B. Audebert, ContributionàContributionà l'analyse des modèles aux tensions de Reynolds pour l'interaction choc turbulence, 2006.

M. Baer and J. Nunziato, A two-phase mixture theory for the deflagration-to-detonation transition (ddt) in reactive granular materials, International Journal of Multiphase Flow, vol.12, issue.6, pp.861-889, 1986.
DOI : 10.1016/0301-9322(86)90033-9

J. B. Bdzil, R. Menikoff, S. F. Son, A. K. Kapila, and D. S. Stewart, Two-phase modeling of deflagration-to-detonation transition in granular materials: A critical examination of modeling issues, Physics of Fluids, vol.11, issue.2, pp.378-402, 1999.
DOI : 10.1063/1.869887

F. Coquel, T. Gallouët, J. Hérard, and N. Seguin, Closure laws for a two-fluid two-pressure model, Comptes Rendus Mathematique, vol.334, issue.10, pp.927-932, 2002.
DOI : 10.1016/S1631-073X(02)02366-X

URL : https://hal.archives-ouvertes.fr/hal-01484345

D. A. Drew and S. L. Passman, Theory of Multicomponent Fluids, 1999.
DOI : 10.1007/b97678

A. Favre, Equations des gaz turbulents compressibles. Méthodes des vitesses moyennes, méthode des vitesses macroscopiques pondérées par la masse volumique, Journal de mecanique, vol.4, issue.4, p.391, 1965.

A. Forestier, J. Hérard, and X. Louis, Solveur de type Godunov pour simuler lesécoulements lesécoulements turbulents compressibles, Comptes Rendus de l'Académie des Sciences - Series I -Mathematics, pp.919-926, 1997.

T. Gallouët, J. Hérard, and N. Seguin, NUMERICAL MODELING OF TWO-PHASE FLOWS USING THE TWO-FLUID TWO-PRESSURE APPROACH, Mathematical Models and Methods in Applied Sciences, vol.14, issue.05, pp.663-700, 2004.
DOI : 10.1142/S0218202504003404

S. Gavrilyuk and R. Saurel, Mathematical and Numerical Modeling of Two-Phase Compressible Flows with Micro-Inertia, Journal of Computational Physics, vol.175, issue.1, pp.326-360, 2002.
DOI : 10.1006/jcph.2001.6951

J. Hérard and Y. Liu, Une approche bifluide statistique de modelisation desécoulements desécoulements diphasiquesàdiphasiquesà phases compressibles. Internal report H-I81, 1162.

J. Hérard and H. Lochon, A simple turbulent two-phase flow model. in preparation, 2014.

M. Ishii, Thermo-fluid dynamic theory of two-phase flows, 1975.

H. Jin, J. Glimm, and D. H. Sharp, Compressible two-pressure two-phase flow models, Physics Letters A, vol.353, issue.6, pp.469-474, 2006.
DOI : 10.1016/j.physleta.2005.11.087

V. H. Ransom and D. L. 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

H. B. Stewart and B. Wendroff, Two-phase flow: Models and methods, Journal of Computational Physics, vol.56, issue.3, pp.363-409, 1984.
DOI : 10.1016/0021-9991(84)90103-7

M. Baer and J. Nunziato, A two-phase mixture theory for the deflagration-to-detonation transition (ddt) in reactive granular materials, International Journal of Multiphase Flow, vol.12, issue.6, pp.861-889, 1986.
DOI : 10.1016/0301-9322(86)90033-9

F. Coquel, T. Gallouët, J. Hérard, and N. Seguin, Closure laws for a two-fluid two-pressure model, Comptes Rendus Mathematique, vol.334, issue.10, pp.927-932, 2002.
DOI : 10.1016/S1631-073X(02)02366-X

URL : https://hal.archives-ouvertes.fr/hal-01484345

F. Daude and P. Galon, Développement d'un modèle diphasiquè a deux pressions dans Europlexus et vérifications numériques -Partie convective. Internal report H-T63, 1003.

S. Gavrilyuk, The structure of pressure relaxation terms : one-velocity case, 2014.

J. Hérard and O. Hurisse, A fractional step method to compute a class of compressible gas???liquid flows, Computers & Fluids, vol.55, pp.57-69, 2012.
DOI : 10.1016/j.compfluid.2011.11.001

J. Hérard and Y. Liu, Une approche bifluide statistique de modelisation desécoulements desécoulements diphasiquesàdiphasiquesà phases compressibles. Internal report H-I81, 1162.

H. Lochon, Modélisation d'´ ecoulements diphasiques : fermetures entropiques de modèles bifluides. Internal report H-T63, 2014.

E. User, Commissariatàriatà l'´ energie atomique et auxénergiesauxénergies alternatives (CEA), 2016, Joint Research Centre (JRC)

A. Ambroso, C. Chalons, and P. 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. Andrianov and G. Warnecke, The Riemann problem for the Baer???Nunziato two-phase flow model, Journal of Computational Physics, vol.195, issue.2, pp.434-464, 2004.
DOI : 10.1016/j.jcp.2003.10.006

M. Baer and J. Nunziato, A two-phase mixture theory for the deflagration-to-detonation transition (ddt) in reactive granular materials, International Journal of Multiphase Flow, vol.12, issue.6, pp.861-889, 1986.
DOI : 10.1016/0301-9322(86)90033-9

J. B. Bdzil, R. Menikoff, S. F. Son, A. K. Kapila, and D. S. Stewart, Two-phase modeling of deflagration-to-detonation transition in granular materials: A critical examination of modeling issues, Physics of Fluids, vol.11, issue.2, pp.378-402, 1999.
DOI : 10.1063/1.869887

R. Berry, L. Zou, H. Zhao, D. Andrs, J. Peterson et al., Relap-7 : Demonstrating Seven-Equation, Two-Phase Flow Simulation in a Single-Pipe, Two-Phase Reactor Core and Steam Separator/Dryer

A. Chinnayya, E. Daniel, and R. Saurel, Modelling detonation waves in heterogeneous energetic materials, Journal of Computational Physics, vol.196, issue.2, pp.490-538, 2004.
DOI : 10.1016/j.jcp.2003.11.015

F. Coquel, T. Gallouët, J. Hérard, and N. Seguin, Closure laws for a two-fluid two-pressure model, Comptes Rendus Mathematique, vol.334, issue.10, pp.927-932, 2002.
DOI : 10.1016/S1631-073X(02)02366-X

URL : https://hal.archives-ouvertes.fr/hal-01484345

F. Coquel, J. Hérard, K. Saleh, and N. Seguin, A robust entropy???satisfying finite volume scheme for the isentropic Baer???Nunziato model, ESAIM: Mathematical Modelling and Numerical Analysis, vol.48, issue.1, pp.165-206, 2014.
DOI : 10.1051/m2an/2013101

URL : https://hal.archives-ouvertes.fr/hal-00795568

F. Crouzet, F. Daude, P. Galon, J. Hérard, O. Hurisse et al., Validation of a two-fluid model on unsteady liquid???vapor water flows, Computers & Fluids, vol.119, pp.131-142, 2015.
DOI : 10.1016/j.compfluid.2015.06.035

F. Daude, P. Galon, Z. Gao, and E. Blaud, Numerical experiments using a HLLC-type scheme with ALE formulation for compressible two-phase flows five-equation models with phase transition, Computers & Fluids, vol.94, pp.112-138, 2014.
DOI : 10.1016/j.compfluid.2014.02.008

V. Deledicque and M. V. Papalexandris, An exact Riemann solver for compressible two-phase flow models containing non-conservative products, Journal of Computational Physics, vol.222, issue.1, pp.217-245, 2007.
DOI : 10.1016/j.jcp.2006.07.025

P. Downar-zapolski, Z. Bilicki, L. Bolle, and J. Franco, The non-equilibrium relaxation model for one-dimensional flashing liquid flow, International Journal of Multiphase Flow, vol.22, issue.3, pp.473-483, 1996.
DOI : 10.1016/0301-9322(95)00078-X

D. A. Drew and S. L. Passman, Theory of Multicomponent Fluids, 1999.
DOI : 10.1007/b97678

T. Gallouët, P. Helluy, J. Hérard, and J. Nussbaum, Hyperbolic relaxation models for granular flows, ESAIM: Mathematical Modelling and Numerical Analysis, vol.44, issue.2, pp.371-400, 2010.
DOI : 10.1051/m2an/2010006

T. Gallouët, J. Hérard, and N. Seguin, NUMERICAL MODELING OF TWO-PHASE FLOWS USING THE TWO-FLUID TWO-PRESSURE APPROACH, Mathematical Models and Methods in Applied Sciences, vol.14, issue.05, pp.663-700, 2004.
DOI : 10.1142/S0218202504003404

S. Gavrilyuk, The structure of pressure relaxation terms : one-velocity case, 2014.

S. Gavrilyuk and R. Saurel, Mathematical and Numerical Modeling of Two-Phase Compressible Flows with Micro-Inertia, Journal of Computational Physics, vol.175, issue.1, pp.326-360, 2002.
DOI : 10.1006/jcph.2001.6951

J. Glimm, D. Saltz, and D. H. Sharp, Renormalization group solution of two-phase flow equations for Rayleigh-Taylor mixing, Physics Letters A, vol.222, issue.3, pp.171-176, 1996.
DOI : 10.1016/0375-9601(96)00648-2

V. Guillemaud, Modélisation et simulation numérique desécoulementsdesécoulements diphasiques par une approche bifluidè a deux pressions URL https, 2007.

J. Hérard, A three-phase flow model, Mathematical and Computer Modelling, vol.45, issue.5-6, pp.732-755, 2007.
DOI : 10.1016/j.mcm.2006.07.018

J. Hérard, Une classe de modèles diphasiques bifluides avec changement de régime. Internal report H-I81, 2010.

J. Hérard and O. Hurisse, A fractional step method to compute a class of compressible gas???liquid flows, Computers & Fluids, vol.55, pp.57-69, 2012.
DOI : 10.1016/j.compfluid.2011.11.001

J. Hérard and Y. Liu, Une approche bifluide statistique de modelisation desécoulements desécoulements diphasiquesàdiphasiquesà phases compressibles. Internal report H-I81, 1162.

M. Ishii, Thermo-fluid dynamic theory of two-phase flows, 1975.

H. Jin, J. Glimm, and D. H. Sharp, Entropy of averaging for compressible two-pressure two-phase flow models, Physics Letters A, vol.360, issue.1, pp.114-121, 2006.
DOI : 10.1016/j.physleta.2006.07.064

A. K. Kapila, S. F. Son, J. B. Bdzil, R. Menikoff, and D. S. Stewart, Two-phase modeling of DDT: Structure of the velocity-relaxation zone, Physics of Fluids, vol.9, issue.12, pp.3885-3897, 1997.
DOI : 10.1063/1.869488

O. , L. Métayer, J. Massoni, and R. Saurel, ´ Elaboration des lois d'´ etat d'un liquide et de sa vapeur pour les modèles d'´ ecoulements diphasiques, International Journal of Thermal Sciences, vol.43, issue.3, pp.265-276, 2004.

O. , L. Métayer, J. Massoni, and R. Saurel, Dynamic relaxation processes in compressible multiphase flows. Application to evaporation phenomena, ESAIM : Proceedings, pp.103-123, 2013.

H. Lochon, Modélisation d'´ ecoulements diphasiques : fermetures entropiques de modèles bifluides. Internal report H-T63, 2014.

S. Müller, M. Hantke, and P. Richter, Closure conditions for non-equilibrium multicomponent models, Continuum Mechanics and Thermodynamics, pp.1-33, 2015.

M. Pelanti and K. Shyue, A mixture-energy-consistent six-equation two-phase numerical model for fluids with interfaces, cavitation and evaporation waves, Journal of Computational Physics, vol.259, pp.331-357, 2014.
DOI : 10.1016/j.jcp.2013.12.003

URL : https://hal.archives-ouvertes.fr/hal-01135994

V. H. Ransom and D. L. 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

R. Saurel and R. Abgrall, A Multiphase Godunov Method for Compressible Multifluid and Multiphase Flows, Journal of Computational Physics, vol.150, issue.2, pp.425-467, 1999.
DOI : 10.1006/jcph.1999.6187

D. W. Schwendeman, C. W. Wahle, and A. K. Kapila, The Riemann problem and a high-resolution Godunov method for a model of compressible two-phase flow, Journal of Computational Physics, vol.212, issue.2, pp.490-526, 2006.
DOI : 10.1016/j.jcp.2005.07.012

A. R. Simpson, Large water hammer pressures due to column separation in sloping pipes, 1986.

S. Tokareva and E. Toro, HLLC-type Riemann solver for the Baer???Nunziato equations of compressible two-phase flow, Journal of Computational Physics, vol.229, issue.10, pp.3573-3604, 2010.
DOI : 10.1016/j.jcp.2010.01.016

A. Ambroso, C. Chalons, F. Coquel, and T. Galié, Relaxation and numerical approximation of a two-fluid two-pressure diphasic model, ESAIM: Mathematical Modelling and Numerical Analysis, vol.43, issue.6, pp.431063-1097, 2009.
DOI : 10.1051/m2an/2009038

A. Ambroso, C. Chalons, and P. 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. Andrianov and G. Warnecke, The Riemann problem for the Baer???Nunziato two-phase flow model, Journal of Computational Physics, vol.195, issue.2, pp.434-464, 2004.
DOI : 10.1016/j.jcp.2003.10.006

M. Baer and J. Nunziato, A two-phase mixture theory for the deflagration-to-detonation transition (ddt) in reactive granular materials, International Journal of Multiphase Flow, vol.12, issue.6, pp.861-889, 1986.
DOI : 10.1016/0301-9322(86)90033-9

P. Batten, N. Clarke, C. Lambert, and D. Causon, On the Choice of Wavespeeds for the HLLC Riemann Solver, SIAM Journal on Scientific Computing, vol.18, issue.6, pp.1553-1570, 1997.
DOI : 10.1137/S1064827593260140

A. Chinnayya, E. Daniel, and R. Saurel, Modelling detonation waves in heterogeneous energetic materials, Journal of Computational Physics, vol.196, issue.2, pp.490-538, 2004.
DOI : 10.1016/j.jcp.2003.11.015

F. Coquel, T. Gallouët, J. Hérard, and N. Seguin, Closure laws for a two-fluid two-pressure model, Comptes Rendus Mathematique, vol.334, issue.10, pp.927-932, 2002.
DOI : 10.1016/S1631-073X(02)02366-X

URL : https://hal.archives-ouvertes.fr/hal-01484345

F. Coquel, J. Hérard, K. Saleh, and N. Seguin, A robust entropy???satisfying finite volume scheme for the isentropic Baer???Nunziato model, ESAIM: Mathematical Modelling and Numerical Analysis, vol.48, issue.1, pp.165-206, 2014.
DOI : 10.1051/m2an/2013101

URL : https://hal.archives-ouvertes.fr/hal-00795568

F. Coquel, J. Hérard, K. Saleh, and N. Seguin, A Positive and Entropy-Satisfying Finite Volume Scheme for the Baer-Nunziato Model, 2016

F. Crouzet, F. Daude, P. Galon, J. Hérard, O. Hurisse et al., Validation of a two-fluid model on unsteady liquid???vapor water flows, Computers & Fluids, vol.119, pp.131-142, 2015.
DOI : 10.1016/j.compfluid.2015.06.035

G. Dal-maso, P. G. Lefloch, and F. Murat, Definition and weak stability of nonconservative products, Journal de mathématiques pures et appliquées, vol.74, issue.6, pp.483-548, 1995.

S. Dallet, A comparative study of numerical schemes for the Baer-Nunziato model. submitted to International Journal On Finite Volumes, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01412148

F. Daude and P. Galon, On the computation of the Baer???Nunziato model using ALE formulation with HLL- and HLLC-type solvers towards fluid???structure interactions, Journal of Computational Physics, vol.304, pp.189-230, 2016.
DOI : 10.1016/j.jcp.2015.09.056

URL : https://hal.archives-ouvertes.fr/hal-01416109

V. Deledicque and M. V. Papalexandris, An exact Riemann solver for compressible two-phase flow models containing non-conservative products, Journal of Computational Physics, vol.222, issue.1, pp.217-245, 2007.
DOI : 10.1016/j.jcp.2006.07.025

D. A. Drew and S. L. Passman, Theory of Multicomponent Fluids, 1999.
DOI : 10.1007/b97678

M. Dumbser and E. F. 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, 2010.
DOI : 10.1007/s10915-010-9400-3

P. Embid and M. Baer, Mathematical analysis of a two-phase continuum mixture theory, Continuum Mechanics and Thermodynamics, vol.10, issue.4, pp.279-312, 1992.
DOI : 10.1007/BF01129333

D. Furfaro and R. Saurel, A simple HLLC-type Riemann solver for compressible non-equilibrium two-phase flows, Computers & Fluids, vol.111, pp.159-178, 2015.
DOI : 10.1016/j.compfluid.2015.01.016

URL : https://hal.archives-ouvertes.fr/hal-01278892

T. Gallouët, J. Hérard, and N. Seguin, NUMERICAL MODELING OF TWO-PHASE FLOWS USING THE TWO-FLUID TWO-PRESSURE APPROACH, Mathematical Models and Methods in Applied Sciences, vol.14, issue.05, pp.663-700, 2004.
DOI : 10.1142/S0218202504003404

S. Gavrilyuk and R. Saurel, Mathematical and Numerical Modeling of Two-Phase Compressible Flows with Micro-Inertia, Journal of Computational Physics, vol.175, issue.1, pp.326-360, 2002.
DOI : 10.1006/jcph.2001.6951

J. Glimm, D. Saltz, and D. H. Sharp, Renormalization group solution of two-phase flow equations for Rayleigh-Taylor mixing, Physics Letters A, vol.222, issue.3, pp.171-176, 1996.
DOI : 10.1016/0375-9601(96)00648-2

J. W. Grove and R. Menikoff, Anomalous reflection of a shock wave at a fluid interface, Journal of Fluid Mechanics, vol.10, issue.-1, pp.313-336, 1990.
DOI : 10.1063/1.1761113

V. Guillemaud, Modélisation et simulation numérique desécoulementsdesécoulements diphasiques par une approche bifluidè a deux pressions URL https, 2007.

J. Haas and B. Sturtevant, Interaction of weak shock waves with cylindrical and spherical gas inhomogeneities, Journal of Fluid Mechanics, vol.201, issue.-1, pp.41-76, 1987.
DOI : 10.1121/1.387106

A. Harten, P. 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

J. Hérard, A three-phase flow model, Mathematical and Computer Modelling, vol.45, issue.5-6, pp.732-755, 2007.
DOI : 10.1016/j.mcm.2006.07.018

J. Hérard and O. Hurisse, A fractional step method to compute a class of compressible gas???liquid flows, Computers & Fluids, vol.55, pp.57-69, 2012.
DOI : 10.1016/j.compfluid.2011.11.001

M. Ishii, Thermo-fluid dynamic theory of two-phase flows, 1975.

H. Jin, J. Glimm, and D. H. Sharp, Entropy of averaging for compressible two-pressure two-phase flow models, Physics Letters A, vol.360, issue.1, pp.114-121, 2006.
DOI : 10.1016/j.physleta.2006.07.064

S. Kokh and F. Lagoutì-ere, An anti-diffusive numerical scheme for the simulation of interfaces between compressible fluids by means of a five-equation model, Journal of Computational Physics, vol.229, issue.8, pp.2773-2809, 2010.
DOI : 10.1016/j.jcp.2009.12.003

J. J. Kreeft and B. Koren, A new formulation of Kapila???s five-equation model for compressible two-fluid flow, and its numerical treatment, Journal of Computational Physics, vol.229, issue.18, pp.6220-6242, 2010.
DOI : 10.1016/j.jcp.2010.04.025

S. Liang, W. Liu, and L. Yuan, Solving seven-equation model for compressible two-phase flow using multiple GPUs, Computers & Fluids, vol.99, pp.156-171, 2014.
DOI : 10.1016/j.compfluid.2014.04.021

T. G. Liu, B. C. Khoo, and K. S. Yeo, The simulation of compressible multi-medium flow, Computers & Fluids, vol.30, issue.3, pp.315-337, 2001.
DOI : 10.1016/S0045-7930(00)00021-9

H. Lochon, F. Daude, P. Galon, and J. Hérard, Comparison of two-fluid models on steam-water transients, ESAIM: Mathematical Modelling and Numerical Analysis, vol.50, issue.6, 2016.
DOI : 10.1051/m2an/2016001

URL : https://hal.archives-ouvertes.fr/hal-01286670

Z. Ma, D. Causon, L. Qian, H. Gu, C. Mingham et al., A GPU based compressible multiphase hydrocode for modelling violent hydrodynamic impact problems, Computers & Fluids, vol.120, pp.1-23, 2015.
DOI : 10.1016/j.compfluid.2015.07.010

S. Müller, M. Hantke, and P. Richter, Closure conditions for non-equilibrium multicomponent models, Continuum Mechanics and Thermodynamics, pp.1-33, 2015.

V. H. Ransom and D. L. 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

R. Saurel and R. Abgrall, A Multiphase Godunov Method for Compressible Multifluid and Multiphase Flows, Journal of Computational Physics, vol.150, issue.2, pp.425-467, 1999.
DOI : 10.1006/jcph.1999.6187

D. W. Schwendeman, C. W. Wahle, and A. K. Kapila, The Riemann problem and a high-resolution Godunov method for a model of compressible two-phase flow, Journal of Computational Physics, vol.212, issue.2, pp.490-526, 2006.
DOI : 10.1016/j.jcp.2005.07.012

S. Tokareva and E. Toro, HLLC-type Riemann solver for the Baer???Nunziato equations of compressible two-phase flow, Journal of Computational Physics, vol.229, issue.10, pp.3573-3604, 2010.
DOI : 10.1016/j.jcp.2010.01.016

E. F. Toro, M. Spruce, and W. Speares, Restoration of the contact surface in the HLL-Riemann solver, Shock Waves, vol.54, issue.1, pp.25-34, 1994.
DOI : 10.1007/BF01414629

W. Xie, T. Liu, and B. Khoo, Application of a one-fluid model for large scale homogeneous unsteady cavitation: The modified Schmidt model, Computers & Fluids, vol.35, issue.10, pp.1177-1192, 2006.
DOI : 10.1016/j.compfluid.2005.05.006

M. Baer and J. Nunziato, A two-phase mixture theory for the deflagration-to-detonation transition (ddt) in reactive granular materials, International Journal of Multiphase Flow, vol.12, issue.6, pp.861-889, 1986.
DOI : 10.1016/0301-9322(86)90033-9

Z. Bilicki and J. Kestin, Physical Aspects of the Relaxation Model in Two-Phase Flow, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.428, issue.1875, pp.428379-397, 1875.
DOI : 10.1098/rspa.1990.0040

Z. Bilicki, R. Kwidzi´nskikwidzi´nski, and S. A. Mohammadein, Evaluation of the relaxation time of heat and mass exchange in the liquid-vapour bubble flow, International Journal of Heat and Mass Transfer, vol.39, issue.4, pp.753-759, 1996.
DOI : 10.1016/0017-9310(95)00169-7

F. Coquel, T. Gallouët, J. Hérard, and N. Seguin, Closure laws for a two-fluid two-pressure model, Comptes Rendus Mathematique, vol.334, issue.10, pp.927-932, 2002.
DOI : 10.1016/S1631-073X(02)02366-X

URL : https://hal.archives-ouvertes.fr/hal-01484345

F. Crouzet, F. Daude, P. Galon, J. Hérard, O. Hurisse et al., Validation of a two-fluid model on unsteady liquid???vapor water flows, Computers & Fluids, vol.119, pp.131-142, 2015.
DOI : 10.1016/j.compfluid.2015.06.035

F. Daude, P. Galon, Z. Gao, and E. Blaud, Numerical experiments using a HLLC-type scheme with ALE formulation for compressible two-phase flows five-equation models with phase transition, Computers & Fluids, vol.94, pp.112-138, 2014.
DOI : 10.1016/j.compfluid.2014.02.008

P. Downar-zapolski, Z. Bilicki, L. Bolle, and J. Franco, The non-equilibrium relaxation model for one-dimensional flashing liquid flow, International Journal of Multiphase Flow, vol.22, issue.3, pp.473-483, 1996.
DOI : 10.1016/0301-9322(95)00078-X

A. R. Edwards and T. P. O-'brien, Studies of phenomena connected with the depressurization of water reactors, Journal of the British Nuclear Energy Society, vol.9, pp.125-135, 1970.

E. Faucher, J. Hérard, M. Barret, and C. Toulemonde, Computation of Flashing Flows In Variable Cross-Section Ducts, International Journal of Computational Fluid Dynamics, vol.47, issue.4, pp.365-391, 2000.
DOI : 10.1016/0301-9322(93)90071-2

J. Gale, I. Tiselj, and A. Horvat, TWO-FLUID MODEL OF THE WAHA CODE FOR SIMULATIONS OF WATER HAMMER TRANSIENTS, Multiphase Science and Technology, vol.20, issue.3-4, pp.3-4291, 2008.
DOI : 10.1615/MultScienTechn.v20.i3-4.40

T. Gallouët, J. Hérard, and N. Seguin, NUMERICAL MODELING OF TWO-PHASE FLOWS USING THE TWO-FLUID TWO-PRESSURE APPROACH, Mathematical Models and Methods in Applied Sciences, vol.14, issue.05, pp.663-700, 2004.
DOI : 10.1142/S0218202504003404

S. Gavrilyuk and R. Saurel, Mathematical and Numerical Modeling of Two-Phase Compressible Flows with Micro-Inertia, Journal of Computational Physics, vol.175, issue.1, pp.326-360, 2002.
DOI : 10.1006/jcph.2001.6951

J. Glimm, D. Saltz, and D. H. Sharp, Renormalization group solution of two-phase flow equations for Rayleigh-Taylor mixing, Physics Letters A, vol.222, issue.3, pp.171-176, 1996.
DOI : 10.1016/0375-9601(96)00648-2

J. Glimm, D. Saltz, and D. H. Sharp, Two-phase modelling of a fluid mixing layer, Journal of Fluid Mechanics, vol.378, pp.119-143, 1999.
DOI : 10.1017/S0022112098003127

J. Hérard and O. Hurisse, A fractional step method to compute a class of compressible gas???liquid flows, Computers & Fluids, vol.55, pp.57-69, 2012.
DOI : 10.1016/j.compfluid.2011.11.001

A. K. Kapila, S. F. Son, J. B. Bdzil, R. Menikoff, and D. S. Stewart, Two-phase modeling of DDT: Structure of the velocity-relaxation zone, Physics of Fluids, vol.9, issue.12, pp.3885-3897, 1997.
DOI : 10.1063/1.869488

H. Lochon, Modélisation d'´ ecoulements diphasiques : fermetures entropiques de modèles bifluides. Internal report H-T63, 2014.

H. Lochon, F. Daude, P. Galon, and J. Hérard, Comparison of two-fluid models on steam-water transients, ESAIM: Mathematical Modelling and Numerical Analysis, vol.50, issue.6, 2016.
DOI : 10.1051/m2an/2016001

URL : https://hal.archives-ouvertes.fr/hal-01286670

H. Lochon, F. Daude, P. Galon, and J. Hérard, HLLC-type Riemann solver with approximated two-phase contact for the computation of the Baer???Nunziato two-fluid model, Journal of Computational Physics, vol.326, 2016.
DOI : 10.1016/j.jcp.2016.09.015

URL : https://hal.archives-ouvertes.fr/hal-01367268

V. H. Ransom and D. L. 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

M. Reocreux, ContributionàContribution`Contributionà l'´ etude des débits critiques enécoulementenécoulement diphasique eauvapeur, 1974.

R. Saurel and R. Abgrall, A Multiphase Godunov Method for Compressible Multifluid and Multiphase Flows, Journal of Computational Physics, vol.150, issue.2, pp.425-467, 1999.
DOI : 10.1006/jcph.1999.6187

]. B. Audebert, ContributionàContributionà l'analyse des modèles aux tensions de Reynolds pour l'interaction choc turbulence, 2006.

M. Baer and J. Nunziato, A two-phase mixture theory for the deflagration-to-detonation transition (ddt) in reactive granular materials, International Journal of Multiphase Flow, vol.12, issue.6, pp.861-889, 1986.
DOI : 10.1016/0301-9322(86)90033-9

J. B. Bdzil, R. Menikoff, S. F. Son, A. K. Kapila, and D. S. Stewart, Two-phase modeling of deflagration-to-detonation transition in granular materials: A critical examination of modeling issues, Physics of Fluids, vol.11, issue.2, pp.378-402, 1999.
DOI : 10.1063/1.869887

R. Berry, L. Zou, H. Zhao, D. Andrs, J. Peterson et al., Relap-7 : Demonstrating Seven-Equation, Two-Phase Flow Simulation in a Single-Pipe, Two-Phase Reactor Core and Steam Separator/Dryer

R. A. Berry, R. Saurel, and O. Lemetayer, The discrete equation method (DEM) for fully compressible, two-phase flows in ducts of spatially varying cross-section, Nuclear Engineering and Design, vol.240, issue.11, pp.3797-3818, 2010.
DOI : 10.1016/j.nucengdes.2010.08.003

C. Berthon, ContributionàContributionà l'analyse numérique deséquationsdeséquations de Navier-Stokes compressiblesàpressibles`pressiblesà deux entropies spécifiques ApplicationsàApplicationsà la turbulence compressible, 1999.

F. Coquel, T. Gallouët, J. Hérard, and N. Seguin, Closure laws for a two-fluid two-pressure model, Comptes Rendus Mathematique, vol.334, issue.10, pp.927-932, 2002.
DOI : 10.1016/S1631-073X(02)02366-X

URL : https://hal.archives-ouvertes.fr/hal-01484345

D. A. Drew and S. L. Passman, Theory of Multicomponent Fluids, 1999.
DOI : 10.1007/b97678

A. Forestier, J. Hérard, and X. Louis, Solveur de type Godunov pour simuler lesécoulements lesécoulements turbulents compressibles, Comptes Rendus de l'Académie des Sciences - Series I -Mathematics, pp.919-926, 1997.

T. Gallouët, J. Hérard, and N. Seguin, NUMERICAL MODELING OF TWO-PHASE FLOWS USING THE TWO-FLUID TWO-PRESSURE APPROACH, Mathematical Models and Methods in Applied Sciences, vol.14, issue.05, pp.663-700, 2004.
DOI : 10.1142/S0218202504003404

S. Gavrilyuk, The structure of pressure relaxation terms : one-velocity case, 2014.

S. Gavrilyuk and H. Gouin, Geometric evolution of the Reynolds stress tensor, International Journal of Engineering Science, vol.59, pp.65-73, 2012.
DOI : 10.1016/j.ijengsci.2012.03.008

URL : https://hal.archives-ouvertes.fr/hal-00371444

S. Gavrilyuk and R. Saurel, Mathematical and Numerical Modeling of Two-Phase Compressible Flows with Micro-Inertia, Journal of Computational Physics, vol.175, issue.1, pp.326-360, 2002.
DOI : 10.1006/jcph.2001.6951

J. Glimm, D. Saltz, and D. H. Sharp, Renormalization group solution of two-phase flow equations for Rayleigh-Taylor mixing, Physics Letters A, vol.222, issue.3, pp.171-176, 1996.
DOI : 10.1016/0375-9601(96)00648-2

V. Guillemaud, Modélisation et simulation numérique desécoulementsdesécoulements diphasiques par une approche bifluidè a deux pressions URL https, 2007.

J. Hérard, Numerical Modelling of Turbulent Two Phase Flows Using the Two Fluid Approach, 16th AIAA Computational Fluid Dynamics Conference, pp.2003-4113, 2003.
DOI : 10.2514/6.2003-4113

J. Hérard, Probì eme de Riemann pour un modèle simple de turbulence monophasique compressible. Internal report CR-I81, 2014.

J. Hérard, A class of compressible multiphase flow models, Comptes Rendus Mathematique, vol.354, issue.9, pp.954-959, 2016.
DOI : 10.1016/j.crma.2016.07.004

J. Hérard and Y. Liu, Une approche bifluide statistique de modelisation desécoulements desécoulements diphasiquesàdiphasiquesà phases compressibles. Internal report H-I81, 1162.

M. Ishii, Thermo-fluid dynamic theory of two-phase flows, 1975.

H. Jin, J. Glimm, and D. H. Sharp, Compressible two-pressure two-phase flow models, Physics Letters A, vol.353, issue.6, pp.469-474, 2006.
DOI : 10.1016/j.physleta.2005.11.087

A. K. Kapila, S. F. Son, J. B. Bdzil, R. Menikoff, and D. S. Stewart, Two-phase modeling of DDT: Structure of the velocity-relaxation zone, Physics of Fluids, vol.9, issue.12, pp.3885-3897, 1997.
DOI : 10.1063/1.869488

S. Müller, M. Hantke, and P. Richter, Closure conditions for non-equilibrium multicomponent models, Continuum Mechanics and Thermodynamics, pp.1-33, 2015.

V. H. Ransom and D. L. 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

R. Saurel and R. Abgrall, A Multiphase Godunov Method for Compressible Multifluid and Multiphase Flows, Journal of Computational Physics, vol.150, issue.2, pp.425-467, 1999.
DOI : 10.1006/jcph.1999.6187

R. Saurel, S. Gavrilyuk, and F. Renaud, A multiphase model with internal degrees of freedom: application to shock???bubble interaction, Journal of Fluid Mechanics, vol.495, pp.283-321, 2003.
DOI : 10.1017/S002211200300630X

J. Smoller, Shock waves and reaction diffusion equations, 1983.

P. Spalart and S. Allmaras, A one-equation turbulence model for aerodynamic flows In 30th Aerospace Sciences Meeting and Exhibit, 1992.

M. Baer and J. Nunziato, A two-phase mixture theory for the deflagration-to-detonation transition (ddt) in reactive granular materials, International Journal of Multiphase Flow, vol.12, issue.6, pp.861-889, 1986.
DOI : 10.1016/0301-9322(86)90033-9

D. A. Drew and S. L. Passman, Theory of Multicomponent Fluids, 1999.
DOI : 10.1007/b97678

A. K. Kapila, R. Menikoff, J. B. Bdzil, S. F. Son, and D. S. Stewart, Two-phase modeling of deflagration-to-detonation transition in granular materials: Reduced equations, Physics of Fluids, vol.13, issue.10, pp.3002-3024, 2001.
DOI : 10.1063/1.1398042

H. Lochon, Modélisation d'´ ecoulements diphasiques : fermetures entropiques de modèles bifluides. Internal report H-T63, 2014.

R. Saurel, F. Petitpas, and R. Abgrall, Modelling phase transition in metastable liquids: application to cavitating and flashing flows, Journal of Fluid Mechanics, vol.15, pp.313-350, 2008.
DOI : 10.1017/S0022112087003227

URL : https://hal.archives-ouvertes.fr/inria-00333908

A. B. Wood, A testbook of sound, 1930.

B. Générale, RELAP5-3D Code Manual Volume IV : Models and Correlations, p.2012

E. User, Commissariatàsariatà l'´ energie atomique et auxénergiesauxénergies alternatives (CEA), 2016, Joint Research Centre (JRC)

G. Allaire, S. Clerc, and S. Kokh, A Five-Equation Model for the Simulation of Interfaces between Compressible Fluids, Journal of Computational Physics, vol.181, issue.2, pp.577-616, 2002.
DOI : 10.1006/jcph.2002.7143

A. Ambroso, C. Chalons, F. Coquel, and T. Galié, Relaxation and numerical approximation of a two-fluid two-pressure diphasic model, ESAIM: Mathematical Modelling and Numerical Analysis, vol.43, issue.6, pp.431063-1097, 2009.
DOI : 10.1051/m2an/2009038

A. Ambroso, C. Chalons, and P. 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. Andrianov and G. Warnecke, The Riemann problem for the Baer???Nunziato two-phase flow model, Journal of Computational Physics, vol.195, issue.2, pp.434-464, 2004.
DOI : 10.1016/j.jcp.2003.10.006

B. Audebert, ContributionàContributionà l'analyse des modèles aux tensions de Reynolds pour l'interaction choc turbulence, 2006.

M. Baer and J. Nunziato, A two-phase mixture theory for the deflagration-to-detonation transition (ddt) in reactive granular materials, International Journal of Multiphase Flow, vol.12, issue.6, pp.861-889, 1986.
DOI : 10.1016/0301-9322(86)90033-9

T. Barberon and P. Helluy, Finite volume simulation of cavitating flows, Computers & Fluids, vol.34, issue.7, pp.832-858, 2005.
DOI : 10.1016/j.compfluid.2004.06.004

URL : https://hal.archives-ouvertes.fr/inria-00071762

F. Barre and M. Bernard, The CATHARE code strategy and assessment, Nuclear Engineering and Design, vol.124, issue.3, pp.257-284, 1990.
DOI : 10.1016/0029-5493(90)90296-A

P. Batten, N. Clarke, C. Lambert, and D. Causon, On the Choice of Wavespeeds for the HLLC Riemann Solver, SIAM Journal on Scientific Computing, vol.18, issue.6, pp.1553-1570, 1997.
DOI : 10.1137/S1064827593260140

J. B. Bdzil, R. Menikoff, S. F. Son, A. K. Kapila, and D. S. Stewart, Two-phase modeling of deflagration-to-detonation transition in granular materials: A critical examination of modeling issues, Physics of Fluids, vol.11, issue.2, pp.378-402, 1999.
DOI : 10.1063/1.869887

R. Berry, L. Zou, H. Zhao, D. Andrs, J. Peterson et al., Relap- 7 : Demonstrating Seven-Equation, Two-Phase Flow Simulation in a Single-Pipe, Two- Phase Reactor Core and Steam Separator/Dryer

R. A. Berry, R. Saurel, and O. Lemetayer, The discrete equation method (DEM) for fully compressible, two-phase flows in ducts of spatially varying cross-section, Nuclear Engineering and Design, vol.240, issue.11, pp.3797-3818, 2010.
DOI : 10.1016/j.nucengdes.2010.08.003

C. Berthon, ContributionàContributionà l'analyse numérique deséquationsdeséquations de Navier-Stokes compressiblesàpressiblesà deux entropies spécifiques ApplicationsàApplicationsà la turbulence compressible, 1999.

Z. Bilicki and J. Kestin, Physical Aspects of the Relaxation Model in Two-Phase Flow, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.428, issue.1875, pp.428379-397, 1875.
DOI : 10.1098/rspa.1990.0040

Z. Bilicki, R. Kwidzi´nskikwidzi´nski, and S. A. Mohammadein, Evaluation of the relaxation time of heat and mass exchange in the liquid-vapour bubble flow, International Journal of Heat and Mass Transfer, vol.39, issue.4, pp.753-759, 1996.
DOI : 10.1016/0017-9310(95)00169-7

A. Chinnayya, E. Daniel, and R. Saurel, Modelling detonation waves in heterogeneous energetic materials, Journal of Computational Physics, vol.196, issue.2, pp.490-538, 2004.
DOI : 10.1016/j.jcp.2003.11.015

S. Clerc, Numerical Simulation of the Homogeneous Equilibrium Model for Two-Phase Flows, Journal of Computational Physics, vol.161, issue.1, pp.354-375, 2000.
DOI : 10.1006/jcph.2000.6515

F. Coquel, T. Gallouët, J. Hérard, and N. Seguin, Closure laws for a two-fluid two-pressure model, Comptes Rendus Mathematique, vol.334, issue.10, pp.927-932, 2002.
DOI : 10.1016/S1631-073X(02)02366-X

URL : https://hal.archives-ouvertes.fr/hal-01484345

F. Coquel, J. Hérard, K. Saleh, and N. Seguin, A robust entropy???satisfying finite volume scheme for the isentropic Baer???Nunziato model, ESAIM: Mathematical Modelling and Numerical Analysis, vol.48, issue.1, pp.165-206, 2014.
DOI : 10.1051/m2an/2013101

URL : https://hal.archives-ouvertes.fr/hal-00795568

F. Coquel, J. Hérard, K. Saleh, and N. Seguin, A Positive and Entropy-Satisfying Finite Volume Scheme for the Baer-Nunziato Model, 2016

F. Crouzet, F. Daude, P. Galon, J. Hérard, O. Hurisse et al., Validation of a two-fluid model on unsteady liquid???vapor water flows, Computers & Fluids, vol.119, pp.131-142, 2015.
DOI : 10.1016/j.compfluid.2015.06.035

G. Dal-maso, P. G. Lefloch, and F. Murat, Definition and weak stability of nonconservative products, Journal de mathématiques pures et appliquées, vol.74, issue.6, pp.483-548, 1995.

S. Dallet, A comparative study of numerical schemes for the Baer-Nunziato model. submitted to International Journal On Finite Volumes, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01412148

F. Daude and P. Galon, Développement d'un modèle diphasiquè a deux pressions dans Europlexus et vérifications numériques -Partie convective. Internal report H-T63, 1003.

F. Daude and P. Galon, On the computation of the Baer???Nunziato model using ALE formulation with HLL- and HLLC-type solvers towards fluid???structure interactions, Journal of Computational Physics, vol.304, pp.189-230, 2016.
DOI : 10.1016/j.jcp.2015.09.056

URL : https://hal.archives-ouvertes.fr/hal-01416109

F. Daude, P. Galon, Z. Gao, and E. Blaud, Numerical experiments using a HLLC-type scheme with ALE formulation for compressible two-phase flows five-equation models with phase transition, Computers & Fluids, vol.94, pp.112-138, 2014.
DOI : 10.1016/j.compfluid.2014.02.008

V. Deledicque and M. V. Papalexandris, An exact Riemann solver for compressible two-phase flow models containing non-conservative products, Journal of Computational Physics, vol.222, issue.1, pp.217-245, 2007.
DOI : 10.1016/j.jcp.2006.07.025

P. Downar-zapolski, Z. Bilicki, L. Bolle, and J. Franco, The non-equilibrium relaxation model for one-dimensional flashing liquid flow, International Journal of Multiphase Flow, vol.22, issue.3, pp.473-483, 1996.
DOI : 10.1016/0301-9322(95)00078-X

D. A. Drew and S. L. Passman, Theory of Multicomponent Fluids, 1999.
DOI : 10.1007/b97678

M. Dumbser and E. F. 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, 2010.
DOI : 10.1007/s10915-010-9400-3

A. R. Edwards and T. P. O-'brien, Studies of phenomena connected with the depressurization of water reactors, Journal of the British Nuclear Energy Society, vol.9, pp.125-135, 1970.

P. Embid and M. Baer, Mathematical analysis of a two-phase continuum mixture theory, Continuum Mechanics and Thermodynamics, vol.10, issue.4, pp.279-312, 1992.
DOI : 10.1007/BF01129333

G. Faccanoni, Study of a Fine Model of Liquid-Vapor Phase Change.Contribution to the Boiling Crisis Study, Thèse en cotutelle entre l' ´ Ecole Polytechnique et l'Università di Trento (Italie), 2008.
URL : https://hal.archives-ouvertes.fr/tel-00363460

E. Faucher, J. Hérard, M. Barret, and C. Toulemonde, Computation of Flashing Flows In Variable Cross-Section Ducts, International Journal of Computational Fluid Dynamics, vol.47, issue.4, pp.365-391, 2000.
DOI : 10.1016/0301-9322(93)90071-2

A. Favre, Equations des gaz turbulents compressibles. Méthodes des vitesses moyennes, méthode des vitesses macroscopiques pondérées par la masse volumique, Journal de mecanique, vol.4, issue.4, p.391, 1965.

T. Flåtten and H. Lund, RELAXATION TWO-PHASE FLOW MODELS AND THE SUBCHARACTERISTIC CONDITION, Mathematical Models and Methods in Applied Sciences, vol.21, issue.12, pp.2379-2407, 2011.
DOI : 10.1142/S0218202511005775

A. Forestier, J. Hérard, and X. Louis, Solveur de type Godunov pour simuler lesécoulements lesécoulements turbulents compressibles, Comptes Rendus de l'Académie des Sciences - Series I -Mathematics, pp.919-926, 1997.

D. Furfaro and R. Saurel, A simple HLLC-type Riemann solver for compressible non-equilibrium two-phase flows, Computers & Fluids, vol.111, pp.159-178, 2015.
DOI : 10.1016/j.compfluid.2015.01.016

URL : https://hal.archives-ouvertes.fr/hal-01278892

J. Gale, I. Tiselj, and A. Horvat, TWO-FLUID MODEL OF THE WAHA CODE FOR SIMULATIONS OF WATER HAMMER TRANSIENTS, Multiphase Science and Technology, vol.20, issue.3-4, pp.3-4291, 2008.
DOI : 10.1615/MultScienTechn.v20.i3-4.40

T. Gallouët, P. Helluy, J. Hérard, and J. Nussbaum, Hyperbolic relaxation models for granular flows, ESAIM: Mathematical Modelling and Numerical Analysis, vol.44, issue.2, pp.371-400, 2010.
DOI : 10.1051/m2an/2010006

T. Gallouët, J. Hérard, and N. Seguin, NUMERICAL MODELING OF TWO-PHASE FLOWS USING THE TWO-FLUID TWO-PRESSURE APPROACH, Mathematical Models and Methods in Applied Sciences, vol.14, issue.05, pp.663-700, 2004.
DOI : 10.1142/S0218202504003404

S. Gavrilyuk, The structure of pressure relaxation terms : one-velocity case, 2014.

S. Gavrilyuk and H. Gouin, Geometric evolution of the Reynolds stress tensor, International Journal of Engineering Science, vol.59, pp.65-73, 2012.
DOI : 10.1016/j.ijengsci.2012.03.008

URL : https://hal.archives-ouvertes.fr/hal-00371444

S. Gavrilyuk and R. Saurel, Mathematical and Numerical Modeling of Two-Phase Compressible Flows with Micro-Inertia, Journal of Computational Physics, vol.175, issue.1, pp.326-360, 2002.
DOI : 10.1006/jcph.2001.6951

J. Glimm, D. Saltz, and D. H. Sharp, Renormalization group solution of two-phase flow equations for Rayleigh-Taylor mixing, Physics Letters A, vol.222, issue.3, pp.171-176, 1996.
DOI : 10.1016/0375-9601(96)00648-2

J. Glimm, D. Saltz, and D. H. Sharp, Two-phase modelling of a fluid mixing layer, Journal of Fluid Mechanics, vol.378, pp.119-143, 1999.
DOI : 10.1017/S0022112098003127

J. W. Grove and R. Menikoff, Anomalous reflection of a shock wave at a fluid interface, Journal of Fluid Mechanics, vol.10, issue.-1, pp.313-336, 1990.
DOI : 10.1063/1.1761113

A. Guelfi, D. Bestion, M. Boucker, P. Boudier, P. Fillion et al., NEPTUNE: A New Software Platform for Advanced Nuclear Thermal Hydraulics, Nuclear Science and Engineering, vol.156, issue.3, pp.281-324, 2007.
DOI : 10.13182/NSE05-98

V. Guillemaud, Modélisation et simulation numérique desécoulementsdesécoulements diphasiques par une approche bifluidè a deux pressions URL https, 2007.

J. Haas and B. Sturtevant, Interaction of weak shock waves with cylindrical and spherical gas inhomogeneities, Journal of Fluid Mechanics, vol.201, issue.-1, pp.41-76, 1987.
DOI : 10.1121/1.387106

A. Harten, P. 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

J. Hérard and O. Hurisse, A simple method to compute standard two-fluid models, International Journal of Computational Fluid Dynamics, vol.334, issue.7, pp.475-482, 2005.
DOI : 10.1006/jcph.1996.0060

J. Hérard, Numerical Modelling of Turbulent Two Phase Flows Using the Two Fluid Approach, 16th AIAA Computational Fluid Dynamics Conference, pp.2003-4113, 2003.
DOI : 10.2514/6.2003-4113

J. Hérard, A three-phase flow model, Mathematical and Computer Modelling, vol.45, issue.5-6, pp.732-755, 2007.
DOI : 10.1016/j.mcm.2006.07.018

J. Hérard, Une classe de modèles diphasiques bifluides avec changement de régime. Internal report H-I81, 2010.

J. Hérard, Probì eme de Riemann pour un modèle simple de turbulence monophasique compressible. Internal report CR-I81, 2014.

J. Hérard, A class of compressible multiphase flow models, Comptes Rendus Mathematique, vol.354, issue.9, pp.954-959, 2016.
DOI : 10.1016/j.crma.2016.07.004

J. Hérard and O. Hurisse, A fractional step method to compute a class of compressible gas???liquid flows, Computers & Fluids, vol.55, pp.57-69, 2012.
DOI : 10.1016/j.compfluid.2011.11.001

J. Hérard and Y. Liu, Une approche bifluide statistique de modelisation desécoulements desécoulements diphasiquesàdiphasiquesà phases compressibles. Internal report H-I81, 1162.

J. Hérard and H. Lochon, A simple turbulent two-phase flow model. in preparation, 2014.

M. Ishii, Thermo-fluid dynamic theory of two-phase flows, 1975.

S. Jaouen, Etude mathématique et numérique de stabilité pour des modeles hydrodynamiques avec transition de phase, 2001.

H. Jin, J. Glimm, and D. H. Sharp, Compressible two-pressure two-phase flow models, Physics Letters A, vol.353, issue.6, pp.469-474, 2006.
DOI : 10.1016/j.physleta.2005.11.087

H. Jin, J. Glimm, and D. H. Sharp, Entropy of averaging for compressible two-pressure two-phase flow models, Physics Letters A, vol.360, issue.1, pp.114-121, 2006.
DOI : 10.1016/j.physleta.2006.07.064

A. K. Kapila, R. Menikoff, J. B. Bdzil, S. F. Son, and D. S. Stewart, Two-phase modeling of deflagration-to-detonation transition in granular materials: Reduced equations, Physics of Fluids, vol.13, issue.10, pp.3002-3024, 2001.
DOI : 10.1063/1.1398042

A. K. Kapila, S. F. Son, J. B. Bdzil, R. Menikoff, and D. S. Stewart, Two-phase modeling of DDT: Structure of the velocity-relaxation zone, Physics of Fluids, vol.9, issue.12, pp.3885-3897, 1997.
DOI : 10.1063/1.869488

S. Kokh and F. Lagoutì-ere, An anti-diffusive numerical scheme for the simulation of interfaces between compressible fluids by means of a five-equation model, Journal of Computational Physics, vol.229, issue.8, pp.2773-2809, 2010.
DOI : 10.1016/j.jcp.2009.12.003

J. J. Kreeft and B. Koren, A new formulation of Kapila???s five-equation model for compressible two-fluid flow, and its numerical treatment, Journal of Computational Physics, vol.229, issue.18, pp.6220-6242, 2010.
DOI : 10.1016/j.jcp.2010.04.025

M. Labois, Modélisation des déséquilibres mécaniques pour lesécoulementslesécoulements diphasiques : approches par relaxation et par modèle réduit

I. Aix-marseille, URL https, 2008.

G. , L. Coq, S. Aubry, J. Cahouet, P. Lequesne et al., Le logiciel THYC. modélisation en volume finis desécoulementsdesécoulements tridimensionnels diphasiques dans les faisceaux de tubes. Bulletin de la Direction desétudesdesétudes et recherches-Electricité de France, pp.61-76, 1989.

O. , L. Métayer, J. Massoni, and R. Saurel, ´ Elaboration des lois d'´ etat d'un liquide et de sa vapeur pour les modèles d'´ ecoulements diphasiques, International Journal of Thermal Sciences, vol.43, issue.3, pp.265-276, 2004.

O. , L. Métayer, J. Massoni, and R. Saurel, Dynamic relaxation processes in compressible multiphase flows. Application to evaporation phenomena, ESAIM : Proceedings, pp.103-123, 2013.

D. Lhuillier, C. Chang, and T. G. Theofanous, On the quest for a hyperbolic effective-field model of disperse flows, Journal of Fluid Mechanics, vol.58, pp.184-194, 2013.
DOI : 10.1016/0301-9322(79)90013-2

S. Liang, W. Liu, and L. Yuan, Solving seven-equation model for compressible two-phase flow using multiple GPUs, Computers & Fluids, vol.99, pp.156-171, 2014.
DOI : 10.1016/j.compfluid.2014.04.021

T. G. Liu, B. C. Khoo, and K. S. Yeo, The simulation of compressible multi-medium flow, Computers & Fluids, vol.30, issue.3, pp.315-337, 2001.
DOI : 10.1016/S0045-7930(00)00021-9

Y. Liu, ContributionàContributionà la vérification etàetà la validation d'un modèle diphasique bifluide instationnaire

H. Lochon, Modélisation d'´ ecoulements diphasiques : fermetures entropiques de modèles bifluides. Internal report H-T63, 2014.

H. Lochon, F. Daude, P. Galon, and J. Hérard, Comparison of two-fluid models on steam-water transients, ESAIM: Mathematical Modelling and Numerical Analysis, vol.50, issue.6, 2016.
DOI : 10.1051/m2an/2016001

URL : https://hal.archives-ouvertes.fr/hal-01286670

H. Lochon, F. Daude, P. Galon, and J. Hérard, HLLC-type Riemann solver with approximated two-phase contact for the computation of the Baer???Nunziato two-fluid model, Journal of Computational Physics, vol.326, 2016.
DOI : 10.1016/j.jcp.2016.09.015

URL : https://hal.archives-ouvertes.fr/hal-01367268

H. Lund, A Hierarchy of Relaxation Models for Two-Phase Flow, SIAM Journal on Applied Mathematics, vol.72, issue.6, pp.1713-1741, 2012.
DOI : 10.1137/12086368X

Z. Ma, D. Causon, L. Qian, H. Gu, C. Mingham et al., A GPU based compressible multiphase hydrocode for modelling violent hydrodynamic impact problems, Computers & Fluids, vol.120, pp.1-23, 2015.
DOI : 10.1016/j.compfluid.2015.07.010

A. Murrone and H. Guillard, A five equation reduced model for compressible two phase flow problems, Journal of Computational Physics, vol.202, issue.2, pp.664-698, 2005.
DOI : 10.1016/j.jcp.2004.07.019

URL : https://hal.archives-ouvertes.fr/hal-00871724

S. Müller, M. Hantke, and P. Richter, Closure conditions for non-equilibrium multicomponent models, Continuum Mechanics and Thermodynamics, pp.1-33, 2015.

W. L. Oberkampf and T. G. Trucano, Verification and validation in computational fluid dynamics, Progress in Aerospace Sciences, pp.209-272, 2002.

W. L. Oberkampf and T. G. Trucano, Verification and validation benchmarks, Nuclear Engineering and Design, vol.238, issue.3, pp.716-743, 2008.
DOI : 10.1016/j.nucengdes.2007.02.032

M. Pelanti and K. Shyue, A mixture-energy-consistent six-equation two-phase numerical model for fluids with interfaces, cavitation and evaporation waves, Journal of Computational Physics, vol.259, pp.331-357, 2014.
DOI : 10.1016/j.jcp.2013.12.003

URL : https://hal.archives-ouvertes.fr/hal-01135994

V. H. Ransom and D. L. 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

M. Reocreux, ContributionàContributionà l'´ etude des débits critiques enécoulementenécoulement diphasique eauvapeur, 1974.

P. J. Roache, QUANTIFICATION OF UNCERTAINTY IN COMPUTATIONAL FLUID DYNAMICS, Annual Review of Fluid Mechanics, vol.29, issue.1, pp.123-160, 1997.
DOI : 10.1146/annurev.fluid.29.1.123

P. J. Roache, Code Verification by the Method of Manufactured Solutions, Journal of Fluids Engineering, vol.124, issue.1, pp.4-10, 2002.
DOI : 10.1115/1.1436090

P. J. Roache, K. N. Ghia, and F. M. White, Editorial Policy Statement on the Control of Numerical Accuracy, Journal of Fluids Engineering, vol.108, issue.1, pp.2-2, 1986.
DOI : 10.1115/1.3242537

K. Saleh, Analysis and Numerical Simulation of Compressible Two-Phase Flows Using Relaxation Methods. Contribution to the Treatment of Vanishing Phases
URL : https://hal.archives-ouvertes.fr/tel-00761099

R. Saurel and R. Abgrall, A Multiphase Godunov Method for Compressible Multifluid and Multiphase Flows, Journal of Computational Physics, vol.150, issue.2, pp.425-467, 1999.
DOI : 10.1006/jcph.1999.6187

R. Saurel, S. Gavrilyuk, and F. Renaud, A multiphase model with internal degrees of freedom: application to shock???bubble interaction, Journal of Fluid Mechanics, vol.495, pp.283-321, 2003.
DOI : 10.1017/S002211200300630X

R. Saurel, F. Petitpas, and R. Abgrall, Modelling phase transition in metastable liquids: application to cavitating and flashing flows, Journal of Fluid Mechanics, vol.15, pp.313-350, 2008.
DOI : 10.1017/S0022112087003227

URL : https://hal.archives-ouvertes.fr/inria-00333908

R. Saurel, F. Petitpas, and R. A. Berry, Simple and efficient relaxation methods for interfaces separating compressible fluids, cavitating flows and shocks in multiphase mixtures, Journal of Computational Physics, vol.228, issue.5, pp.1678-1712, 2009.
DOI : 10.1016/j.jcp.2008.11.002

D. W. Schwendeman, C. W. Wahle, and A. K. Kapila, The Riemann problem and a high-resolution Godunov method for a model of compressible two-phase flow, Journal of Computational Physics, vol.212, issue.2, pp.490-526, 2006.
DOI : 10.1016/j.jcp.2005.07.012

A. R. Simpson, Large water hammer pressures due to column separation in sloping pipes, 1986.

J. Smoller, Shock waves and reaction diffusion equations, 1983.

P. Spalart and S. Allmaras, A one-equation turbulence model for aerodynamic flows In 30th Aerospace Sciences Meeting and Exhibit, 1992.

H. B. Stewart and B. Wendroff, Two-phase flow: Models and methods, Journal of Computational Physics, vol.56, issue.3, pp.363-409, 1984.
DOI : 10.1016/0021-9991(84)90103-7

I. Tiselj and S. Petelin, Modelling of Two-Phase Flow with Second-Order Accurate Scheme, Journal of Computational Physics, vol.136, issue.2, pp.503-521, 1997.
DOI : 10.1006/jcph.1997.5778

S. Tokareva and E. Toro, HLLC-type Riemann solver for the Baer???Nunziato equations of compressible two-phase flow, Journal of Computational Physics, vol.229, issue.10, pp.3573-3604, 2010.
DOI : 10.1016/j.jcp.2010.01.016

E. F. Toro, M. Spruce, and W. Speares, Restoration of the contact surface in the HLL-Riemann solver, Shock Waves, vol.54, issue.1, pp.25-34, 1994.
DOI : 10.1007/BF01414629

I. Toumi, A. Bergeron, D. Gallo, E. Royer, and D. Caruge, 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, pp.139-155, 2000.
DOI : 10.1016/S0029-5493(99)00332-5

A. B. Wood, A testbook of sound, 1930.

W. Xie, T. Liu, and B. Khoo, Application of a one-fluid model for large scale homogeneous unsteady cavitation: The modified Schmidt model, Computers & Fluids, vol.35, issue.10, pp.1177-1192, 2006.
DOI : 10.1016/j.compfluid.2005.05.006