/. Cdmath, http ://www.salome-platform.org/ 4, p.31

. [. Bibliography, C. Aguillon, and . Chalons, « Nondiffusive conservative schemes based on approximate Riemann solvers for Lagrangian gas dynamics, p.submitted, 2015.

J. [. Aragonaa, S. O. Colombeau, and . Juriaans, Nonlinear generalized functions and jump conditions for a standard one pressure liquid???gas model, Journal of Mathematical Analysis and Applications, vol.418, issue.2, pp.964-977, 2014.
DOI : 10.1016/j.jmaa.2014.04.002

C. [. Ambroso, P. A. Chalons, and . Raviart, A Godunov-type method for the seven-equation model of compressible two-phase flow, Computers & Fluids, vol.54, pp.67-91, 2012.
DOI : 10.1016/j.compfluid.2011.10.004

URL : https://hal.archives-ouvertes.fr/hal-00517375

]. N. Agu15 and . Aguillon, « Problèmes d'interfaces et couplages singuliers dans les systèmes hyperboliques : analyse et analyse numérique, 2015.

S. [. Abgrall and . Karni, A comment on the computation of non-conservative products, Journal of Computational Physics, vol.229, issue.8, pp.2759-2763, 2010.
DOI : 10.1016/j.jcp.2009.12.015

URL : https://hal.archives-ouvertes.fr/inria-00535567

]. K. Ami97 and . Amine, « Modélisation et analyse numérique des écoulements diphasiques en déséquilibre, 1997.

T. [. Buffard, J. Gallouet, and . Hérard, A sequel to a rough Godunov scheme: application to real gases, Computers & Fluids, vol.29, issue.7, 2000.
DOI : 10.1016/S0045-7930(99)00026-2

B. Boutin, Convergent and conservative schemes for non-classical solutions based on kinetic relations, Interfaces and Free Boundaries, 2008.

]. F. Bou00, . ]. Bouchutbre00, and . Bressan, Nonlinear stability of finite volume methods for hyperbolic conservation laws and well-balances scheme for sources Hyperbolic Systems of Conservation Laws : The One-dimentional Cauchy Problem, Oxford Lecture Series in Mathematics et Its ApplicationsBre88] A. Bressan. « Unique solutions for a class of discontinuous differential equations ». In : Proceedings of the AMS, 1988.

M. [. Bermudez and . Vazquez, Upwind methods for hyperbolic conservation laws with source terms, Computers & Fluids, vol.23, issue.8, pp.1049-1071, 1994.
DOI : 10.1016/0045-7930(94)90004-3

[. Cordier, P. Degond, and A. Kumbaro, Phase Appearance or Disappearance in Two-Phase Flows, Journal of Scientific Computing, vol.204, issue.329, p.58, 2014.
DOI : 10.1007/s10915-013-9725-9

URL : https://hal.archives-ouvertes.fr/hal-00628644

]. S. Cha81 and . Chandrasekhar, Hydrodynamic and Hydromagnetic Stability, 1981.

M. [. Chalons, P. Delle-monache, and . Goatin, « A numerical scheme for moving bottlenecks in traffic flow, submitted to the Proceedings of HYP2014 international conference, 2014.

H. [. Garcìa-cascales and . Paillère, Application of AUSM schemes to multi-dimensional compressible two-phase flow problems, Nuclear Engineering and Design, vol.236, issue.12, pp.1225-1239, 2006.
DOI : 10.1016/j.nucengdes.2005.11.013

]. C. Daf10 and . Dafermos, Hyperbolic conservation laws in continuum physics. T. 325. Grundlehren der mathematischen Wissenschaften, 2010.

F. [. Després and . Lagoutière, « Contact discontinuity capturing schemes for linear advection and compressible gas dynamics, Journal of Scientific Computing, vol.16, issue.4, 2001.

G. [. Dubois and . Mehlman, A non-parameterized entropy correction for Roe's approximate Riemann solver, Numerische Mathematik, vol.73, issue.2, pp.169-208, 1996.
DOI : 10.1007/s002110050190

D. Estelle, P. Fabien, D. Référence, and . Lmes, Documentation of the Interface for Code Coupling : ICoCo Theory of Multicomponents Fluids, 1999.

E. [. Dumbser and . Toro, A Simple Extension of the Osher Riemann Solver to??Non-conservative Hyperbolic Systems, Journal of Scientific Computing, vol.32, issue.1-3, pp.70-88, 2011.
DOI : 10.1007/s10915-010-9400-3

T. [. Evje and . Flatten, Hybrid flux-splitting schemes for a common two-fluid model, Journal of Computational Physics, vol.192, issue.1, pp.175-210, 2003.
DOI : 10.1016/j.jcp.2003.07.001

T. [. Evje and . Flatten, « Hybrid central-upwind schemes for numerical resolution, pp.2-39, 2005.

T. [. Evje and . Flatten, « On the wave struecture of two-phase flow models, In : SIAM J. APPL. MATH, p.67, 2007.

]. Fer10 and . Ferrer, « Numerical and mathematical analysis of a five-equation model for twophase flow, 2010.

H. Gene, C. F. Golub, and . Van-loan, Matrix computations, 4th, 2013.

P. [. Godlewski and . Raviart, Numerical Approximation of Hyperbolic Systems of Conservation Laws. T. 118 Appllied Mathematical Sciences, Har83] A. Harten. « High resolution schemes for hyperbolic conservation laws, pp.357-393, 1983.

J. [. Harten and . Hyman, Self adjusting grid methods for one-dimensional hyperbolic conservation laws, Journal of Computational Physics, vol.50, issue.2, pp.253-269, 1983.
DOI : 10.1016/0021-9991(83)90066-9

N. [. Holden and . Risebro, Front tracking for hyperbolic conservation laws, 2000.

M. Ishii and T. Hibiki, Thermo-Fluid Dynamics of Two-Phase Flow, 2011.

]. M. Ish75 and . Ishii, Thermo-fluid dynamic theory of two-phase flow, 1975.

P. [. Jamet, . J. Emonotjeo+08-]-j, and . Jeong, Rapport d'avancement Diphasique à 6 équations et une pression A semi-implicit numerical scheme for transient two-phase flows on unstructured grids, Rapp. tech. CEA Nuclear Engineering and Design, vol.238, 2007.

M. [. Kakac and . Ishii, Advances in Two-Phase Flow and Heat Transfer Fundamentals and Applications. T. 1. Martinus Nijhoff Publishers, Th. Katsaounis, B. Perthame et C. Simeoni. « Upwinding sources at interfaces in conservation laws, pp.309-316, 1983.

R. [. Keyfitz, M. Sanders, and . Sever, « Lack of Hyperbolicity in the Two-Fluid Model for Two-Phase Incompressible Flow, Discrete and Continuous Dynamical Systems- Series B 3, pp.541-563, 2003.

]. F. Lag04 and . Lagoutière, « A non-dissipative entropic scheme for convex scalar equations via discontinuous cell-reconstruction, C. R. Acad. Sci. Paris, Ser. I, vol.338, 2004.

]. P. Lef02, . J. Leflochlev04-]-r, and . Leveque, Hyperbolic Systems of Conservation Laws, the Theory of Classical and Nonclassical Shock Waves Finite Volume Methods for Hyperbolic Problems, 2002.

]. R. Lev92 and . Leveque, Numerical Methods for Conservation Laws, 1992.

P. Lions, Benoît Perthame et Panagiotis E. Souganidis. « Existence and stability of entropy solutions for the hyperbolic systems of isentropic gas dynamics in Eulerian and Lagrangian coordinates, Communications on Pure and Applied Mathematics, vol.496, pp.599-638, 1996.

[. Liu and J. A. Smolle, On the vacuum state for the isentropic gas dynamics equations, Advances in Applied Mathematics, vol.1, issue.4, pp.345-359, 1980.
DOI : 10.1016/0196-8858(80)90016-0

S. [. Munkejord, T. Evje, and . Fltten, A MUSTA Scheme for a Nonconservative Two-Fluid Model, SIAM Journal on Scientific Computing, vol.31, issue.4, pp.31-2587, 2009.
DOI : 10.1137/080719273

A. Morin, T. Fltten-et-svend-tollak, and . Munkejord, A Roe scheme for a compressible six-equation two-fluid model, International Journal for Numerical Methods in Fluids, vol.66, issue.4, pp.1-28, 2010.
DOI : 10.1002/fld.3752

P. [. Dal-maso, F. Lefloch, and . Murat, « Definition and weak stability on non conservative products, Journal of Math Pures Application, vol.74, pp.483-548, 1995.

]. S. Mun05 and . Munkejord, Analysis of the two-fluid model and the drift-flux model for numerical calculation of two-phase flow, 2005.

]. S. Mun07 and . Munkejord, « Comparison of Roe-type methods for solving the two-fluid model with and without pressure relaxation, In : Computers & Fluids, vol.36, 2007.

L. [. Mottura, M. Vigevano, and . Zaccanti, An Evaluation of Roe's Scheme Generalizations for Equilibrium Real Gas Flows, Journal of Computational Physics, vol.138, issue.2, 1997.
DOI : 10.1006/jcph.1997.5838

M. Ndjinga, Numerical simulation of hyperbolic two-phase flow models using a Roe-type solver, Nuclear Engineering and Design, vol.238, issue.8, 2008.
DOI : 10.1016/j.nucengdes.2007.11.014

]. M. Ndj07b and . Ndjinga, « Quelques aspects de modélisation et d'analyse des systèmes issus des écoulements diphasiques », 2007.

[. Nguyen, M. Ndjinga, and C. Chalons, « Numerical simulation of an incompressible two-fluid model ». In : Finite Volumes for Complex Applications VII-Methods and Theoretical Aspects

M. Ndjinga, T. Nguyen, and C. Chalons, « Mathematical analysis an numerical simulation of the two-fluid model with counter current phase dynamics, p.In preparation, 2015.

C. [. Paillère, J. R. Corre, . Garcìa, and . Cascales, On the extension of the AUSM+ scheme to compressible two-fluid models, Computers & Fluids, vol.32, issue.6, pp.891-916, 2003.
DOI : 10.1016/S0045-7930(02)00021-X

]. V. Ran87 and . Ransom, « Numerical bencmark tests, Multiphase Sci, 1987.

D. [. Ransom and . Hicks, Hyperbolic two-pressure models for two-phase flow, Journal of Computational Physics, vol.53, issue.1, pp.124-151, 1984.
DOI : 10.1016/0021-9991(84)90056-1

]. P. Roe81 and . Roe, « Approximate Riemann Solvers, Parameter Vectors, and Difference Schemes, Journal of Computational Physics, vol.43, pp.357-372, 1981.

]. J. [-rom98 and . Romate, « An approximate Riemann solver for a two-phase flow model with numerically given slip relation, In : Computers & Fluids, vol.27, 1998.

F. [. Sahmim, F. Benkhaldoun, and . Alcrudo, A sign matrix based scheme for non-homogeneous PDE???s with an analysis of the convergence stagnation phenomenon, Journal of Computational Physics, vol.226, issue.2, pp.1753-1783, 2007.
DOI : 10.1016/j.jcp.2007.06.017

D. Serre, System of Conservation Laws 1 : Hyperbolicity, Entropies, Shock Waves, 1999.
DOI : 10.1017/CBO9780511612374

E. [. Shekari and . Hajidavalloo, Application of Osher and PRICE-C schemes to solve compressible isothermal two-fluid models of two-phase flow, Computers & Fluids, vol.86, pp.363-379, 2013.
DOI : 10.1016/j.compfluid.2013.07.018

B. [. Stewart and . Wendroff, « Two-phase flow : Models and methods, J. of Comp. Physics, vol.563, 1984.

]. J. Tem81 and . Temple, « Solutions in the Large for the Nonlinear Hyperbolic Conservation Laws of Gas Dynamics, Journal of differential equations, vol.41, pp.96-161, 1981.

A. [. Toumi and . Kumbaro, An Approximate Linearized Riemann Solver for a Two-Fluid Model, Journal of Computational Physics, vol.124, issue.2, pp.286-300, 1996.
DOI : 10.1006/jcph.1996.0060

A. [. Toumi, H. Kumbaro, and . Paillere, « Approximate Riemann solvers and flux vector splitting schemes for two-phase flow, 30th Computational Fluid Dynamics, 1999.

I. Toumi, FLICA-4: a three-dimensional two-phase flow computer code with advanced numerical methods for nuclear applications, Nuclear Engineering and Design, vol.200, issue.1-2, 2000.
DOI : 10.1016/S0029-5493(99)00332-5

]. I. Tou87 and . Toumi, « Etude du problème de Riemann et construction de schéma numériques type Godunov multidimensionnels des modèles d'écoulements diphasiques, 1987.

]. A. Ver06 and . Vernier, Validation de Modèles Multichamps dans le Logiciel OVAP, 2006.