T. V5, Theory Manual, Field Equations, Solution Methods and Physical Models, U.S. Nuclear Regulatory Commission, 2008.

A. Acrivos, Method of Characteristics Technique. Application to Heat and Mass Transfer Problems, Industrial & Engineering Chemistry, vol.48, issue.4, p.703710, 1956.
DOI : 10.1021/ie50556a012

G. Allaire, G. Faccanoni, and S. Kokh, A strictly hyperbolic equilibrium phase transition model, Comptes Rendus Mathematique, vol.344, issue.2, p.135140, 2007.
DOI : 10.1016/j.crma.2006.11.008
URL : https://hal.archives-ouvertes.fr/hal-00976919

A. S. Almgren, J. B. Bell, C. A. Rendleman, and M. Zingale, Low Mach Number Modeling of Type Ia Supernovae. I. Hydrodynamics, The Astrophysical Journal, vol.637, issue.2, p.922, 2006.
DOI : 10.1086/498426

A. S. Almgren, J. B. Bell, C. A. Rendleman, and M. Zingale, Low Mach Number Modeling of Type Ia Supernovae. II. Energy Evolution, The Astrophysical Journal, vol.649, issue.2, p.927, 2006.
DOI : 10.1086/507089

M. Bernard, S. Dellacherie, G. Faccanoni, B. Grec, O. Latte et al., Study of low Mach nuclear core model for single-phase ow, ESAIM Proc, vol.38, p.118134, 2012.

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

V. Casulli and D. Greenspan, Pressure method for the numerical solution of transient, compressible uid ows, Internat. J. Numer. Methods Fluids, vol.4, issue.11, p.10011012, 1984.

S. Clerc, Numerical Simulation of the Homogeneous Equilibrium Model for Two-Phase Flows, Journal of Computational Physics, vol.161, issue.1, p.577616, 2002.
DOI : 10.1006/jcph.2000.6515

P. Colella and K. Pao, A projection method for low speed ows, J. Comput. Phys, vol.149, issue.2, p.245269, 1999.

S. Dellacherie, On a diphasic low mach number system, ESAIM: Mathematical Modelling and Numerical Analysis, vol.39, issue.3, p.487514, 2005.
DOI : 10.1051/m2an:2005020

S. Dellacherie, Numerical resolution of a potential diphasic low Mach number system, Journal of Computational Physics, vol.223, issue.1, p.151187, 2007.
DOI : 10.1016/j.jcp.2006.09.009

S. Dellacherie, Analysis of Godunov type schemes applied to the compressible Euler system at low Mach number, Journal of Computational Physics, vol.229, issue.4, p.9781016, 2010.
DOI : 10.1016/j.jcp.2009.09.044

S. Dellacherie, On a low Mach nuclear core model, ESAIM: Proceedings, vol.35, p.79106, 2012.
DOI : 10.1051/proc/201235005

S. Dellacherie, G. Faccanoni, B. Grec, F. Lagoutière, E. Nayir et al., 2D numerical simulation of a low Mach nuclear core model with stiened gas using Freefem++, ESAIM. Proc

S. Dellacherie, G. Faccanoni, B. Grec, and Y. Penel, Study of low Mach nuclear core model for two-phase ows with phase transition II: tabulated EOS

M. Drouin, O. Grégoire, and O. Simonin, A consistent methodology for the derivation and calibration of a macroscopic turbulence model for flows in porous media, International Journal of Heat and Mass Transfer, vol.63, issue.0, pp.401-413, 2013.
DOI : 10.1016/j.ijheatmasstransfer.2013.03.060
URL : https://hal.archives-ouvertes.fr/hal-00952032

D. R. Durran, Numerical methods for uid dynamics, Texts in Applied Mathematics, vol.32, 2010.

P. Embid, Well-posedness of the nonlinear equations for zero mach number combustion, Communications in Partial Differential Equations, vol.20, issue.11
DOI : 10.1137/0142059

G. Faccanoni, Étude d'un modèle n de changement de phase liquide-vapeur. Contribution à l'étude de la crise d'ébullition, 2008.

G. Faccanoni, S. Kokh, and G. Allaire, Modelling and simulation of liquid-vapor phase transition in compressible ows based on thermodynamical equilibrium, ESAIM Math. Model. Numer. Anal, vol.46, p.10291054, 2012.

P. Fillion, A. Chanoine, S. Dellacherie, and A. Kumbaro, FLICA-OVAP: A new platform for core thermal???hydraulic studies, Nuclear Engineering and Design, vol.241, issue.11, p.43484358, 2011.
DOI : 10.1016/j.nucengdes.2011.04.048

E. Goncalvès and R. F. Patella, Numerical study of cavitating ows with thermodynamic eect, Comput. & Fluids, vol.39, issue.1, p.99113, 2010.

J. M. Gonzalez-santalo and R. T. Lahey, An exact solution for ow transients in two-phase systems by the method of characteristics, J. Heat Transf, vol.95, issue.4, p.470476, 1973.

W. Greiner, L. Neise, and H. Stöcker, Thermodynamics and statistical mechanics, 1997.
DOI : 10.1007/978-1-4612-0827-3

H. Guillard and C. Viozat, On the behaviour of upwind schemes in the low Mach number limit, Comput. & Fluids, vol.28, issue.1, p.6386, 1999.
URL : https://hal.archives-ouvertes.fr/hal-00871725

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

M. F. Lai, J. B. Bell, and P. Colella, A projection method for combustion in the zero Mach number limit, 11th Computational Fluid Dynamics Conference, p.776783, 1993.
DOI : 10.2514/6.1993-3369

O. , L. Métayer, J. Massoni, and R. Saurel, Elaborating equations of state of a liquid and its vapor for two-phase ow models, Int. J. Therm. Sci, vol.43, issue.3, p.265276, 2004.

O. , L. Métayer, J. Massoni, and R. Saurel, Modelling evaporation fronts with reactive Riemann solvers, J. Comput. Phys, vol.205, p.567610, 2005.

A. Majda and K. G. Lamb, Simplied equations for low Mach number combustion with strong heat release, Dynamical issues in combustion theory, 1991.

A. Majda and J. Sethian, The Derivation and Numerical Solution of the Equations for Zero Mach Number Combustion, Combustion Science and Technology, vol.6, issue.3-4, pp.3-4185205, 1985.
DOI : 10.1080/00102208508960376

R. Meniko and B. J. Plohr, The Riemann problem for uid ow of real materials, Rev. Modern Phys, vol.61, issue.1, p.75130, 1989.

S. Müller and A. Voss, The Riemann Problem for the Euler Equations with Nonconvex and Nonsmooth Equation of State: Construction of Wave Curves, SIAM Journal on Scientific Computing, vol.28, issue.2, p.651681, 2006.
DOI : 10.1137/040619909

R. Saurel, F. Petitpas, and R. Abgrall, Modelling phase transition in metastable liquids: application to cavitating and ashing ows, J. Fluid Mech, vol.607, p.313350, 2008.

G. I. Sivashinsky, Hydrodynamic theory of ame propagation in an enclosed volume, Acta Astronaut, vol.6, p.631645, 1979.

G. Volpe, Performance of compressible flow codes at low Mach numbers, AIAA Journal, vol.31, issue.1, pp.49-56, 1993.
DOI : 10.2514/3.11317

A. Voss, Exact Riemann solution for the Euler equations with nonconvex and nonsmooth equation of state, 2005.

N. Zuber, Flow excursions and oscillations in boiling, two-phase ow systems with heat addition, Symposium on Two-phase Flow Dynamics, pp.1071-1089, 1967.