkonga, Behavior of the finite volumes schemes in material and numerical interfaces, Finite Volumes for Complex Applications III (Porquerolles, pp.139-146, 2002.

L. Barna, A. Bihari, and . Harten, Multiresolution schemes for the numerical solution of 2-D conservation laws, I. SIAM J. Sci. Comput, vol.18, issue.2, pp.315-354, 1997.

F. Bouchut, . Ch, B. Bourdarias, and . Perthame, A MUSCL method satisfying all the numerical entropy inequalities, Mathematics of Computation, vol.65, issue.216, pp.1439-1461, 1996.
DOI : 10.1090/S0025-5718-96-00752-1

F. Bourdel, P. Mazet, and P. Helluy, Resolution of the non-stationary or harmonic maxwell equations by a discontinuous finite element method. application to an e.m.i. (electromagnetic impulse) case, 10th international conference on computing methods in applied sciences and engineering, pp.11-14, 1992.
URL : https://hal.archives-ouvertes.fr/hal-00974964

F. Bourdel, J. Croisille, P. Delorme, and P. Mazet, On the approximation of K-diagonalizable hyperbolic systems by finite elements. Applications to the Euler equations and to gaseous mixtures, Rech. Aérospat, issue.5, pp.15-34, 1989.

A. Bourgeade, . Ph, P. Lefloch, and . Raviart, An asymptotic expansion for the solution of the generalized Riemann problem. Part 2 : application to the equations of gas dynamics, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, vol.6, issue.6, pp.437-480, 1989.
DOI : 10.1016/S0294-1449(16)30310-9

Y. Brenier, Averaged Multivalued Solutions for Scalar Conservation Laws, SIAM Journal on Numerical Analysis, vol.21, issue.6, pp.1013-1037, 1984.
DOI : 10.1137/0721063

Y. Brenier, Averaged multivalued solutions and time discretization for conservation laws In Large-scale computations in fluid mechanics, Lectures in Appl. Math, vol.22, pp.41-55, 1983.

Y. Brenier, Un algorithme rapide pour le calcul de transformées de Legendre- Fenchel discrètes, C. R. Acad. Sci. Paris Sér. I Math, vol.308, issue.20, pp.587-589, 1989.

H. B. Callen, Thermodynamics and an introduction to thermostatistics, second edition, 1985.

Y. C. Chang, T. Y. Hou, B. Merriman, and S. Osher, A Level Set Formulation of Eulerian Interface Capturing Methods for Incompressible Fluid Flows, Journal of Computational Physics, vol.124, issue.2, pp.449-464, 1996.
DOI : 10.1006/jcph.1996.0072

G. Chanteperdrix, P. Villedieu, and J. Vila, A Compressible Model for Separated Two-Phase Flows Computations, Volume 1: Fora, Parts A and B, 2002.
DOI : 10.1115/FEDSM2002-31141

B. Cockburn and C. 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

A. Cohen, N. Dyn, S. M. Kaber, and M. Postel, Multiresolution Schemes on Triangles for Scalar Conservation Laws, Journal of Computational Physics, vol.161, issue.1, pp.264-286, 2000.
DOI : 10.1006/jcph.2000.6503

A. Cohen, S. M. Kaber, S. Müller, and M. Postel, Fully adaptive multiresolution finite volume schemes for conservation laws, Mathematics of Computation, vol.72, issue.241, pp.183-225, 2003.
DOI : 10.1090/S0025-5718-01-01391-6

F. Coquel, P. Helluy, and J. Schneider, Second-order entropy diminishing scheme for the Euler equations, International Journal for Numerical Methods in Fluids, vol.39, issue.9
DOI : 10.1002/fld.1104
URL : https://hal.archives-ouvertes.fr/hal-00139605

F. Coquel and B. Perthame, Relaxation of Energy and Approximate Riemann Solvers for General Pressure Laws in Fluid Dynamics, SIAM Journal on Numerical Analysis, vol.35, issue.6, pp.2223-2249, 1998.
DOI : 10.1137/S0036142997318528

F. Coquel and P. G. Lefloch, An entropy satisfying MUSCL scheme for systems of conservation laws, Numerische Mathematik, vol.74, issue.1, pp.1-33, 1996.
DOI : 10.1007/s002110050205

J. Croisille, ContributionàContributionà l'´ etude théorique etàetà l'approximation parélémentsparéléments finis du système hyperbolique de la dynamique des gaz multidimensionnelle et multiespèces, 1991.

M. Csík, H. Ricchiuto, and . Deconinck, A Conservative Formulation of the Multidimensional Upwind Residual Distribution Schemes for General Nonlinear Conservation Laws, Journal of Computational Physics, vol.179, issue.1, pp.286-312, 2002.
DOI : 10.1006/jcph.2002.7057

S. Dellacherie, Relaxation schemes for the multicomponent Euler system, ESAIM: Mathematical Modelling and Numerical Analysis, vol.37, issue.6, pp.909-936, 2003.
DOI : 10.1051/m2an:2003061

B. Després, F. Lagoutì, and D. Ramos, Stability of a Thermodynamically Coherent Multiphase Model, Mathematical Models and Methods in Applied Sciences, vol.13, issue.10, pp.1463-1487, 2003.
DOI : 10.1142/S0218202503002994

B. Després and F. Ere, Contact discontinuity capturing schemes for linear advection and compressible gas dynamics, Journal of Scientific Computing, vol.16, issue.4, pp.479-524, 2001.
DOI : 10.1023/A:1013298408777

F. Dubois, Partial Riemann problem, boundary conditions and gas dynamics In Absorbing Boundaries and Layers, Domain Decomposition Methods. Applications to Large Scale Computations, pp.16-77

F. Dubois and P. Lefloch, Boundary conditions for nonlinear hyperbolic systems of conservation laws, Journal of Differential Equations, vol.71, issue.1, pp.93-122, 1988.
DOI : 10.1016/0022-0396(88)90040-X

L. C. Evans, Entropy and partial differential equations, 2004.

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, pp.457-492, 1999.
DOI : 10.1006/jcph.1999.6236

M. Feistauer, J. Felcman, and I. Straskraba, Mathematical and Computational Methods for Compressible Flow, 2004.

T. Gallouët, J. Hérard, and N. Seguin, A hybrid scheme to compute contact discontinuities in one-dimensional Euler systems, ESAIM: Mathematical Modelling and Numerical Analysis, vol.36, issue.6, pp.1133-1159, 2002.
DOI : 10.1051/m2an:2003009

T. Gallouët, J. Hérard, and N. Seguin, True rate of convergence of some upwinding finite volume schemes for Euler equations, Finite volumes for complex applications, III (Porquerolles, pp.731-738, 2002.

E. Godlewski and P. Raviart, Hyperbolic systems of conservation laws, of Mathématiques & Applications (Paris) [Mathematics and Applications] . Ellipses, 1991.
URL : https://hal.archives-ouvertes.fr/hal-00113734

E. Godlewski and P. Raviart, Numerical approximation of hyperbolic systems of conservation laws, Applied Mathematical Sciences, vol.118, 1996.
DOI : 10.1007/978-1-4612-0713-9

S. K. Godunov, A difference scheme for numerical computation of discontinuous solutions of equations of fluids mechanics, Math Sbornik, vol.47, pp.271-306, 1959.

F. Golay and P. Helluy, Numerical simulation of viscous compressible fluid based on a splitting method. soumisàsoumisà Num
URL : https://hal.archives-ouvertes.fr/hal-01419015

J. B. Goodman and R. J. Leveque, On the Accuracy of Stable Schemes for 2D Scalar Conservation Laws, Mathematics of Computation, vol.45, issue.171, pp.15-21, 1985.
DOI : 10.2307/2008046

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, pp.35-61, 1983.
DOI : 10.1137/1025002

A. Harten, ENO schemes with subcell resolution, Journal of Computational Physics, vol.83, issue.1, pp.148-184, 1989.
DOI : 10.1016/0021-9991(89)90226-X

P. Helluy, Couplagé equation intégrale-volumes finis pour la résolution deséquationsdeséquations de maxwell harmoniques European symposium on numerical methods in electromagnetics, november 17-19th, JEE'93, pp.217-226, 1993.

P. Helluy, Résolution numérique deséquationsdeséquations de Maxwell harmoniques par une méthode d'´ eléments finis discontinus, 1994.

P. Helluy, Modélisation de la chambre de refroidissement d'un générateur de gaz, 2002.

P. Helluy, Quelques exemples de méthodes numériques récentes pour le calcul desécoulements desécoulements multiphasiques, Thèse de HDR, 2005.

P. Helluy and F. Golay, Numerical simulations of wave breaking, ESAIM: Mathematical Modelling and Numerical Analysis, vol.39, issue.3
DOI : 10.1051/m2an:2005024
URL : https://hal.archives-ouvertes.fr/hal-00017441

P. Helluy, S. Maire, and P. , New higher order numeric quadratures for regular or singular functions on an interval, applications for the helmotz integral equation, Second Symposium on Multibody Dynamics and Vibration, pp.12-16, 1999.

P. Helluy, P. Mazet, and P. Klotz, Sur une approximation en domaine non borné deséquations deséquations de Maxwell instationnaires, comportements asymptotiques, Rech. Aérospat, issue.5, pp.365-377, 1994.

P. Helluy and V. Rey, Modélisation numérique de la houle dans le port de banyuls, 1998.

P. Helluy and S. Dayma, Convergence d'une approximation discontinue des systèmes du premier ordre, C. R. Acad. Sci. Paris Sér. I Math, issue.12, pp.3191331-1335, 1994.

P. Helluy, S. Maire, and P. Ravel, Int??gration num??rique d'ordre ??lev?? de fonctions r??guli??res ou singuli??res sur un intervalle, Comptes Rendus de l'Acad??mie des Sciences - Series I - Mathematics, vol.327, issue.9, pp.843-848, 1998.
DOI : 10.1016/S0764-4442(99)80116-5

J. Hiriart-urruty and C. Lemaréchal, Fundamentals of convex analysis . Grundlehren Text Editions, 2001.

T. Y. 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, ´ Etude mathématique et numérique de stabilité pour des modèles hydrodynamiques avec transition de phase, 2001.

S. Karni, Multicomponent Flow Calculations by a Consistent Primitive Algorithm, Journal of Computational Physics, vol.112, issue.1, pp.31-43, 1994.
DOI : 10.1006/jcph.1994.1080

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

P. D. Lax, Hyperbolic systems of conservation laws and the mathematical theory of shock waves, CBMS Regional Conf. Ser. In Appl. Math. 11, 1972.

D. Peter, X. Lax, and . Liu, Solution of two-dimensional Riemann problems of gas dynamics by positive schemes, SIAM J. Sci. Comput, vol.19, issue.2, pp.319-340, 1998.

P. Lesaint, Continuous and discontinuous finite element methods for solving the transport equation In The mathematics of finite elements and applications, II, Proc. Second Brunel Univ. Conf. Inst, pp.151-161, 1975.

M. Liou, C. J. Steffen, and J. , A New Flux Splitting Scheme, Journal of Computational Physics, vol.107, issue.1, pp.23-39, 1993.
DOI : 10.1006/jcph.1993.1122

T. P. Liu, The Riemann problem for general systems of conservation laws, Journal of Differential Equations, vol.18, issue.1, pp.218-234, 1975.
DOI : 10.1016/0022-0396(75)90091-1

Y. Lucet, A fast computational algorithm for the Legendre-Fenchel transform, Computational Optimization and Applications, vol.311, issue.3, pp.27-57, 1996.
DOI : 10.1007/BF00248008

Y. Lucet, Faster than the fast Legendre transform, the linear-time Legendre transform, Numerical Algorithms, vol.16, issue.2, pp.171-185, 1997.
DOI : 10.1023/A:1019191114493

P. Mazet and F. Bourdel, Multidimensional case of an entropic variational formulation of conservative hyperbolic systems, Rech. Aérospat, issue.5, pp.369-378, 1984.

R. Menikoff and B. J. Plohr, The Riemann problem for fluid flow of real materials, Reviews of Modern Physics, vol.61, issue.1, pp.75-130, 1989.
DOI : 10.1103/RevModPhys.61.75

W. Mulder, S. Osher, and J. A. Sethian, Computing interface motion in compressible gas dynamics, Journal of Computational Physics, vol.100, issue.2, pp.209-228, 1992.
DOI : 10.1016/0021-9991(92)90229-R

]. J. Nussbaum, ´ Ecoulement diphasique réactif dans la chambre de combustion d'une armè a feu

F. Pelestor, Modélisation numériques d'´ ecoulements multiphasiques par des méthodes particulaires

B. Perthame, Boltzmann Type Schemes for Gas Dynamics and the Entropy Property, SIAM Journal on Numerical Analysis, vol.27, issue.6
DOI : 10.1137/0727081

H. Preston-thomas, The International Temperature Scale of 1990 (ITS-90), Metrologia, vol.27, issue.1, pp.3-10, 1990.
DOI : 10.1088/0026-1394/27/1/002

J. Rauch, BV estimates fail for most quasilinear hyperbolic systems in dimensions greater than one, Communications in Mathematical Physics, vol.11, issue.3, pp.481-484, 1986.
DOI : 10.1007/BF01207258

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

S. Rouy, Modélisation mathématique et numérique d'´ ecoulements diphasiques compressibles, 2000.

S. Rouy and P. Helluy, Mathematical and numerical modeling of a twophase flow by a level set method, Finite volumes for complex applications II, pp.833-840, 1999.

L. Sainsaulieu, Finite Volume Approximation of Two Phase-Fluid Flows Based on an Approximate Roe-Type Riemann Solver, Journal of Computational Physics, vol.121, issue.1, pp.1-28, 1995.
DOI : 10.1006/jcph.1995.1176

R. Saurel and R. Abgrall, A Simple Method for Compressible Multifluid Flows, SIAM Journal on Scientific Computing, vol.21, issue.3, pp.1115-1145, 1999.
DOI : 10.1137/S1064827597323749

L. Joseph, R. F. Steger, and . Warming, Flux vector splitting of the inviscid gasdynamic equations with application to finite-difference methods, J. Comput. Phys, vol.40, issue.2, pp.263-293, 1981.

M. Tanaka, The stability of solitary waves, Physics of Fluids, vol.29, issue.3, pp.650-6555, 1986.
DOI : 10.1063/1.865459

E. F. Toro, Riemann solvers and numerical methods for fluid dynamics, 1999.

E. H. Van-brummelen and B. Koren, A pressure-invariant conservative Godunov-type method for barotropic two-fluid flows, Journal of Computational Physics, vol.185, issue.1, pp.289-308, 2003.
DOI : 10.1016/S0021-9991(02)00058-X

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, pp.101-136, 1979.
DOI : 10.1016/0021-9991(79)90145-1

T. Yasuda, H. Mutsuda, and N. Mizutani, Kinematics of overturning solitary waves and their relations to breaker types, Coastal Engineering, vol.29, issue.3-4, pp.317-346, 1997.
DOI : 10.1016/S0378-3839(96)00032-4

. Spécialité, Résolution numérique deséquationsdeséquations de Maxwell harmoniques par une méthode d'´ eléments finis discontinus Soutenue en janvier 1994, 1989.

@. Méthodes-numériques-pour-l-'acoustique-et-l-'´-electromagnétisme, @. P. Publications-articles, P. Helluy, P. Mazet, and . Klotz, Sur une approximation en domaine non borné deséquations deséquations de Maxwell instationnaires, comportements asymptotiques, Rech. Aérospat, issue.5, pp.365-377, 1994.

@. P. Helluy, S. Maire, P. Ravel, /. Admin-/-cv-/-fvca3, @. M. Pdf et al., New higher order numeric quadratures for regular or singular functions on an interval, applications for the helmotz integral equation http://helluy.univ-tln.fr/ADMIN/CV/asme99.pdf ? Thomas Barberon and Philippe Helluy. Finite volume simulations of cavitating flows An adjoint method for geoacoustic inversions, Second Symposium on Multibody Dynamics and Vibration, september 12-16. ASME, Las Vegas, Nevada Finite volumes for complex applications, III (Porquerolles 2nd Conference on Inverse Problems, Control and Shape Optimization, pp.441-448, 1999.

@. P. Helluy, F. Golay, @. F. Golay, P. Helluy, /. Admin-/-cv-/-nastocomp et al., Numerical simulation of viscous compressible fluid based on a splitting method Second order entropy diminishing scheme for the euler equations. soumisàsoumisà International Journal for Numerical Methods in Fluids http Quelques exemples de méthodes numériques récentes pour le calcul desécoulements desécoulements multiphasiques Résolution numérique deséquationsdeséquations de Maxwell harmoniques par une méthode d'´ eléments finis discontinus, Thèse de HDRzip Encadrement doctoral ? S. Rouy. Modélisation mathématique et numérique d'´ ecoulements diphasiques compressibles Modélisation mathématique et numérique de la cavitation dans lesécoulesécoulements multiphasiques compressibles, 1994.

/. Fr, . Theses-/-barberon, @. F. Pdf, @. J. Pelestor-en-cours, @. P. Nussbaum-recherche et al., Modélisation numériques d'´ ecoulements multiphasiques par des méthodes particulaires ´ Ecoulement diphasique réactif dans la chambre de combustion d'une armèarmè a feu Contrat de recherche avec la Mairie de Banyuls-sur-mer http, Modélisation numérique de la houle dans le port de banyuls, 1998.