P. [. Amsden, T. D. O-'rourke, and . Butler, Kiva II, a computer program for chemical reactive flows with spray, 1989.

A. Astillero and A. Santos, A granular fluid modeled as a driven system of elastic hard spheres La fisica dei sistemi complessi. (Nuovi sviluppi e prospettive) Rendiconti della Scuola Internazionale di Fisica " Enrico Fermi Bologna: Società Italiana di Fisica, Proceedings of the International School of Physics " Enrico Fermi, pp.1-11, 2003.

C. Baranger, MODELLING OF OSCILLATIONS, BREAKUP AND COLLISIONS FOR DROPLETS: THE ESTABLISHMENT OF KERNELS FOR THE T.A.B. MODEL, Mathematical Models and Methods in Applied Sciences, vol.14, issue.05, pp.775-794, 2004.
DOI : 10.1142/S0218202504003441

A. V. Bobylev, J. A. Carrillo, and I. M. Gamba, On some properties of kinetic and hydrodynamic equations for inelastic interactions, J. Statist. Phys, vol.98, pp.3-4743, 2000.

P. L. Bhatnagar, E. P. Gross, and M. Krook, A Model for Collision Processes in Gases. I. Small Amplitude Processes in Charged and Neutral One-Component Systems, Physical Review, vol.94, issue.3, pp.511-525, 1954.
DOI : 10.1103/PhysRev.94.511

A. V. Bobylev, I. M. Gamba, and V. Panferov, Moment Inequalities and High-Energy Tails for Boltzmann Equations with Inelastic Interactions, Journal of Statistical Physics, vol.116, issue.5/6, pp.5-61651, 2004.
DOI : 10.1023/B:JOSS.0000041751.11664.ea

G. L. Caraffini, M. Groppi, and G. Spiga, On Bgk Approximation for Reactive and Nonreactive Flows, Transport Theory and Statistical Physics, vol.7, issue.4-6, pp.4-6475, 2007.
DOI : 10.1016/S0378-4371(99)00336-2

L. Desvillettes and J. Mathiaud, Some Aspects of the Asymptotics Leading from??Gas-Particles Equations Towards Multiphase Flows Equations, Journal of Statistical Physics, vol.34, issue.8, pp.120-141
DOI : 10.1007/s10955-010-0044-3

M. Groppi and W. Koller, Kinetic calculations for chemical reactions and inelastic transitions in a gas mixture, Zeitschrift für Angewandte Mathematik und Physik (ZAMP), pp.855-876, 2002.

I. M. Gamba, V. Panferov, and C. Villani, On the Boltzmann Equation for Diffusively Excited Granular Media, Communications in Mathematical Physics, vol.246, issue.3, pp.503-541, 2004.
DOI : 10.1007/s00220-004-1051-5

M. Groppi and G. Spiga, Kinetic approach to chemical reactions and inelastic transitions in a rarefied gas, Journal of Mathematical Chemistry, vol.26, issue.1/3, pp.197-2191019194113816, 1023.
DOI : 10.1023/A:1019194113816

. Jr, H. Lowell, and . Holway, New statistical models for kinetic theory: Methods of construction, Physics of Fluids, vol.9, issue.9, pp.1658-1673, 1966.

B. Lapeyre, E. Pardoux, and R. Sentis, Méthodes de Monte-Carlo pour leséquationsleséquations de transport et de diffusion, ) [Mathematics & Applications, 1998.

J. M. Montanero and A. Santos, Computer simulation of uniformly heated granular fluids, Granular Matter, vol.2, issue.2, pp.53-64, 1007.
DOI : 10.1007/s100350050035

J. Mathiaud, Etude de systèmes de type gaz-particules, 2006.

]. [. O-'rourkesan03 and . Santos, Collective drop effects on vaporizing liquid sprays Transport coefficients of d-dimensional inelastic maxwell models. Physica A: Statistical Mechanics and its Applications Appendix C. [Vil02] C. Villani. A review of mathematical topics in collisional kinetic theory Mathematics of granular materials, J. Statist. Phys, vol.321, issue.124 10, pp.3-4442, 1007.

F. A. Williams, Combustion Theory. The Fundamental Theory of Chemically Reacting Flow Systems, 1985.
URL : https://hal.archives-ouvertes.fr/hal-00014918

A. Ambroso, C. Chalons, F. Coquel, T. Galié, E. Godlewski et al., The drift-flux asymptotic limit of barotropic two-phase two-pressure models, Proceedings of the International School of Physics " Enrico Fermi Modelling of oscillations, breakup and collisions for droplets : the establishment of kernels for the T.A.B. model. Math. Models Methods Appl. SciBar04b] C. Baranger. Modélisation, étude mathématique et simulation des collisions dans les fluidescomplexes, pp.521-529, 1987.
DOI : 10.4310/CMS.2008.v6.n2.a13

M. Baudin, C. Berthon, F. Coquel, R. Masson, Q. H. Tran-[-bcg00-]-a et al., A relaxation method for two-phase flow models with hydrodynamic closure law, Numerische Mathematik, vol.48, issue.3, pp.411-4403, 2000.
DOI : 10.1007/s00211-004-0558-1

L. Boudin, L. Desvillettes, R. H. Motteben84-]-k, . J. Bendiksenben92-]-d, and . Benson, A modeling of compressible droplets in a fluid An experimental investigation of the motion of long bubbles in inclined tubes Computational methods in Lagrangian and Eulerian hydrocodes, Commun. Math. Sci. International Journal of Multiphase Flow Computer Methods in Applied Mechanics and Engineering, vol.1, issue.992-3, pp.657-669467, 1984.

D. Bestion, The physical closure laws in the CATHARE code, Nuclear Engineering and Design, vol.124, issue.3, pp.229-245, 1990.
DOI : 10.1016/0029-5493(90)90294-8

E. [. Bhatnagar, M. Gross, and . Krook, A Model for Collision Processes in Gases. I. Small Amplitude Processes in Charged and Neutral One-Component Systems, Physical Review, vol.94, issue.3, pp.511-525, 1954.
DOI : 10.1103/PhysRev.94.511

I. [. Bobylev, V. Gamba, and . Panferov, Moment Inequalities and High-Energy Tails for Boltzmann Equations with Inelastic Interactions, Journal of Statistical Physics, vol.116, issue.5/6, pp.5-61651, 2004.
DOI : 10.1023/B:JOSS.0000041751.11664.ea

]. G. Bir94 and . Bird, Molecular Gas Dynamics and the Direct Simulation of Gas Flows, Oxford Engineering Science Series, 1994.

D. [. Bendiksen, R. Maines, S. Moe, and . Nuland, The Dynamic Two-Fluid Model OLGA: Theory and Application, SPE Production Engineering, vol.6, issue.02, pp.171-180, 1991.
DOI : 10.2118/19451-PA

J. [. Baer and . 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

M. [. Caraffini, G. Groppi, and . Spiga, On Bgk Approximation for Reactive and Nonreactive Flows, Transport Theory and Statistical Physics, vol.7, issue.4-6, pp.4-6475, 2007.
DOI : 10.1016/S0378-4371(99)00336-2

]. S. Cle00 and . Clerc, Numerical simulation of the homogeneous equilibrium model for two-phase flows, J. Comput. Phys, vol.161, issue.1, pp.354-375, 2000.

A. E. Carver, D. S. Tahir, A. Rowe, S. Y. Tapucu, . [. Ahmad et al., Computational analysis of two-phase flow in horizontal bundles, Nuclear Engineering and Design, vol.82, issue.2-3, pp.215-226233, 1976.
DOI : 10.1016/0029-5493(84)90213-9

]. R. Deb74 and . Debar, Fundamentals of the Kraken code, 1974.

]. B. Des10 and . Després, Lois de conservations eulériennes, lagrangiennes et méthodes numériques, of Mathématiques & Applications (Berlin) [Mathematics & Applications, 2010.

R. [. Drew and . Lahey, Application of general constitutive principles to the derivation of multidimensional two-phase flow equations, International Journal of Multiphase Flow, vol.5, issue.4, pp.243-264, 1979.
DOI : 10.1016/0301-9322(79)90024-7

L. Desvillettes and J. Mathiaud, Some Aspects of the Asymptotics Leading from??Gas-Particles Equations Towards Multiphase Flows Equations, Journal of Statistical Physics, vol.34, issue.8, pp.120-141
DOI : 10.1007/s10955-010-0044-3

S. [. Drew and . Passman, Theory of multicomponent fluids, Applied Mathematical Sciences, vol.135, 1999.
DOI : 10.1007/b97678

]. J. Duk80 and . Dukowicz, A particle-fluid numerical model for liquid sprays, Journal of Computational Physics, vol.35, issue.2, pp.229-253, 1980.

]. N. Dum04 and . Dumont, Modélisation de l'écoulement diphasique dans les injecteurs diesel, 2004.

E. [. Enwald, A. E. Peirano, and . Almstedt, Eulerian two-phase flow theory applied to fluidization, International Journal of Multiphase Flow, vol.22, pp.21-66, 1996.
DOI : 10.1016/S0301-9322(96)90004-X

E. [. Faille and . Heintzé, A rough finite volume scheme for modeling two-phase flow in a pipeline, Computers & Fluids, vol.28, issue.2, pp.213-241, 1999.
DOI : 10.1016/S0045-7930(98)00023-1

R. [. França and . Lahey-jr, The use of drift-flux techniques for the analysis of horizontal two-phase flows, International Journal of Multiphase Flow, vol.18, issue.6, pp.787-801, 1992.
DOI : 10.1016/0301-9322(92)90059-P

K. [. Fjelde and . Karlsen, High-resolution hybrid primitive???conservative upwind schemes for the drift flux model, Computers & Fluids, vol.31, issue.3, pp.335-367, 2002.
DOI : 10.1016/S0045-7930(01)00041-X

]. T. Gal09 and . Galié, Couplage interfacial de modèles en dynamique des fluides. Application aux écoulements diphasiques, 2009.

F. [. Guillard and . Duval, A Darcy law for the drift velocity in a two-phase flow model, Journal of Computational Physics, vol.224, issue.1, pp.288-313, 2007.
DOI : 10.1016/j.jcp.2007.02.025

F. [. Guillard, J. C. Duval, R. Latche, and . Panescu, Numerical multiphase modeling of bubbly flows, ANNALI DELL'UNIVERSITA' DI FERRARA, vol.87, issue.4, pp.243-253, 2007.
DOI : 10.1007/s11565-007-0029-6

W. [. Groppi and . Koller, Kinetic calculations for chemical reactions and inelastic transitions in a gas mixture, Zeitschrift für Angewandte Mathematik und Physik (ZAMP), pp.855-876, 2002.

M. [. Grégoire and . Martin, Derivation of a well-posed and multidimensional drift-flux model for boiling flows, Comptes Rendus M??canique, vol.333, issue.6, pp.459-466, 2005.
DOI : 10.1016/j.crme.2005.05.002

O. [. Ghidaglia and . Poujade, Modélisation d'écoulements fluideparticules par des modèles Euler-Euler conservatifs, 2006.

I. M. Gamba, V. Panferov, and C. Villani, On the Boltzmann Equation for Diffusively Excited Granular Media, Communications in Mathematical Physics, vol.246, issue.3, pp.503-541, 2004.
DOI : 10.1007/s00220-004-1051-5

P. [. Godlewski, M. Raviart, G. Groppi, and . Spiga, Numerical approximation of hyperbolic systems of conservation laws Kinetic approach to chemical reactions and inelastic transitions in a rarefied gas Eno schemes with subcell resolution, Applied Mathematical Sciences Journal of Mathematical Chemistry J. Comput. Phys, vol.118, issue.831, pp.197-219148, 1989.

M. [. Hibiki, . Ishiihi03-]-t, M. Hibiki, . Ishiihjj09-]-o, S. Heuzé et al., Distribution parameter and drift velocity of drift-flux model in bubbly flow, Offshore Technology Conference, pp.707-7214935, 2002.
DOI : 10.1016/S0017-9310(01)00195-8

M. Ishii and K. Mishima, Two-fluid model and hydrodynamic constitutive relations, Nuclear Engineering and Design, vol.82, issue.2-3, pp.107-126, 1984.
DOI : 10.1016/0029-5493(84)90207-3

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

]. M. Ish77 and . Ishii, One-dimensional drift-flux model and constitutive equations for relative motion between phases in various two-phase flow regimes, 1977.

N. [. Ishii and . Zuber, Drag coefficient and relative velocity in bubbly, droplet or particulate flows, AIChE Journal, vol.25, issue.5, pp.843-855, 1979.
DOI : 10.1002/aic.690250513

J. [. Kreiss and . Lorenz, Initial-boundary value problems and the Navier-Stokes equations [Lag00] F. Lagoutière. Modélisation mathématique et résolution numérique de problèmes de fluides à plusieurs constituants, 1989.

R. T. Lahey, The prediction of phase distribution and separation phenomena using two-fluid models. Boiling Heat Transfer, pp.85-121, 1992.

]. G. Lav04, . Lavergne, ]. R. Onera-/-supaerolev02, and . Leveque, Modélisation de l'écoulement multiphasique dans le propulseur à poudre P230 d'Ariane V [Lee79] B. Van Leer. Towards the ultimate conservative difference scheme. 5. a second-order sequel to godunov's method Finite volume methods for hyperbolic problems, Cambridge Texts in Applied Mathematics, pp.101-136, 1979.

. Jr, H. Lowell, and . Holway, New statistical models for kinetic theory : Methods of construction, Physics of Fluids, vol.9, issue.9, pp.1658-1673, 1966.

M. [. Longest, . Oldhamlou02-]-r, and . Loubère, Numerical and experimental deposition of fine respiratory aerosols: Development of a two-phase drift flux model with near-wall velocity corrections, LPS98] B. Lapeyre, E. Pardoux, and R. Sentis. Méthodes de Monte-Carlo pour les équations de transport et de diffusion of Mathématiques & Applications (Berlin) [Mathematics & Applications, pp.48-70, 1998.
DOI : 10.1016/j.jaerosci.2007.10.001

A. [. Montanero and . Santos, Computer simulation of uniformly heated granular fluids, Granular Matter, vol.2, issue.2, pp.53-64, 1007.
DOI : 10.1007/s100350050035

R. [. Maire, J. Abgrall, J. Breil, and . Ovadia, A Cell-Centered Lagrangian Scheme for Two-Dimensional Compressible Flow Problems, SIAM Journal on Scientific Computing, vol.29, issue.4, pp.1781-1824, 2007.
DOI : 10.1137/050633019

URL : https://hal.archives-ouvertes.fr/inria-00334022

]. J. Mat06 and . Mathiaud, Etude de systèmes de type gaz-particules, 2006.

]. J. Mat07 and . Mathiaud, Ordres de grandeur pour le passage d'un modèle gazparticules vers un modèle hem, 2007.

Q. [. Masella, D. Tran, C. Ferre, . Pauchon-[-o-'r81-]-p, and . O-'rourke, Transient simulation of two-phase flows in pipes, International Journal of Multiphase Flow, vol.24, issue.5, pp.739-755, 1981.
DOI : 10.1016/S0301-9322(98)00004-4

R. Panescu, Modélisation Eulerienne d'écoulements diphasiques à phase dispersée et simulation numérique par une méthode volumes -éléments finis, 2006.

R. [. Patience and . Bockrath, Drift flux modelling of entrained gas???solids suspensions, Powder Technology, vol.190, issue.3, pp.415-425, 2009.
DOI : 10.1016/j.powtec.2008.08.025

O. [. Piriz, J. J. Cortazar, N. A. Lopez-cela, and . Tahir, The Rayleigh-Taylor instability, American Journal of Physics, vol.74, issue.12, pp.1095-1098, 2006.
DOI : 10.1119/1.2358158

]. D. Ram00 and . Ramos, Quelques résultats mathématiques et simulations numériques d'écoulements régis par des modèles bifluides, 2000.

]. P. Ray87 and . Raymond, Flica 4 : A computer code for multidimensional thermal analysis of nuclear reactor core, numerical methods for threedimensional two-phase flow, 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. Roe86 and . Roe, Characteristic-based schemes for the Euler equations, In Annual review of fluid mechanics Annual Reviews, vol.18, pp.337-365, 1986.

E. [. Romenski and . Toro, Compressible two-phase flows : Twopressure models and numerical methods, 2004.

R. [. Saurel and . 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

]. A. San03 and . Santos, Transport coefficients of d-dimensional inelastic maxwell models. Physica A : Statistical Mechanics and its Applications, pp.442-466, 2003.

G. [. Sokolichin, A. Eigenberger, and . Lapin, Simulation of buoyancy driven bubbly flow: Established simplifications and open questions, AIChE Journal, vol.21, issue.1, pp.24-45, 2004.
DOI : 10.1002/aic.10003

H. Staedtke, G. Franchello, B. Worth, U. Graf, P. Romstedt et al., Advanced three-dimensional two-phase flow simulation tools for application to reactor safety (ASTAR), Nuclear Engineering and Design, vol.235, issue.2-4, pp.2-4379, 2005.
DOI : 10.1016/j.nucengdes.2004.08.052

URL : https://hal.archives-ouvertes.fr/hal-00402590

J. Schlegel, T. Hibiki, and M. Ishii, Development of a comprehensive set of drift-flux constitutive models for pipes of various hydraulic diameters, Progress in Nuclear Energy, pp.666-677, 2010.
DOI : 10.1016/j.pnucene.2010.03.007

M. [. Song and . Ishii, On the stability of a one-dimensional two-fluid model, Nuclear Engineering and Design, vol.204, issue.1-3, pp.101-115, 2001.
DOI : 10.1016/S0029-5493(00)00253-3

S. [. Sheppard and . Morris, Drift-flux correlation disengagement models: Part I ??? Theory: Analytic and numeric integration details, Consequence Modeling for Plant Safety and Environmental Impact, pp.111-125, 1995.
DOI : 10.1016/0304-3894(95)00051-U

B. [. Stewart and . 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. Tou96 and . Toumi, An upwind numerical method for a six equation two-phase flow model, 1619.

]. C. Vil02 and . Villani, A review of mathematical topics in collisional kinetic theory Mathematics of granular materials, J. Stat. Phys, vol.124, issue.2 4, pp.781-822, 2002.

R. [. Vonneumann and . Richtmyer, A Method for the Numerical Calculation of Hydrodynamic Shocks, Journal of Applied Physics, vol.21, issue.3, pp.232-237, 1950.
DOI : 10.1063/1.1699639

]. G. Wal69 and . Wallis, One Dimensional Two-Phase Flow, 1969.

P. [. Woodward and . Colella, The numerical simulation of two-dimensional fluid flow with strong shocks, Journal of Computational Physics, vol.54, issue.1, pp.115-173, 1963.
DOI : 10.1016/0021-9991(84)90142-6

]. M. Wil80 and . Wilkins, Use of artificial viscosity in multidimensional fluid dynamic calculations, Journal of Computational Physics, vol.36, issue.3, pp.281-303, 1980.

]. F. Wil85 and . Williams, Combustion Theory. The Fundamental Theory of Chemically Reacting Flow Systems, 1985.

]. D. You84 and . Youngs, Numerical simulation of turbulent mixing by Rayleigh- Taylor instability, Physica D : Nonlinear Phenomena, vol.12, issue.1-3, pp.32-44, 1984.

]. D. You89 and . Youngs, Modelling turbulent mixing by Rayleigh-Taylor instability, Physica D : Nonlinear Phenomena, vol.37, issue.1-3, pp.270-287, 1989.

J. [. Zuber and . Findlay, Average Volumetric Concentration in Two-Phase Flow Systems, Journal of Heat Transfer, vol.87, issue.4, pp.453-468, 1965.
DOI : 10.1115/1.3689137

N. Zuber, Flow excursions and oscillations in boiling, two-phase systems with heat addition, Proc, EURaTOMSymp.Two-Phase Flow Dynamics, vol.1, pp.1070-1089, 1967.