R. Abgrall and S. Karni, A comment on the computation of non-conservative products, J. Comput. Phys, vol.229, pp.2759-63, 2010.
URL : https://hal.archives-ouvertes.fr/inria-00535567

R. Abgrall and H. Kumar, Numerical approximation of a compressible multiphase system, Commun. Comput. Phys, vol.15, pp.1237-65, 2014.

M. Alamgir and J. H. Lienhard, Correlation of pressure undershoot during hot water depressurization, J. Heat Transfer, vol.103, pp.52-55, 1981.

R. A. Alberty, Use of Legendre transforms in chemical thermodynamics, Pure Appl. Chem, vol.73, issue.8, pp.1349-80, 2001.

L. Allievi, Teoria del colpo d'ariete, Atti Collegio Ing. Arch, 1913.

A. Ambroso, J. Hérard, and O. Hurisse, A method to couple HEM and HRM two-phase flow models, Comput. Fluids, vol.38, pp.738-56, 2009.
URL : https://hal.archives-ouvertes.fr/hal-01265379

C. N. Amos and V. E. Schrock, Critical discharge of initially subcooled water through slits, 1983.

R. E. Apfel, The tensile strength of liquids, Sci. Amer, vol.227, pp.58-71, 1972.

K. H. Ardron, A two-fluid model for critical vapor-liquid flow, Int. J. Multhiphase Flow, vol.4, pp.323-337, 1978.

K. A. Ardron and M. C. Ackerman, Studies of the critical flow of subcooled water in a pipe, CSNI, 1978.

A. Attou, L. Bolle, and J. M. Seynhaeve, Experimental study of the critical flashing flow through a relief line: evidence of the double-choked flow phenomenon, Int. J. Multiphase Flow, vol.26, pp.921-947, 2000.

M. R. Baer and J. W. Nunziato, A two-phase mixture theory for the deflagration-to-detonation transition (ddt) in reactive granular materials, Int. J. Multiphase Flow, vol.12, pp.861-89, 1986.

P. Baiti, P. G. Lefloch, and B. Piccoli, Uniqueness of Classical and Nonclassical Solutions for Nonlinear Hyperbolic Systems, J. Differential Equations, vol.172, pp.59-82, 2001.

D. S. Balsara, Self-adjusting, positivity preserving high order schemes for hydrodynamics and magnetohydrodynamics, J. Comput. Phys, vol.231, pp.7504-7521, 2012.

. Barois, Etude expérimentale de l'autovaporisation d'un écoulement ascendant adiabatique d'eau dans un canal de section uniforme, 1969.

J. Bartak, A study of the rapid depressurization of hot water and the dynamics of vapour bubble generation in superheated water, Int. J. Multiphase Flow, vol.16, pp.789-98, 1990.

Y. Bartosiewicz and J. M. Seynhaeve, Delayed equilibrium model (DEM) of flashing choked flows relevant to LOCA, Multiphase Science & Technology, vol.25, pp.117-131, 2013.

Y. Bartosiewicz and J. Seynhaeve, Delayed Equilibrium Model (DEM) of flashing choked flows relevant to LOCA and implementation in system codes, pp.22-30957, 2014.

A. F. Babitskiy, Concerning the discharge of boiling fluids, 1975.

K. H. Bendiksen, The dynamic two-fluid model OLGA: Theory and application, SPE 221 BIBLIOGRAPHY Prod. Eng, pp.171-80, 1991.

F. Bereux and L. Sainsaulieu, A roe-type Riemann solver for hyperbolic systems with relaxation based on time-dependent wave decomposition, Numer. Math, vol.77, pp.143-185, 1997.

R. A. Berry, L. Zou, H. Zhao, H. Zhang, J. W. Peterson et al., RELAP-7 Theory Manual, Idaho National Laboratory technical report, 2016.

G. Berthoud, Heat transfer modeling during a vapor explosion, Nuclear Technology, vol.130, pp.39-58, 2000.

D. Bestion, The physical closure laws in the CATHARE code, vol.124, pp.229-245, 1990.

H. Bethe, The theory of shock waves for an arbitrary equation of state, Clearinghouse for Federal Scientific and Technical Information, 1942.

S. Bianchini and A. Bressan, Vanishing viscosity solutions of nonlinear hyperbolic systems, Ann. of Math, vol.161, pp.223-342, 2005.

Z. Bilicki, C. Dafermos, J. Kestin, G. Majda, and D. L. Zeng, Trajectories and singular points in steady-state models of the two-phase flows, Int. J. Multiphase Flow, vol.13, pp.511-533, 1987.

Z. Bilicki and J. Kestin, Physical aspects of the relaxation model in two-phase flow, Proceedings of the Royal Society A, Math. Phy. Sciences, vol.428, pp.379-97, 1990.

Z. Bilicki, J. Kestin, and M. M. Pratt, A reinterpretation of the results of the Moby Dick experiments in terms on the nonequilibrium model, ASME J. Fluids Engineering, vol.112, pp.212-229, 1990.

Z. Bilicki, R. Kwidzinski, and S. A. Mohammadein, Evaluation of th relaxation time of heat and mass exchange in the liquid-vapour bubble flow, Int. J. Heat and Mass Transfer, vol.39, pp.753-59, 1996.

G. Birkhoff and E. H. Zarantonello, Jets. Wakes, and Cavities, 1957.

M. Blander and J. L. Katz, Bubble nucleation in liquids, AIChE Journal, vol.21, pp.833-881, 1975.

S. J. Board, R. W. Hall, and R. S. Hall, Detonation of Fuel Coolant Explosions, Nature, vol.254, p.319, 1975.

J. Y. Boivin, Two-phase critical flow in long nozzles, Nuclear Technologies, vol.46, pp.540-545, 1979.

F. Bouchut, Nonlinear stability of finite volume methods for hyperbolic conservation laws and well-balanced schemes for sources, Frontiers in Mathematics, 2004.

J. A. Bouré, Dynamique des écoulements diphasique: propagation de petites perturbations, 1973.

J. A. Bouré, A. A. Fritte, M. M. Giot, and M. L. Réocreux, Highlights of two-phase critical flow: On the links between maximum flow rates, sonic velocities, propagation and transfer phenomena in single and two-phase flows, Int. J. Multiphase Flow, vol.3, pp.1-22, 1976.

. Bourgine, , 1979.

C. E. Brennen, Fundamentals of multiphase flows, 2005.

J. G. Burnell, Flow of boiling water, through nozzles orifices and pipes. Engineering, vol.164, pp.572-576, 1947.

H. B. Callen, Thermodynamics and an Introduction to Thermostatistics, 1985.

C. Canuto and A. Tabacco, Mathematical Analysis II, 2015.

V. P. Carey, Liquid-Vapor Phase-Change Phenomena

J. H. Carpenter, N. Belcourt, and R. Nourgaliev, General Purpose Steam Table Library, 2013.

M. J. Castro, P. G. Lefloch, M. L. Muñoz-ruiz, and C. Parés, Why many theories of shock waves are necessary: convergence error in formally path-consistent schemes, J. Comput. Phys, vol.227, pp.8107-8136, 2008.

M. J. Castro-diaz, E. D. Fernández-nieto, T. Morales-de-luna, G. Narbona-reina, and C. Parés, A HLLC scheme for nonconservative hyperbolic problems. Application to turbidity currents with sediment transport, ESAIM: Math. Model. Numer. Anal, vol.47, pp.1-32, 2013.

M. J. Castro-diaz and E. D. Fernandez-nieto, A class of computationally fast first order finite volume solvers: PVM methods, SIAM J. Sci. Comput, vol.34, pp.2173-96, 2012.

F. Caupin and E. Herbert, Cavitation in water: a review, Comptes Rendus Physique, vol.7, issue.9, p.1000, 2006.

F. Caupin and A. D. Stroock, The stability limit and other open questions on water at negative pressure. Liquid Polymorphism: Advances in Chemical Physics, vol.152, pp.51-80, 2013.

G. P. Celata, M. Cumo, F. D'annibale, and G. E. Farello, The influence on non-condensable gas on two-phase critical flow, Int. J. Multiphase Flow, vol.14, pp.175-187, 1988.

N. Chalmers and E. Lorin, Approximation of non-conservative hyperbolic systems based on different shock curve definitions, Canad. Appl. Math. Quart, vol.17, p.447, 2009.

C. Chalons and F. Coquel, A new comment on the computation of non conservative products using Roe-type path conservative schemes, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01424306

J. S. Chang, Fracture probability and leak before break analysis for the cold neutron source moderator vessel, ASME PVP, 1998.

G. Chen, C. Levermore, and T. Liu, Hyperbolic conservation laws with stiff relaxation terms and entropy, Communications on Pure & Applied Mathematics, vol.47, pp.787-830, 1994.

A. Chiapolino, R. Saurel, and B. Nkonga, Sharpening diffuse interfaces with compressible fluids on unstructured meshes, J. Comput. Phys, vol.340, pp.389-417, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01455167

S. Clerc, Numerical Simulation of the Homogeneous Equilibrium Model for Two-Phase Flows, J. Comput. Phys, vol.161, pp.354-75, 2000.

P. Colella, Glimm's method for gas dynamics, SIAM J. Sci. Stat. Comput, vol.3, pp.76-110, 1982.

R. P. Collier, J. S. Liu, M. E. Mayfield, and F. B. Stuben, Study of critical two-phase flow through simulated cracks, 1980.

J. C. Collier and J. R. Thome, Convective boiling and condensation, 1994.

J. F. Colombeau, L. Roux, and A. Y. , Proceeding on Nonlinear Hyperbolic Problems, Lect. Notes in Maths, vol.1270, 1986.

F. Coquel, T. Gallouet, J. Hérard, and N. Seguin, Closure laws for a two-fluid two-pressure model, C. R. Math. Acad. Sci. Paris, vol.334, pp.927-959, 2002.
URL : https://hal.archives-ouvertes.fr/hal-01484345

F. Cordier, P. Degond, and A. Kumbaro, Phase appearance or disappearance in two-phase flows, Journal of Scientific Computing, 2014.
URL : https://hal.archives-ouvertes.fr/hal-00628644

M. Cowperthwaite, Relationships between Incomplete Equations of State, J. Franklin Institute, vol.285, pp.379-87, 1969.

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.131-173, 2015.

D. F. D'arcy, On acoustic wave propagation and critical mass flux in two-phase flow, J. Heat Transfer, vol.93, issue.4, pp.413-421, 1971.

F. D'auria and P. Vigni, Two-phase critical flow models. Comitato nazionale per l'energia nucleare, 1980.

R. Dagan, E. Elias, E. Wacholder, and S. Olek, A two-fluid model for critical flashing flows in pipes, Int. J. Multhiphase Flow, vol.19, pp.15-25, 1993.

D. Maso, G. Lefloch, P. G. Murat, and F. , Definition and weak stability of nonconservative products, J. Math. Pures Appl, vol.74, pp.483-548, 1995.

F. Daude, J. Berland, T. Emmert, L. Ph, F. Crouzet et al., A high-order finitedifference algorithm for direct computation of aerodynamic sound, Comput. Fluids, vol.61, pp.223-269, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00780113

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, Comput. Fluids, vol.94, pp.112-150, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01761071

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, J. Comput. Phys, vol.304, pp.189-230, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01416109

S. F. Davis, Simplified second-order Godunov-type methods, SIAM J. Sci. Stat. Comput, vol.9, pp.445-73, 1988.

P. G. Debenedetti, Metastable Liquids: Concepts and Principles, 1996.

M. O. Delchini, J. C. Ragusa, and R. A. Berry, Viscous regularization for the non-equilibrium seven-equation two-phase flow model, J. Sci. Comput, vol.69, pp.764-804, 2016.

M. O. Delchini, J. C. Ragusa, and R. A. Berry, Simulations of single-and two-phase shock tubes and gravity-driven wave problems with the RELAP-7 nuclear reactor system analysis code, Nucl. Engng. Des, vol.319, pp.106-122, 2017.

J. M. Delhaye and J. A. Boure, General equations and two-phase flow modeling, Handbook of multiphase systems, 1982.

D. Lorenzo, M. , L. Ph, Y. Bartosiewicz, and J. Seynhaeve, Physical and Numerical Investigations for the Development of a New Experimental Facility for Studying Blowdown Phenomena, Proc. ICONE24, 2016.

D. Lorenzo, M. , L. Ph, J. Seynhaeve, and Y. Bartosiewicz, Benchmark of Delayed Equilibrium Model (DEM) and Classic Two-Phase Critical Flow Models against Experimental Data, Int. J. Multiphase Flow, vol.92, pp.112-142, 2017.

D. Lorenzo, M. , L. Ph, D. Matteo, M. Pelanti et al., Homogeneous Two-Phase Flow Models and Accurate Steam-Water Table Look-up Method for Fast Transient Simulations, Int. J. Multiphase Flow, vol.95, pp.199-219, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01633862

D. Lorenzo, M. Pelanti, M. , and L. Ph, HLLC-type and path-conservative schemes for a single-velocity six-equation two-phase flow model: a comparative study, Applied Mathematics and Computation, vol.333, pp.95-117, 2018.

D. Lorenzo, M. , L. Ph, and M. Pelanti, A hyperbolic phase-transition model with noninstantaneous EoS-independent relaxation procedures, J. Comput. Phys, 2018.

D. Vuyst, F. Ghidaglia, J. , L. Coq, and G. , On the numerical simulation of multiphase water flows with changes of phase and strong gradients using the Homogeneous Equilibrium Model, Int. J. Finite, vol.2, 2005.
URL : https://hal.archives-ouvertes.fr/hal-01123347

D. Matteo and M. , Overview of Equations of State for real gases and their application. Thesis, Politecnico di Torino, 2014.

P. Downar-zapolski, Z. Bilicki, L. Bolle, and J. Franco, The non-equilibrium relaxation model for one-dimensional flashing liquid flow, Int. J. Multiphase Flow, vol.22, pp.473-83, 1996.

D. Drew, L. Cheng, and R. T. Lahey, The analysis of virtual mass effects in two-phase flow, Int. J. Multiphase Flow, 1979.

D. A. Drew, Mathematical modeling of two-phase flow, Ann. Rev. Fluid. Mech, vol.15, pp.261-91, 1983.

D. A. Drew and L. A. Segel, Averaged equations for two-phase flows, Stud. appl. Math, vol.1, pp.205-236, 1971.

M. Dumbser and D. S. Balsara, A new efficient formulation of the HLLEM Riemann solver for general conservative and non-conservative hyperbolic systems, J. Comput. Phys, vol.304, pp.275-319, 2016.

M. Dumbser, M. Castro, C. Parés, and E. F. Toro, ADER schemes on unstructured meshes for 224 BIBLIOGRAPHY non-conservative hyperbolic systems: applications to geophysical flows, Comput. Fluids, vol.38, pp.1731-1779, 2009.

M. Dumbser and E. F. Toro, A Simple Extension of the Osher Riemann Solver to Nonconservative Hyperbolic Systems, J. Sci. Comput, vol.48, pp.70-88, 2011.

M. Dumbser and E. F. Toro, On universal Osher-type schemes for general nonlinear hyperbolic conservation laws, Commun. Comput. Phys, vol.10, pp.635-71, 2011.

M. Duponcheel, J. Seynhaeve, and Y. Bartosiewicz, Implementation and validation of the DEM model in NEPTUNE_CFD and its application to the simulation of double, 2013.

J. G. Eberhart, A New Four-Parameter Equation of State and Its Application in Predicting the Spinodal Temperature of Water, Water Journal, vol.1, pp.85-91, 2009.

A. R. Edwards and T. P. O'brien, Studies of Phenomena Connected with the Depressurization of Water Reactors, J. British Nuclear Society, vol.9, pp.125-160, 1970.

B. Einfeldt, On Godunov-type methods for gas dynamics, SIAM J. Numer. Anal, vol.25, pp.294-318, 1988.

E. Elias and P. L. Chambré, Flashing inception in water during rapid decompression, ASME J. Heat Transfer, vol.115, pp.231-238, 1993.

E. Elias and P. L. Chambré, Bubble transport in flashing flow, Int. J. Multhiphase Flow, vol.26, pp.191-206, 2000.

E. Elias and G. S. Lellouche, Two-Phase Critical Flow, Int. J. Multiphase Flow, vol.20, pp.91-168, 1994.

E. Mekki-azouzi and M. , Étude éxpérimentale de l'eau et de solutions aqueuses mètastables, 2010.

T. Emmert, L. Ph, and C. Bailly, Numerical study of self-induced transonic flow oscillations behind a sudden duct enlargement, Physics of Fluids, vol.21, p.106105, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00461435

M. Europlexus-user,

N. A. Evans, D. E. Mitchell, L. S. Nelson, and M. L. Corradini, , pp.82-2269, 1982.

Y. Fang, D. Lorenzo, M. , L. Ph, S. Poncet et al., An Accurate and Efficient Look-up Table Equation of State for Two-phase Compressible Flow Simulations of Carbon Dioxide, 2018.

E. Faucher, J. M. Hérard, M. Barret, and C. Toulemonde, Computation of flashing flows in variable cross section ducts, Int. J. of Comp. Fluid Dynamics, vol.13, pp.365-91, 2000.
URL : https://hal.archives-ouvertes.fr/hal-01580046

V. Faucher, F. Crouzet, and F. Debaud, Mechanical consequences of LOCA in PWR: Full scale coupled 1D/3Dsimulations with fluid-structure interaction, Nucl. Engng. Des, vol.270, pp.359-78, 2014.

H. K. Fauske, Contribution to the theory two phase one component critical flow, p.6633, 1962.

V. Feburie, J. M. Giot, S. Granger, and J. M. Seynhaeve, A model for choked flow through cracks with inlet subcooling, Int. J. Multiphase Flow, vol.19, pp.541-562, 1993.

E. Fehlberg, Low-order classical Runge-Kutta formulas with step size control and their application to some heat transfer problems, 1969.

T. Fl-?-atten and H. Lund, Relaxation two-phase flow models and the subcharacteristic conditions, Math. Models Methods Appl. Sci, vol.21, pp.2374-2407, 2012.

J. Flinta, Calculation equation which gives the critical flow in an explicit form for reactor safety analysis, Phase Flow Group Meeting, 1984.

D. W. Fraser and A. H. Abdelmessih, A study of the effects of the location of flashing inception on maximum and minimum critical two-phase flow rates: Part II: analysis and modelling, vol.213, pp.11-30, 2002.

J. Gale, I. Tiselj, and A. Horvat, Two-fluid model of the WAHA code for simulations of water 225 BIBLIOGRAPHY hammer transients, Multiphase Science and Technology, vol.20, pp.291-322, 2008.

P. Germain and E. H. Lee, On shock waves in elastic-plastic solids, J. Mech. Phys. Solids, vol.21, pp.359-82, 1973.
DOI : 10.1016/0022-5096(73)90006-9

S. M. Ghiaasiaan, Two-Phase Flow, Boiling, and Condensation: In Conventional and Miniature Systems, 2007.
DOI : 10.1017/cbo9780511619410.003

D. Gidaspow, R. W. Li'czkowski, C. W. Solbrig, E. D. Hughes, and G. A. Mortensen, Amer. Nuclear Sot. Trans, vol.17, p.249

E. Godlewski and P. Raviart, Numerical Approximation of Hyperbolic Systems of Conservation Laws, 1996.

E. Goncalvès and R. F. Patella, Constraints on equation of state for cavitating flows with thermodynamic effects, Appl. Math. Comput, vol.217, pp.5095-102

S. W. Gouse and G. A. Brown, A survey of the velocity of sound in two-phase mixtures, 1964.

V. Guillemaud, Modélisation et simulation des écoulements diphasique par une approche bifluide à deux pressions, 2007.

C. Ha, W. Park, and C. Jung, Numerical simulations of compressible flows using multi-fluid models, Int. J. of Multiphase Flow, vol.74, pp.5-18, 2015.

L. Haar, J. S. Gallagher, and G. S. Kell, NBS/NRC Steam Tables. Hemisphere, 1984.

J. Hadamard, Lectures on Cauchy's Problem in Linear Partial Differential Equations, 1923.

. Hardy-ph and P. Mali, Validation and development of a model describing subcooled critical flow through long tubes. Energie Primarie, vol.18, pp.5-23, 1983.

R. E. Henry, A Study of One-and-Two Component, Two-Phase Critical Flows at Low Qualities, 1968.

R. E. Henry and H. K. Fauske, The Two-Phase Critical Flow of One-Component Mixtures in Nozzles, Orifices, and Short Tubes, J. Heat Transfer, vol.93, pp.179-187, 1971.

T. Y. Hou and P. G. Lefloch, Why nonconservative schemes converge to wrong solutions: error analysis, Math. Comput, vol.62, pp.497-530, 1994.
DOI : 10.2307/2153520

I. Huhtiniemi, D. Magallon, and H. Hohmann, Results of recent KROTOS FCI tests: alumina versus corium melts, Nucl. Engng. Des, vol.189, pp.379-89, 1999.
DOI : 10.1016/s0029-5493(98)00269-6

T. J. Hughes, The Finite Element Method, 2000.

O. Hurisse, Numerical simulations of steady and unsteady two-phase flows using a homogeneous model, Comput. Fluids, vol.152, pp.88-103, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01489039

V. Ilic, A qualified data base for critical flow of water, 1986.

A. Imre, K. Martinas, and L. P. Rebelo, Thermodynamics of negative pressures in liquids, J. Non-Equilib. Thermodyn, vol.23, pp.351-75, 1998.

A. L. Imre, Estimation of the Thermodynamic Limit of Overheating for Bulk Water from Interfacial Properties, Int. J. of Thermophysics, vol.34, pp.2053-64, 2013.

, Guideline on the Fast Calculation of Steam and Water Properties with the Spline-Based Table Look-Up Method (SBTL), International Association for the Properties of Water and Steam, 2015.

, Revised Release on the IAPWS Industrial Formulation 1997 for the Thermodynamic Properties of Water and Steam, 2007.

, The 1967 Formulation for Industrial Use, International Formulation Committee of the 6th International Conference on the Properties of Steam, 1967.

M. Ishii, Thermo Fluid Dynamic Theory of Two Phase-Flow. Eyrolles, 1975.

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

H. Kanno and R. J. Speedy, Supercooling of water to-92 o C under pressure, Science, vol.189, pp.880-881, 1975.

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, Phys Fluids, vol.13, pp.3002-3027, 2001.

H. Karplus, The velocity of sound in a liquid containing gas bubbles, Illinois Inst. Tech. Rep. COO, p.248, 1958.

S. W. Kieffer, Sound speed in liquid-gas mixtures: water-air and water-steam, J. Geophys. Res, vol.82, pp.2895-2904, 1977.

S. Kim and I. Mudawar, Review of two-phase critical flow models and investigation of the relationship between choking, premature CHF, and CHF in micro-channel heat sinks, Int. J. Heat and Mass Transfer, vol.87, pp.497-511, 2015.

S. B. Kiselev and J. F. Ely, Curvature effect on the physical boundary of metastable states in liquids, Physica A, vol.299, pp.357-370, 2001.

N. I. Kolev, Transiente Zweiphasenstromung, 1986.

N. I. Kolev, Multiphase flow dynamics I-II-III, 2005.

J. J. Kreeft and B. Koren, A new formulation of Kapila's five-equation model for compressible two-fluid flow, and its numerical treatment, J. Comput. Phys, vol.229, pp.6220-6262, 2010.

M. Kunick, CFD Analysis of steam turbines with the IAPWS standard on the Spline-Based Table Look-Up Method (SBTL) for the fast calculation of real fluid properties, Turbine Technical Conference and Exposition: Proceedings of ASME Turbo Expo, 2015.

M. Kunick, R. A. Berry, R. C. Martineau, H. Kretzschmar, and U. Gampe, Application of the new IAPWS Guideline on the fast and accurate calculation of steam and water properties with the Spline-Based Table Look-Up Method (SBTL, RELAP-7. Kerntechnik, vol.82, pp.1-16, 2017.

C. Jeandey, L. Gros-d'aillon, R. Bourgine, and G. Barriere, Auto vaporisation d'écoulements eau/vapeur, 1981.

C. Jeandey and L. Gros-d'aillon, Débit critique en tuyere courte, Super Moby Dick, 1983.

J. S. Jin and Z. P. Xin, The relaxation schemes for systems of conservation laws in arbitrary space dimensions, Comm. Pure Appl. Math, vol.48, pp.235-276, 1995.

H. John, J. Reimann, F. Westphal, and L. Friedel, Critical two-phase flow through rough slits, Int. J. Multhiphase Flow, vol.14, pp.155-174, 1988.

E. Johnsen and T. Colonius, Implementation of WENO schemes in compressible multicomponent flow problems, J. Comput. Phys, vol.219, pp.715-747, 2006.

D. Jou, J. Casas-vázquez, and G. Lebon, Extended irreversible thermodynamics, Rep. Prog. Phys, vol.51, pp.1105-79, 1988.

M. Labois, Modélisation des dé´sequilibresdé´sequilibres mécaniques pour les écoulements diphasiques: approches par relaxation et par modèle réduit, 2008.

C. Labourdette, J. Ghidaglia, J. A. Redford, and S. Faure, Accurate state variables for fluid flow simulation using Quicksteam and Quickmethane, European Journal of MechanicsB/Fluids, vol.65, pp.132-172, 2017.

C. Lackmé, Autovaporisation dans une conduite d'un liquide saturé ou sous-refroidi a l'entrée, 1979.

C. Lackmé, Incompleteness of the flashing of a supersaturated liquid and sonic ejection of the produced phases, Int. J. Multhiphase Flow, vol.5, pp.131-141, 1979.

C. Lackmé, Cinetique de la vaporisation de l'eau chaude qui se détand dans un tube, p.227, 1981.

P. Lafon, M. Essadki, Y. Bartosiewicz, and J. Seynhaeve, Assessment of two phase critical flow models and implementation in fast transient flow dynamics software, Proc. of the ASME, PVP2015, 2015.

M. Larsen, PeTra: a novel computer code for simulation of slug flow, SPE Annual Technical Conference and Exhibition, vol.3884, 1997.

L. Floch and P. G. , Shock Waves for Nonlinear Hyperbolic Systems in Nonconservative Form. IMA series, 1989.

L. Floch and P. G. , Propagating phase boundaries. Formulation of the problem and existence via the Glimm method, Arch. Rational Mech. Anal, vol.123, pp.153-97, 1993.

L. Metayer, O. Massoni, J. Saurel, and R. , Elaborating equations of state of a liquid and its vapor for two-phase flow models, Int. J. Thermal Sciences, vol.43, pp.265-76, 2004.

H. Lemonnier, An Attempt to Apply the Homogeneous Relaxation Model to the Wahaloads Benchmark Tests with Interaction with the Mechanical Structure, 2002.

M. Lepareux, Materiau EAU, 1994.

M. Lepareux, Programme-Plexus, les modèls de débit critique, 1997.

R. Leveque, Finite Volume Methods for Hyperbolic Problems, 2002.

R. J. Leveque and M. Pelanti, A class of approximate Riemann solvers and their relation to relaxation schemes, J. Comput. Phys, vol.172, pp.572-591, 2001.
URL : https://hal.archives-ouvertes.fr/hal-01342280

J. H. Lienhard, N. Shamsundar, and P. O. Biney, Spinodal lines and equations of state-a review, Nucl. Engng. Des, vol.95, pp.297-313, 1986.

G. Linga, A Hierarchy of Non-Equilibrium Two-Phase Flow Models, 2015.

T. Liu, Hyperbolic conservation laws with relaxation, Commun. Math. Phys, vol.108, pp.153-75, 1987.

H. Lochon, F. Daude, P. Galon, and J. M. Hérard, Comparison of two-fluid models on steamwater transients, ESAIM, vol.50, pp.1631-57, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01286670

H. Lochon, Modélisation et simulation d'écoulements transitoires eau-vapeur, 2016.

H. Lochon, F. Daude, P. Galon, and J. M. Hérard, Computation of fast depressurization of water using a two-fluid model: revisiting Bilicki modelling of mass transfer, Computers & Fluids, vol.156, pp.162-74, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01401816

H. Lund, A hierarchy of relaxation models for two-phase flow, SIAM J. Appl. Math, vol.72, pp.1713-1754, 2012.

H. Lund and P. Aursand, Two-Phase Flow of CO2 with Phase Transfer. Energy Procedia, vol.23, pp.246-55, 2012.

M. Ferrer, P. J. , T. Munkejord, and S. T. , On the effect of temperature and velocity relaxation in two-phase flow models, ESAIM: Math. Model. Numer. Anal, vol.46, pp.411-453, 2012.

J. C. Maxwell, On the dynamical evidence of the molecular constitution of bodies, Nature, vol.11, pp.357-59

J. H. Mcfadden, RETRAN-02-A Program for Transient Thermal, Hydraulic Analysis of Complex Fluid Flow Systems, vol.1, 1984.

R. Menikoff and B. J. Plohr, The Riemann problem for fluid flow of real materials, Rev. Mod. Phys, vol.61, pp.75-130, 1989.

P. Y. Meslin, Evidence of 210Po on martian dust at meridiani planum, J. Geophys. Res, vol.111, 2006.
URL : https://hal.archives-ouvertes.fr/hal-00098084

R. E. Milliken, Hydratation state of the Martian surface as seen by Mars Express OMEGA: 2H2O content of surface, J. Geophys. Res, vol.112, 2007.

F. J. Moody, Maximum flow-rate of a single component two-phase mixture, J. Heat Transfer, vol.87, pp.134-141, 1965.

F. J. Moody, A pressure pulse model for two-phase critical flow and sonic velocity, J. Heat Transfer, vol.91, pp.371-381, 1969.

F. J. Moody, Maximum discharge rate of liquid-vapor mixtures from vessels, Non equilibrium two-phase flows, 1975.

A. Murrone and H. Guillard, A five equation reduced model for compressible two phase flow problems, J. Comput. Phys, vol.202, pp.664-98, 2005.
URL : https://hal.archives-ouvertes.fr/inria-00071808

M. Nakagawa, A. Harada, and M. S. Berana, Analysis of expansion waves appearing in the outlets of two-phase flow nozzles, HVAC&R Res, vol.15, pp.1065-79, 2009.

R. Natalini, Recent mathematical results on hyperbolic relaxation problems, Surv. Pure Appl. Math, vol.99, pp.128-98, 1999.

J. W. Nunziato and E. K. Walsh, On ideal multiphase mixtures with chemical reactions and diffusion, Archs Rational Mech. Analysis, vol.73, pp.285-311, 1980.

H. Ogasawara, A theoretical approach to two-phase critical flow, Bull. JSME, 1969.

P. Pana, Berechnung der station/iren Massenstromdichte von Wasserdampfgemischen und der auftretenden RfickstoBkr/ifte, 1976.

C. Parés, Numerical methods for nonconservative hyperbolic systems: a theoretical framework, SIAM J. Numer. Anal, vol.44, pp.300-321, 2006.

C. K. Park, J. W. Park, M. K. Chung, and M. H. Chung, An Empirical Correlation for Critical Flow Rates of Subcooled Water Through Short Pipes with Small Diameters, J. of the Korean Nuclear Society, vol.29, pp.35-44, 1977.

H. Park, Experimental study on a two-phase critical flow with a non-condensable gas at high pressure conditions, Int. J. Multiphase Flow, vol.33, pp.1222-1236, 2007.

S. L. Passman, Mixtures of granular materials, Int. J. Engng Sci, vol.15, pp.117-146, 1977.

S. L. Passman, J. W. Nunziato, and E. K. Walsh, A theory of multiphase mixtures, Rational Thermodynamics, pp.286-325, 1984.

S. V. Patankar, Numerical heat transfer and fluid flow, Comput. Fluids, 1980.

G. Peano, Demonstration de l'intégrabilité des équations différentielles ordinaires, Mathematische Annalen, vol.37, pp.182-228, 1890.

M. Pelanti and K. Shyue, A mixture-energy-consistent six-equation two-phase numerical model for fluids with interfaces, cavitation and evaporation waves, J. Comput. Phys, vol.259, pp.331-57, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01135994

M. Pelanti and K. Shyue, A mixture-energy-consistent numerical approximation of a two-phase flow model for fluids with interfaces and cavitation, Hyperbolic Problems: Theory, Numerics, Applications, Proceedings of the Fourteenth International Conference on Hyperbolic Problems, pp.839-885, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01136009

M. Pelanti, Low Mach number preconditioning techniques for Roe-type and HLLC-type methods for a two-phase compressible flow model, Appl. Math. Comput, vol.310, pp.112-145, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01633857

P. Manes and J. , Validation of NEPTUNE-CFD Two-Phase Flow Models Using Experimental Data, Science and Technology of Nuclear Installations, 2014.

F. Petitpas, E. Franquet, R. Saurel, L. Metayer, and O. , A relaxation-projection method for compressible flows. Part II: Artificial heat exchanges for multiphase shocks, Journal of Computational Physics, vol.225, pp.2214-2262, 2007.
URL : https://hal.archives-ouvertes.fr/hal-02101442

F. Petitpas, R. Saurel, E. Franquet, and A. Chinnayya, Modelling detonation waves in condensed energetic materials: Multiphase CJ conditions and multidimensional computations, Shock Waves, vol.19, pp.377-401, 2009.
URL : https://hal.archives-ouvertes.fr/hal-02101436

M. Pettenati, L. Mercury, and M. Azaroual, Capillary geochemistry in non-saturated zone of soils. Water content and geochemical signatures, Applied Geochem, vol.23, pp.3799-3818, 2008.
URL : https://hal.archives-ouvertes.fr/insu-00356838

G. A. Pinhasi, A. Ullmann, and A. Dayan, Modeling of flashing two-phase flow, Reviews in Chemical Eng, vol.21, pp.133-264, 2005.

M. S. Plesset and S. A. Zwick, The growth of vapor bubbles in superheated liquids, J. Appl. Phys, vol.25, pp.493-500, 1954.

H. Pokharna, M. Mori, and V. H. Ransom, Regularization of Two-Phase Flow Models: A Comparison of Numerical and Differential Approaches, J. Comput. Phys, vol.134, pp.282-95, 1997.

P. H. Poole, F. Sciortino, U. Essmann, and H. E. Stanley, Phase behaviour of metastable water, Nature, vol.360, pp.324-352, 1992.

T. A. Porsching, A finite difference method for thermally expandable fluid transients, Nucl. Sci. Eng, vol.64, p.177, 1977.

W. H. Press, S. A. Teukolsy, W. T. Vetterling, and B. P. Flannery, Numerical Recipes, 1997.

A. Prosperetti and . Tryggvason, Computational methods dor multiphase flow, 2009.

A. Prosperetti and M. S. Plesset, Vapour-bubble growth in a superheated liquid, J. Fluid Mech, vol.85, pp.349-368, 1978.

C. Ramboz and M. Danis, Superheating in the Red Sea? The heat-mass balance of the Atlantis II Deep revisited, Earth Planet. Sci. Lett, vol.97, pp.190-210, 1990.

V. H. Ransom and J. Trapp, Relap5 progress summary analytical choking criterion for two-phase flow, 1978.

V. H. Ransom and D. L. Hicks, Hyperbolic two-pressure models for two-phase flow, Journal of Computational Physics, vol.53, pp.124-151, 1984.

P. Rascle and O. Morvant, Spécifications fonctionnelles de THETIS: Calcul par interpolation des fonctions thermodynamiques de fluides diphasiques, 1994.

P. A. Raviart and L. Sainsaulieu, A nonconservative hyperbolic system modeling spray dynamics. I. Solution of the Riemann problem, Math. Models Methods Appl. Sci, vol.5, pp.297-333, 1995.

S. Rhebergen, O. E. Bokhov, and J. J. Van-der-vegt, Discontinuous Galerkin finite element method for shallow two-phase flows, Comput. Methods in Appl. Mech. Eng, vol.198, pp.819-849, 2009.

B. Riegel, Contribution à l'étude de la décompression d'une capacité en régime diphasique, 1978.

M. F. Robbe and M. Lepareux, Programme PLEXUS, matériau EAU, modèle homogène non equilibré. Rapport DMT 96/142, 1996.

G. A. Roth and F. Aydogan, Theory and implementation of nuclear safety system codes-part I: Conservation equations, flow regimes, numerics and significant assumptions, Progress in Nuclear Energy, vol.76, pp.160-82, 2014.

M. Reocreux, Contribution à l'étude des débits critiques en écoulement diphasique eau-vapeur, 1974.

P. Romstedt and W. Werner, Numerical analysis of critical two-phase flow in a convergentdivergent nozzle, NED, vol.92, pp.71-83, 1986.

V. Ruas, Numerical Methods for Partial Differential Equations: An Introduction, 2016.

L. Sainsaulieu, Finite Volume Approximation of Two Phase-Fluid Flows Based on an Approximate Roe-Type Riemann Solver, J. Comput. Phys, vol.121, pp.1-28, 1995.

C. Sánchez-linares, T. Morales-de-luna, C. Diaz, and M. J. , A HLLC scheme for Ripa model, Appl. Math. Comput, vol.272, pp.369-84, 2016.

R. Saurel and R. Abgrall, A Multiphase Godunov Method for Compressible Multifluid and Multiphase Flows, J. Comput. Phys, vol.150, pp.425-67, 1999.

R. Saurel, L. Metayer, O. Massoni, J. Gavrilyuk, and S. , Shock jump relations for multiphase mixtures with stiff mechanical relaxation, Shock Waves, vol.16, pp.209-241, 2007.

R. Saurel, F. Petitpas, and R. Abgrall, Modelling phase transition in metastable liquids. Application to cavitating and flashing flows, J. Fluid Mech, vol.607, pp.313-50, 2008.
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 mixture, J. Comput. Phys, vol.228, pp.1678-1712, 2009.

R. Saurel, F. Fraysse, D. Furfaro, and E. Lapedie, Multiscale multiphase modeling of detonations in condensed energetic materials, Computers and Fluids, vol.159, pp.95-111, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01707909

S. Schoch, N. Nikiforakis, B. Lee, and R. Saurel, Multi-phase simulation of ammonium nitrate emulsion detonations, Combustion and Flame, vol.160, pp.1883-99, 2013.
URL : https://hal.archives-ouvertes.fr/hal-01459475

V. E. Schrock and C. N. Amos, Two-phase critical flow, Two-Phase Flow and Heat Transfer, 1984.

V. E. Schrock, E. S. Starkman, and R. A. Brown, Flashing flow of initially subcooled water in convergent-divergent nozzles, J. Heat Transfer, p.263, 1977.

L. Schwartz, Sur l'impossibilité de la multiplication des distributions, C. R. Acad. Sci. Paris, vol.239, pp.847-895, 1954.

J. Seynhaeve, Etude experimèntale des écoulements diphasiques critiques a faible titre, 1980.

J. Seynhaeve, A. De-crécy, and Y. Bartosiewicz, Uncertainty Analysis of Delayed Equilibrium Model (DEM) using the CIRCE Methodology. NURETH16, 2015.

A. Shapiro, The Dynamics and Thermodynamics of Compressible Fluid Flow, 1954.

K. I. Shmulovich and C. M. Graham, An experimental study of phase equilibria in the systems H2O-CO2-CaCl2 and H2O-CO2-NaCl at high pressures and temperatures (500-800 o C, 0.5-0.9 GPa): geological and geophysical applications, Contr. Mineral. Petrol, vol.146, pp.450-62, 2004.

A. R. Simpson, Large Water-Hammer Pressures for Column Separation in Pipelines, J. Hydraul. Eng, vol.117, pp.1310-1326, 1989.

V. P. Skripov, , 1972.

V. P. Skripov and P. A. Sinicyn, Teplofizicheskyie Svoyistva Zhidkostey v Metastabil'nom Sostoyanyii, 1980.

L. L. Smith, SIMMER-II: a computer program for LMFBR disrupted core analysis, 1980.

H. Stadtke, Gasdynamic aspects of the two-phase flow, 2006.

L. Sokolowski and T. Kozlowsk, Assessment of Two-Phase Critical Flow Models Performance in RELAP5 and TRACE Against Marviken Critical Flow Tests, 2012.

G. L. Sozzi and W. A. Sutherland, Critical flow of saturated and subcooled water at high pressure, General Electric Company, 1975.

R. Span and W. Wagner, A New Equation of State for Carbon Dioxide Covering the Fluid 231 BIBLIOGRAPHY Region from the Triple-Point Temperature to 1100 K at Pressures up to 800 MPa, J. Phys. Chem. Ref. Data, vol.25, pp.1509-96, 1996.

J. W. Spore, TRAC-M/FORTRAN 90 Theory Manual. Los Alamos National Laboratory, 2001.

E. S. Starkman, V. E. Schrock, and K. F. Neusen, Expansion of a very low quality two-phase fluid through a convergent-divergent nozzle, J. of Basic Engineering, issue.86, 1964.

H. B. Stewart and B. Wendroff, Two-phase flow: models and methods, J. Comput. Phys, vol.56, pp.363-409, 1984.

F. H. Stillinger, Water Revisited. Science, vol.209, p.4455, 1980.

. Strang, On the construction and comparison of difference schemes, SIAM J. Numer. Anal, vol.5, pp.506-523, 1968.

T. Takeda and I. Ohtsu, ROSA/LSTF Test and RELAP5 Analyses on PWR Cold Leg SmallBreak LOCA with Accident Management Measure and PKL Counterpart Test, Nuclear Engineering and Technology, vol.49, pp.928-968, 2017.

A. Tenter and J. Weisman, The Use of the Method of Characteristics for Examination of Two-Phase Flow Behavior, Nuclear Technology, vol.37, pp.19-28, 1978.

R. Thièry and L. Mercury, Explosive properties of water in volcanic and hydrothermal systems, J. Geophys. Res, vol.114, 2009.

P. Thomas, Extension des table de l'eau utilisées dans le code CATHARE 2. EDF-CEAFRAMATOME, 1998.

B. Tian, E. F. Toro, and C. E. Castro, A path-conservative method for a five-equation model of two-phase flow with an HLLC-type Riemann solver, Comput. Fluids, vol.46, pp.122-154, 2011.

I. Tiselj and S. Petelin, Modelling of Two-Phase Flow with Second-Order Accurate Scheme, J. Comput. Phys, vol.136, pp.503-524, 1997.

I. Tiselj, A. Horvat, and J. Gale, Numerical scheme of the WAHA code, Multiphase Science and Technology, vol.20, pp.323-54, 2008.

E. F. Toro, Riemann Solvers and Numerical Methods for Fluid Dynamics, 1997.

E. F. Toro, M. Spruce, and W. Speares, Restoration of the contact surface in the HLL-Riemann solver, Shock Waves, vol.4, pp.25-34, 1994.

I. Toumi, A weak formulation of Roe's approximate Riemann solver, J. Comput. Phys, vol.102, pp.360-73, 1992.

J. A. Trapp and V. H. Ransom, A choked-flow calculation criterion from non-homogeneous non-equilibrium two-phase flows, Int. J. Multiphase Flow, vol.8, pp.669-681, 1982.

G. T. Tremble and W. J. Turner, Characteristics of two-phase one-component flow with slip, NED, vol.42, pp.287-295, 1977.

E. Valero and I. E. Parra, The role of thermal disequilibrium in critical two-phase flow, Int. J. Multiphase Flow, vol.28, pp.21-50, 2002.

J. A. Vogrin, An Experimental Investigation of Two-Phase, Two-components Flow in a Horizontal Converging-Diverging Nozzle, 1963.

A. I. Volpert, Spaces BV and quasilinear equations, Math. USSR Sbornik, vol.73, pp.255-302, 1967.

W. Wagner and A. Pruß, The IAPWS Formulation 1995 for the Thermodynamic Properties of Ordinary Water Substance for General and Scientific Use, J. Phys. Chem. Ref. Data, vol.31, pp.387-535, 2002.

W. Wagner, The IAPWS Industrial Formulation 1997 for the Thermodynamic Properties of Water and Steam, ASME J. Eng. Gas Turbines and Power, vol.122, pp.150-182, 2000.

G. B. Wallis, Critical two-phase flow, Int. J. Multiphase Flow, vol.6, pp.97-112, 1980.

C. A. Ward, The rate of gas absorption at a liquid interface, The Journal of Chemical 232 BIBLIOGRAPHY Physics, vol.67, pp.229-264, 1977.

C. A. Ward, R. D. Findlay, and M. Rizk, Statistical rate theory of interfacial transport. I. Theoretical development, The Journal of Chemical Physics, vol.76, pp.5599-605, 1982.
DOI : 10.1063/1.442865

C. A. Ward and G. Fang, Expression for predicting liquid evaporation flux: Statistical rate theory approach, Phys. Rev, vol.59, pp.429-469, 1999.
DOI : 10.1103/physreve.59.429

P. B. Whalley, Two-Phase Flow and Heat Transfer, 1996.

A. B. Wood, A textbook of sound. G. Bell and Sons Ltd, 1930.

X. Wang, Z. Wang, Y. Duan, B. An, and D. Lee, Efficient evaluation of thermodynamic properties of water and steam on p-h surface, Journal of the Taiwan Institute of Chemical Engineers, vol.45, pp.372-79, 2014.

H. J. Yoon, M. Ishii, and S. T. Revankar, Choking flow modeling with mechanical and thermal non-equilibrium, Int. J. Heat and Mass Transfer, vol.49, pp.171-186, 2006.
DOI : 10.1016/j.ijheatmasstransfer.2005.07.044

F. R. Zaloudek, The critical flow of hot water through short tubes, 1963.

A. Zein, M. Hantke, and G. Warnecke, Modeling phase transition for compressible two-phase flows applied to metastable liquids, J. Comput. Phys, vol.229, pp.2964-98, 2010.
DOI : 10.1016/j.jcp.2009.12.026

Q. Zheng, D. J. Durben, G. H. Wolf, and C. A. Angell, Liquids at large negative pressures: water at the homogeneous nucleation limit, Science, vol.254, issue.5033, pp.829-832, 1991.

R. K. Zia, E. F. Redish, and S. R. Mckay, Making Sense of the Legendre Transform, American Journal of Physics, vol.77, pp.614-636, 2007.
DOI : 10.1119/1.3119512

URL : http://arxiv.org/pdf/0806.1147

V. V. Zhokov, Criteria of leakage occurrence and pressure vessels failure as applied to reactors, Trans. ASME, J. Pres. Ves. Technology, vol.114, pp.378-380, 1992.