R. Abgrall and R. Saurel, Discrete equations for physical and numerical compressible multiphase mixtures, Journal of Computational Physics, vol.186, issue.2, pp.361-396, 2003.

R. Abgrall, H. Beaugendre, and C. Dobrzynski, An immersed boundary method using unstructured anisotropic mesh adaptation combined with level-sets and penalization techniques, Journal of Computational Physics, vol.257, pp.83-101, 2014.
URL : https://hal.archives-ouvertes.fr/hal-00786853

G. Allaire, S. Clerc, and S. Kokh, A five-equation model for the simulation of the interfaces beween compressible fluids, Journal of Compuational Physics, vol.181, issue.2, pp.577-616, 2002.

A. Ambroso, C. Chalons, and P. A. Raviart, A Godunov-type method for the seven-equation model of compressible two-phase flow, Computers & Fluids, vol.54, pp.67-91, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00517375

T. B. Anderson and R. Jackson, Fluid mechanical description of fluidized beds. Equation of motion, Industrial & Engineering Chemistry Fundamentals, vol.6, issue.4, pp.527-539, 1967.

M. Baer and J. W. Nunziato, A two-phase mixture theory for the deflagration-to-detonation transition (DDT) in reactive granular materials, Internation Journal of Multiphase Flow, vol.12, issue.6, pp.861-889, 1986.

D. Balsara, A two-dimensinal HLLC Riemann solver for conservation laws: Application to Euler and magnetohydrodynamic flos, Journal of Computational Physcis, vol.231, issue.22, pp.7476-7503, 2012.

N. Barral and F. Alauzet, Three-dimensional CFD simulations with large displacement of the geometries using a connectivity-change moving mesh approach, Engineering with Computers, pp.1-26, 2018.

T. Barth and D. Jespersen, The disgn and application of upwind schemes on unnstructured meshes, 27th Aerospace sciences meeting, p.366, 1989.

J. Baum, H. Luo, and R. Loehner, A new ALE adaptative unstructured methodology for the simulation of the moving bodies, 32nd Aerospace Sciences Meeting and Exhibit, p.414, 1994.

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

M. J. Berger and P. Colella, Local adaptative mesh refinement for shock hydrodynamics, Journal of Computational Phsycis, vol.82, issue.1, pp.64-84, 1989.

R. R. Bernecker and D. Price, Studies in the transition from deflagration to detonation in granular explosives-II. Transitional characteristics and mechanisms observed in 91/9 RDX/Wax, Combustion and Flame, vol.22, issue.1, pp.119-129, 1974.

F. Bouchut, S. Jin, and X. Li, Numerical approximations of pressureless and isothermal gas dynamics, 2003.

, SIAM Journal on Numerical Analysis, vol.41, issue.1, pp.135-158

J. U. Brackbill, D. B. Kothe, and C. Zemach, A continuum method for modeling surface tension, Journal of Computational Physics, vol.100, issue.2, pp.335-354, 1992.

Q. Carmouze, F. Fraysse, R. Saurel, and B. Nkonga, Coupling rigid bodies motion with single phase and two-phase compressible flows on unstructured meshes, Journal of Computational Physics, vol.375, pp.1314-1338, 2018.
URL : https://hal.archives-ouvertes.fr/hal-02082701

A. Chiapolino and R. Saurel, Extended Noble-Able-Stiffened-Gas equation of state for sub-andsupercritical liquid-gas systems far from the critical point, Fluids, vol.3, issue.3, p.48, 2018.

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

A. Chiapolino, R. Saurel, and B. Nkonga, Sharpening diffuse interfaces with compressible fluids on unstrutured meshes, Journal of Computational Physics, vol.340, pp.389-417, 2017.

A. Chinnayya, E. Daniel, and R. Saurel, Modeling detonation waves in heterogeneous energetic materials, Journal of Computational Physics, vol.196, issue.2, pp.490-538, 2004.

R. Clift and W. H. Gauvin, Motion of entrained particles in gas stream, The Canadian Journal of Chemical Engineering, vol.49, issue.4, pp.439-448, 1971.

S. Davis, Simplified second-order Godunov-type methods, SIAM Journal on Scientific and Statistical Computing, vol.9, issue.3, pp.445-473, 1988.

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.

J. M. Delhaye and J. L. Achard, On the averaging operators introduced in two-phase flow modeling, Proceedings CSNI Specialist Meeting in transient two-phase flow, vol.1, pp.5-84, 1976.

D. A. Drew and S. L. Passman, Theory of multicomponent fluids, p.135, 2006.

S. Ergun, Fluid flow through packed columns, Chemical Engineering Progress, vol.48, pp.89-94, 1952.

C. Farhat, J. F. Gerbeau, and A. Rallu, FIVER: A finite volume method based on exact two-phase Riemann problems and sparse grids for multi-material flows with large density jumps, Journal of Computational Physics, vol.231, issue.19, pp.6360-6379, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00703493

C. Farhat, M. Lesoinne, P. Letallec, K. Pierson, and D. Rixen, FETI-DP: a dual-primal unified FETI method -parti I: A faster alternative to the two-level FETI method, International Journal for Numerical Methods in Engineering, vol.50, issue.7, pp.1523-1544, 2001.

C. Farhat, A. Rallu, and S. Shankaran, A higher-order generalized ghost fluid method for the poor for the three-dimensional two-phase flow computation of underwater implosion, Journal of Computational Physics, vol.227, issue.16, pp.7674-7700, 2008.

R. P. Fedkiw, T. Aslam, B. Merriman, and S. Osher, A non-oscillatory Eulerian approach to interfaces in multimaterial flows (the Ghost Fluid method), Journal of Computational Physics, vol.152, issue.2, pp.457-492, 1999.

A. Forestier and P. Le-floch, Multivalued solutions to some non-linear and non-strictly hyperbolic systems, Japan Journal of Industrial and Applied Mathematics, vol.9, issue.1, p.1, 1992.

. Frost, Jet formation during explosive particle dispersal, Proceedings of the 21st International Symposium on Military Aspects of Blast and Shocks, 2004.

D. Furfaro and R. Saurel, A simple HLLC-type Riemann solver for compressible non-equilibrium twophase flows, Computers & Fluids, vol.111, pp.159-178, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01278892

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.

J. M. Ghidaglia, A. Kumbaro, and G. Le-coq, On the numerical solution to two fluid models via cell centered finite volume method, European Journal of Mechanics-B/Fluids, vol.20, issue.6, pp.841-867, 2001.

J. Glimm, J. Grove, X. Li, Y. Zeng, and Q. Zhang, Three-dimensional front tracking, SIAM Journal of Scientific Computing, vol.19, pp.703-730, 1998.

S. Godunov, A difference method for numerical calculation of discontinuous solution of the equation of hydrodynamics, Matematicheskii Sbomik, vol.89, issue.3, pp.271-306, 1959.

S. Godunov, On approximations for overdetermined hyperbolic equations, Hyperbolic Problems: Theory, Numerics, Appplications, pp.19-33, 2008.

R. W. Houim and E. S. Oran, A multiphase model for compressible granular-gaseous flows: formulation and initial tests, Journal of Fluid Mechanics, vol.789, pp.166-220, 2016.

A. K. Kapila, R. Menikoff, J. B. Bdzil, S. F. Son, and D. S. Stewart, Two-phase modeling of deflagrationto-detonation transition in granular materials: reduced equation, Physics of Fluids, vol.13, issue.10, pp.3002-3024, 2001.

M. H. Lallemand and R. Saurel, Pressure relaxation procedures for multiphase compressible flows, 2000.
URL : https://hal.archives-ouvertes.fr/inria-00072600

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

L. Métayer, O. Saurel, and R. , The Noble-Abel stiffened-gas equation of state, Physics of Fluids, vol.28, issue.4, p.46102, 2016.

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

D. Lhuillier, C. H. Change, and T. G. Theofanous, On the quest for a hyperbolic effective-field model of disperse flows, Journal of Fluid Mechanics, vol.731, pp.184-194, 2013.

S. Li, An HLLC Riemann solver for magneto-hydrodynamics, Journal of Computational Physics, vol.203, issue.1, pp.344-357, 2005.

T. Linde, A practical, general-purpose, two-state HLL Riemann solver for hyperbolic conservation laws, International Journal for Numerical Methods in Fluids, vol.40, issue.3-4, pp.391-402, 2002.

T. G. Liu, J. Y. Ho, B. C. Khoo, and A. W. Chowdhury, Numerical simulation of fluid structure interaction using modified ghost fluid method and Naviers equations, Journal of Scientific Computing, vol.36, issue.1, pp.45-68, 2008.

T. G. Liu, B. C. Khoo, and W. F. Xie, The modified ghost fluid method as applied to extreme fluid-structure interaction in the presence of cavitation, Communications in Compuational Physics, vol.1, issue.5, pp.898-919, 2006.

T. G. Liu, B. C. Khoo, and K. S. Yeo, Ghost fluid method for strong shock impacting on material interface, Journal of Compuationel Physics, vol.190, issue.2, pp.651-681, 2003.

F. Marble, Dynamics of a gas containing small solid particles, Combustion and Propulsion (5th AGARD Colloquium), p.175, 1963.

J. Massoni, R. Saurel, B. Nkonga, and R. Abgrall, Proposition de méthodes et modèles eulériens pour les problèmes à interfaces entre fluides compressibles en présence de transfert de chaleur: some models and Eulerian methods for interface problems between compressible fluids with heat transfer, Internation Journal of Heat and Mass Transfer, vol.45, issue.6, pp.1287-1307, 2002.

T. Mcgrath, J. S. Clair, and S. Balachandar, Modeling compressible multiphase flows with dispersed particules in both dense and dilute regimes, Shock Waves, vol.28, issue.3, pp.533-544, 2018.

A. Milne, C. Parrish, and I. Worland, Dynamic fragmentation of blast mitigants, Shock Waves, vol.20, pp.41-51, 2010.

T. Miyoshi and K. Kusano, A multi-state HLL approximate Riemann solver for ideal magnetohydrodynamics, Journal of Computational Physics, vol.208, issue.1, pp.315-344, 2005.

B. Muralidharan and S. Menon, Simulation of moving boundaries interacting with compressible reacting flows using a second-order adaptative Cartesian cut-cell method, Journal of Computational Physics, vol.357, pp.230-262, 2018.

B. Nkonga and H. Guillard, Godunov type method on non-structured meshes for three-dimensional moving boundary problems, Computer Methods in Applied Mechanics and Engineering, vol.113, issue.1-2, pp.183-204, 1994.
URL : https://hal.archives-ouvertes.fr/inria-00074789

B. Nkonga, On the conservative and accurate CFD approximations for moving meshes and moving boundaries, Computer Methods in Applied Mechanics and Engineering, vol.190, pp.1801-1825, 2000.
URL : https://hal.archives-ouvertes.fr/hal-01313354

E. Olsson, G. Kreiss, and S. Zahedi, A conservative level set method for two phase flow II, Journal of Computational Physics, vol.225, pp.785-807, 2007.

A. N. Osnes, M. Vartdal, and B. P. Reif, Numerical simulation of particle jet formation induced by shock wave acceleration in a Hele-Shaw cell, Shock Waves, vol.28, issue.3, pp.451-461, 2018.

C. Parrish and I. Worland, Dynamic jet formation from mitigation materials, Proceeding of the 21st International Symposium on Military Aspects of Blast and Shocks, 2004.

G. Perigaud and R. Saurel, A compressible flow model with capillary effects, Journal of Compuational Physics, vol.209, issue.1, pp.139-178, 2005.

F. Petitpas, R. Saurel, E. Franquet, and A. Chinnayya, Modelling detonation waves in condensed energetic materials: Multiphase CJ conditions and multidimensional compuations, Shock Waves, vol.19, issue.5, pp.377-401, 2009.

V. Rodriguez, R. Saurel, G. Jourdan, and L. Houas, Solid-particle jet formation under shock-wave acceleration, Physical Review E, vol.88, issue.6, p.63011, 2013.
URL : https://hal.archives-ouvertes.fr/hal-01459462

E. Romenski and E. F. Toro, Compressible two-phase flows: two-pressure models and numerical methods, Computational Fluid Dynamics J, vol.13, pp.403-416, 2004.

T. L. Rossi, Détermination de la caractérisation "chef" en milieu scientifique, Journal des Pébrons, issue.5, pp.0-1, 2019.

V. Rusanov, The calculation of the interaction of non-stationary shock waves and obstacles, USSR Computational Mathematics and Mathematical Physics, vol.1, issue.2, pp.304-320, 1962.

R. Saurel and R. Abgrall, A multiphase Godunov method for compressible multifluid and multiphase flows, Journal of Compuational Physics, vol.150, issue.2, pp.425-467, 1999.

R. Saurel and C. Pantano-rubio, Diffuse interface capturing methods for compressible two-phase flow, Annual Review of Fluid Mechanics, vol.50, issue.1, pp.105-130, 2018.

R. Saurel, P. Boivin, and O. Le-métayer, A general formulation for caviting, boiling and evaporating flows, Computers & Fluids, vol.128, pp.53-64, 2016.

R. Saurel, A. Chinnayya, and Q. Carmouze, Modeling compressible dense and dilute two-phase flows, Physics of Fluids, vol.29, issue.6, p.63301, 2017.

R. Saurel, E. Daniel, and J. C. Loraud, Two-phase flows-second-order schemes and boundary conditions, AIAA Journal, vol.32, issue.6, pp.1214-1221, 1994.

R. Saurel, N. Favrie, F. Petitpas, M. H. Lallemand, and S. Gavrilyuk, Modelling dynamic and irreversible powder compaction, Journal of Fluid Mechanics, vol.664, pp.348-396, 2010.
URL : https://hal.archives-ouvertes.fr/hal-01443539

R. Saurel, E. Franquet, E. Daniel, and O. Le-métayer, A relaxation-projection method for compressible flows. Part I: The numerical equation of state for the Euler equations, Journal of Computational Physics, vol.223, issue.2, pp.822-845, 2007.
URL : https://hal.archives-ouvertes.fr/hal-02101442

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

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.

R. Saurel, S. Le-martelot, R. Tosello, and E. Lapebie, Symmetric model of compressible granular mixtures with permeable interfaces, Physics of Fluids, vol.26, issue.12, p.123304, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01459320

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.

J. Shewchuk, Delaunay refinement algorithms for triangular mesh generation, Computational Geometry, vol.22, issue.1-3, pp.21-74, 2002.

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

P. Sweby, High resolution schemes using flux limiters for hyperbolic conservation laws, SIAM Journal on Numerical Analysis, vol.21, issue.5, pp.995-1011, 1984.

E. Toro, Riemann solvers and numerical methods for fluid dynamics. A practical introduction, 2009.

E. F. Toro, M. Spruce, and W. Speares, Restoration of the contact surface in the HLL-Riemann solver, Shock Waves, vol.4, issue.1, pp.25-34, 1994.

B. Van-leer, Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov's method, Journal of Computational Physics, vol.32, issue.1, pp.101-136, 1979.

C. W. Wang, T. G. Liu, and B. C. Khoo, A real ghost fluid method for the simulationof multimedium compressible flow, SIAM Journal on Scientific Computing, vol.28, issue.1, pp.278-302, 2006.

K. Wang, A. Rallu, J. F. Gerbeau, and C. Farhat, Algorithms for interface treatment and load computation in embedded boundary methods for fluid and fluid-structure interaction problems, International Journal for Numerical Methods in Fluids, vol.67, issue.9, pp.1175-1206, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00651118

A. Wood, A Textbook of Sound, 1930.

P. Woodward and P. Colella, The Numerical Simulation of Two-Dimensional Fluid with Strong Shocks, Journal of Computational Physics, vol.54, pp.115-173, 1984.

K. Xue, K. Du, X. Shi, Y. Gan, and C. Bai, Dual hierarchical particle jetting of a particle ring undergoing radial explosion, Soft Matter, vol.14, p.4422, 2018.

D. Youngs, An interface tracking method for a 3D Eulerian hydrodynamics code, Atomic Weapons Research Establishment (AWRE) Technical Report, p.35, 1984.

S. Zalesak, Fully multidimensional flux-corrected transport algorithms for fluids, Journal of Computational Physics, vol.31, issue.3, pp.335-362, 1979.

Y. Zeldovich, Gravitational instability: An approximate theory for large density perturbations, Astronomy and Astrophysics, vol.5, pp.84-89, 1970.

X. Zeng and C. Farhat, A systematic approach for constructing higher-order immersed boundary and ghost fluid methods for fluid-structure interaction problems, Journal of Computational Physics, vol.231, issue.7, pp.2892-2923, 2012.

F. Zhang, D. L. Frost, P. A. Thibault, and S. B. Murray, Explosive dispersal of solid particles, Shock Waves, vol.10, pp.431-443, 2001.