R. Abgrall, How to prevent pressure oscillations in multicomponent flow calculations: a quasi conservative approach, J. Comput. Phys, vol.125, pp.150-60, 1996.
URL : https://hal.archives-ouvertes.fr/inria-00074304

R. Abgrall and R. Saurel, Discrete equations for physical and numerical compressible multiphase mixtures, J. Comput. Phys, vol.186, pp.361-96, 2003.

B. Abramzon and W. Sirignano, Droplet vaporization model for spray combustion calculations, Int. J. Heat Mass Transf, vol.32, pp.1605-1623, 1989.

G. Allaire, S. Clerc, and S. Kokh, A five-equation model for the simulation of interfaces between compressible fluids, J. Comput. Phys, vol.181, pp.577-616, 2002.

D. M. Anderson, G. B. Mcfadden, and A. A. Wheeler, Diffuse-interface methods in fluid mechanics, Annu. Rev. Fluid Mech, vol.30, pp.139-65, 1998.

T. Aslam, J. Bdzil, and D. Stewart, Level set methods applied to modeling detonation shock dynamics, J. Comput. Phys, vol.126, pp.390-409, 1996.

M. Baer and J. 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.

. Fl50ch05-pantano, , vol.7, p.44, 2017.

J. Bdzil, R. Menikoff, S. Son, A. Kapila, and D. Stewart, Two-phase modeling of deflagration-to-detonation transition in granular materials: a critical examination of modeling issues, Phys. Fluids, vol.11, pp.378-402, 1999.

J. Brackbill, D. Kothe, and C. Zemach, A continuum method for modeling surface tension, J. Comput. Phys, vol.100, pp.335-54, 1992.

J. Cahn and J. Hilliard, Free energy of a nonuniform system. I. Interfacial free energy, J. Chem. Phys, vol.28, pp.258-67, 1958.

A. Chiapolino, P. Boivin, and R. Saurel, A simple and fast phase transition relaxation solver for compressible multicomponent two-phase flows, Comput. Fluids, vol.150, pp.31-45, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01502389

A. Chiapolino, P. Boivin, and R. Saurel, A simple phase transition relaxation solver for liquid-vapor flows, Int. J. Numer. Methods Fluids, vol.83, pp.583-605, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01359203

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

B. Cockburn and C. W. Shu, TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws, II. General framework. Math. Comput, vol.52, pp.411-446, 1989.

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

A. Dervieux and F. Thomasset, A finite element method for the simulation of a Rayleigh-Taylor instability, Approx. Methods Navier-Stokes Prob.: Proc. Symp. Int. Union Theor. Appl. Mech, pp.145-58, 1980.

M. Dumbser, A. Hidalgo, M. Castro, C. Parés, and E. Toro, FORCE schemes on unstructured meshes II: non-conservative hyperbolic systems, Comput. Methods Appl. Mech. Eng, vol.199, pp.625-672, 2010.

N. Favrie, S. Gavrilyuk, and R. Saurel, Solid-fluid diffuse interface model in cases of extreme deformations, J. Comput. Phys, vol.228, pp.6037-77, 2009.

R. Fedkiw, T. Aslam, B. Merriman, and S. Osher, A non-oscillatory Eulerian approach to interfaces in multimaterial flows (the ghost fluid method), J. Comput. Phys, vol.152, pp.457-92, 1999.

E. Franquet and V. Perrier, Runge-Kutta discontinous Galerkin method for the approximation of Baer and Nunziato type multiphase models, J. Comput. Phys, vol.231, pp.4096-141, 2012.

D. Furfaro and R. Saurel, A simple HLLC-type Riemann solver for compressible non-equilibrium two-phase flows, Comput. Fluids, vol.111, pp.159-78, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01278892

D. Furfaro and R. Saurel, Modeling droplet phase change in the presence of a multi-component gas mixture, Appl. Math. Comput, vol.272, pp.518-559, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01278890

J. Glimm, J. Grove, X. Li, K. Shyue, Y. Zeng et al., Three-dimensional front tracking, SIAM J. Sci. Comput, vol.19, pp.703-730, 1998.

R. Glowinski, S. Osher, W. Yin, and E. , Splitting Methods in Communication and Imaging, Science, and Engineering, 2010.

S. K. Godunov, A difference method for numerical calculation of discontinuous solutions of the equations of hydrodynamics, Mat. Sb, vol.89, pp.271-306, 1959.

A. Harten, B. Engquist, S. Osher, and S. Chakravarthy, Uniformly high order accurate essentially nonoscillatory schemes, III. J. Comput. Phys, vol.71, pp.231-303, 1987.

A. Harten, P. Lax, and B. Van-leer, On upstream differencing and Godunov-type schemes for hyperbolic conservation laws, SIAM Rev, vol.25, pp.35-61, 1983.

B. Hejazialhosseini, D. Rossinelli, and P. Koumoutsakos, Vortex dynamics in 3D shock-bubble interaction, Phys. Fluids, vol.25, p.110816, 2013.

C. Hirt, A. Amsden, and J. Cook, Arbitrary Lagrangian-Eulerian computing method for all flow speeds, J. Comput. Phys, vol.14, pp.227-53, 1974.

C. Hirt and B. Nichols, Volume of fluid (VOF) method for the dynamics of free boundaries, J. Comput. Phys, vol.39, pp.201-226, 1981.

E. Johnsen and T. Colonius, Numerical simulations of non-spherical bubble collapse, J. Fluid Mech, vol.629, pp.231-62, 2009.

A. Kapila, R. Menikoff, J. Bdzil, S. Son, and D. Stewart, Two-phase modeling of deflagration-to-detonation transition in granular materials: reduced equations, Phys. Fluids, vol.13, pp.3002-3026, 2001.

M. Lallemand, A. Chinnayya, L. Metayer, and O. , Pressure relaxation procedures for multiphase compressible flows, Int. J. Numer. Methods Fluids, vol.49, pp.1-56, 2005.
URL : https://hal.archives-ouvertes.fr/inria-00072600

. Fl50ch05-pantano, , vol.7, p.44, 2017.

M. Lallemand and R. Saurel, Pressure relaxation procedures for multiphase compressible flows, Inst. Natl. Rech. Inform. Autom. (INRIA), 2000.
URL : https://hal.archives-ouvertes.fr/inria-00072600

G. Layes, L. Metayer, and O. , Quantitative numerical and experimental studies of the shock accelerated heterogeneous bubbles motion, Phys. Fluids, vol.19, p.42105, 2007.

L. Martelot, S. Nkonga, B. Saurel, and R. , Liquid and liquid-gas flows at all speeds, J. Comput. Phys, vol.255, pp.53-82, 2013.

L. Martelot, S. Saurel, R. Nkonga, and B. , Towards the direct numerical simulation of nucleate boiling flows, Int. J. Multiphase Flow, vol.66, pp.62-78, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01313339

L. Metayer, O. Saurel, and R. , The Noble-Abel stiffened-gas equation of state, Phys. Fluids, vol.28, p.46102, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01305974

R. J. Leveque, Wave propagation algorithms for multidimensional hyperbolic systems, J. Comput. Phys, vol.131, pp.327-53, 1997.

R. J. Leveque, U. K. Cambridge, R. Loubere, M. Dumbser, and S. Diot, A new family of high order unstructured MOOD and ADER finite volume schemes for multidimensional systems of hyperbolic conservation laws, Commun. Comput. Phys, vol.16, pp.718-63, 2002.

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

J. Massoni, R. Saurel, B. Nkonga, and R. Abgrall, Some models and Eulerian methods for interface problems between compressible fluids with heat transfer, Int. J. Heat Mass Transf, vol.45, pp.1287-307, 2002.

J. Meng, Numerical simulation of droplet aerobreakup, Calif. Inst. Technol, 2016.

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/hal-00871724

S. Ndanou, N. Favrie, and S. Gavrilyuk, Multi-solid and multi-fluid diffuse interface model: applications to dynamic fracture and fragmentation, J. Comput. Phys, vol.295, pp.523-55, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01459183

E. Olsson, G. Kreiss, and S. Zahedi, A conservative level set method for two phase flow II, J. Comput. Phys, vol.225, pp.785-807, 2007.

S. Osher and F. Solomon, Upwind difference schemes for hyperbolic systems of conservation laws, Math. Comput, vol.38, pp.339-74, 1982.

G. Perigaud and R. Saurel, A compressible flow model with capillary effects, J. Comput. Phys, vol.209, pp.139-78, 2005.

F. Petitpas, E. Franquet, R. Saurel, and O. L. Metayer, A relaxation-projection method for compressible flows. Part II: artificial heat exchanges for multiphase shocks, J. Comput. Phys, 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

P. Roe, Approximate Riemann solvers, parameter vectors, and difference schemes, J. Comput. Phys, vol.43, pp.357-72, 1981.

D. Rossinelli, B. Hejazialhosseini, P. Hadjidoukas, C. Bekas, and A. Curioni, 11 PFLOP/s simulation of cloud cavitation collapse, Proc. Int. Conf. High Perform. Comput., Netw., Storage Anal, pp.17-21, 2013.

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 and R. Abgrall, A simple method for compressible multifluid flows, SIAM J. Sci. Comput, vol.21, pp.1115-1160, 1999.

R. Saurel, P. Boivin, L. Metayer, and O. , A general formulation for cavitating, boiling and evaporating flows, Comput. Fluids, vol.128, pp.53-64, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01277179

R. Saurel, A. Chinnayya, and Q. Carmouze, Modelling compressible dense and dilute two-phase flows, Phys. Fluids, vol.29, p.63301, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01454839

R. Saurel, E. Franquet, E. Daniel, L. Metayer, and O. , A relaxation-projection method for compressible flows. Part I: the numerical equation of state for the Euler equations, J. Comput. Phys, vol.223, pp.822-867, 2007.
URL : https://hal.archives-ouvertes.fr/hal-02101442

R. Saurel, S. Gavrilyuk, and F. Renaud, A multiphase model with internal degrees of freedom: application to shock-bubble interaction, J. Fluid Mech, vol.495, pp.283-321, 2003.

R. Saurel, L. Martelot, S. Tosello, R. Lapébie, and E. , Symmetric model of compressible granular mixtures with permeable interfaces, Phys. Fluids, vol.26, p.123304, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01459320

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.

. Fl50ch05-pantano, , vol.7, p.44, 2017.

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. Berry, Simple and efficient relaxation methods for interfaces separating compressible fluids, cavitating flows and shocks in multiphase mixtures, J. Comput. Phys, vol.228, pp.1678-712, 2009.

R. Scardovelli and S. Zaleski, Direct numerical simulation of free-surface and interfacial flow, Annu. Rev. Fluid Mech, vol.31, pp.567-603, 1999.

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

J. A. Sethian and P. Smereka, Level set methods for fluid interfaces, Annu. Rev. Fluid Mech, vol.35, pp.341-72, 2003.

C. W. Shu and S. Osher, Efficient implementation of essentially non-oscillatory shock-capturing schemes, J. Comput. Phys, vol.77, pp.439-71, 1988.

R. Shukla, Nonlinear preconditioning for efficient and accurate interface capturing in simulation of multicomponent compressible flows, J. Comput. Phys, vol.276, pp.508-548, 2014.

R. K. Shukla, C. Pantano, and J. B. Freund, An interface capturing method for the simulation of multi-phase compressible flows, J. Comput. Phys, vol.229, pp.7411-7450, 2010.

K. M. Shyue, An efficient shock-capturing algorithm for compressible multicomponent problems, J. Comput. Phys, vol.142, pp.208-250, 1998.

K. M. Shyue and X. F. , An Eulerian interface sharpening algorithm for compressible two-phase flow: the algebraic THINC approach, J. Comput. Phys, vol.268, pp.326-54, 2014.

V. Titarev and E. Toro, ADER: arbitrary high order Godunov approach, J. Sci. Comput, vol.17, pp.609-627, 2002.

A. Tiwari, J. Freund, and C. Pantano, A diffuse interface model with immiscibility preservation, J. Comput. Phys, vol.252, pp.290-309, 2013.

A. Tiwari, C. Pantano, and J. Freund, Growth-and-collapse dynamics of small bubble clusters near a wall, J. Fluid Mech, vol.775, pp.1-23, 2015.

S. Tokareva and E. Toro, HLLC-type Riemann solver for the Baer-Nunziato equations of compressible two-phase flow, J. Comput. Phys, vol.229, pp.3573-604, 2010.

E. Toro, Riemann Solvers and Numerical Methods for Fluid Dynamics: A Practical Introduction, Shock Waves, vol.4, pp.25-34, 1994.

B. Van-leer, Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov's method, J. Comput. Phys, vol.32, pp.101-137, 1979.

J. Von-neumann and R. Richtmyer, A method for the numerical calculation of hydrodynamic shocks, J. Appl. Phys, vol.21, pp.232-269, 1950.

A. B. Wood, A. Macmillan-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, 1930.

X. Zhang and C. W. Shu, Positivity-preserving high order finite difference WENO schemes for compressible Euler equations, J. Comput. Phys, vol.231, pp.2245-58, 2012.