[1] D. Scheffler and J. Zukas، “Practical aspects of numerical simulations of dynamic events:Material interfaces”، Int. J. Impact Eng. 24(8), pp: 821–842، 2000.
[2] J. Pilliod and E. Puckett، “Second-order accurate Volume-of-Fluid algorithms for tracking material interfaces”، J. Comput.Phys. 199, pp: 465–502، 2004.
[3] J. A. Sethian. “Level Set Methods: Evolving Interfaces in Geometry، Fluid. Mechanics، Computer Vision and Material Science”.Cambridge University Press، 1996.
[4] S. Osher and R. Fedkiw. “Level set methods:An overview and some recent results”.J.Comput. Phys. 169(2) , pp: 463–502، 2001.
[5] S. Unverdi and G. Tryggvason. “A front tracking method for viscous incompressible flows”. J. Comput. Phys. 100, pp:25–37،1992.
[6] H. Terashima، G. Tryggvason. “A fronttracking/ ghost-fluid method for fluid interfaces in compressible flows”. J. Comput.Phys. 228, pp: 4012-4037, 2009.
[7] H. Terashima، G. Tryggvason. “A fronttracking method with projected interface conditions for compressible multi-fluid flows”. Computers & Fluids 39,pp:1804–1814,2010.
[8] J. Doneal، A. Huerta، J.P. Ponthot، and A.Rodriguez-Ferran. “Arbitrary Lagrangian- Eulerian Methods”. In E. Stein، R. de Borst، and T. J. Hughes، editors، Encyclopedia of Computational Mechanics، chapter 14. John Wiley & Sons،2004.
[9] H.R. Anbarlooei، K. Mazaheri. “Moment of fluid interface reconstruction method in multi-material arbitrary Lagrangian Eulerian (MMALE) algorithms”. Comput. Methods Appl. Mech. Engrg. 198, pp: 3782–3794, 2009.
[10] R. Saurel and O. Le Metayer. “A multiphase model for interfaces، shocks، detonation waves and cavitation”. J. Fluid Mech. 431, pp: 239–271، 2001.
[11] E. Johnsen، T. Colonius.” Implementation of WENO schemes in compressible multicomponent flow problems”. J. Comput. Phys. 219,pp:715–732,2006.
[12] S. Kawai. H. Terashima. “A high-resolution scheme for compressible multicomponent flows With shock waves”. Int. J. Numer. Meth. Fluids, 66(10), pp: 1207-1225, 2010.
[13] E.Johnsen. “Spurious oscillations and conservation errors in interface-capturing schemes”. Annual Research Briefs 2008،Center for Turbulence Research، NASA Ames and Stanford University; 115–126،
2008.
[14] C.-H. Chang، M.-S. Liou. “A robust and accurate approach to computing compressible multiphase flow: Stratified flow model and AUSM +-up scheme”. J. Comput. Phys. 225, pp: 840–873, 2007.
[15] R.Abgrall. “How to prevent pressure oscillations in multicomponent flow calculations: A quasi-conservative approach” . J. Comput. Phys. 125(1) , pp: 150–160،
1996.
[16] K.-M. Shyue. “An efficient shock-capturing algorithm for compressible multi- component problems”. J. Comp. Phys. 142, pp: 208–242،
1998.
[17] K.-M. Shyue. “A high-resolution mapped grid algorithm for compressible multiphase flow problems”. J. Comput. Phys. 229,pp: 8780–8801,2010.
[18] R. Saurel. R.Abgrall. “A multiphase Godunov method for compressbile multifluid and multiphase flows”. J. Comput. Phys. 150(2) , pp: 425–467، 1999.
[19] C.E.Castro ,E.F.Toro. “A Riemann solver and upwind methods for a two-phase flow model non-conservative form”، Int. J. Numer. Meth. Fluids, 50, pp: 275–307, 2006.
[20] S.T.Munkejord.” Comparison of Roe-type methods for solving the two-fluid model with and without pressure relaxation”، Computers & Fluids 36, pp: 1061–1080, 2007.
[21] S.T.Munkejord. “A Numerical Study of Two-Fluid Models with Pressure and Velocity Relaxation”، Adv. Appl. Math. Mech. 2, pp. 131-159, 2010.
[22] S.A.Tokareva,E.F.Toro . “HLLC-type Riemann solver for the Baer–Nunziato equations of compressible two-phase flow”،
Journal of Computational Physics 229, pp: 3573–3604, 2010.
[23] M.Dumbser,E.F. Toro, “A Simple Extension of the Osher Riemann Solver to Non-conservative Hyperbolic Systems”، J. Sci. Comput. DOI 10.1007/s10915-010-9400-3 ،
2010.
[24] R.Kapila، R. Menikoff، J. Bdzil، S. Son، and D. Stewart. “Two-phase modeling of DDT in granular materials: Reduced equations”. Phys. Fluid، 13, pp: 3002–3024، 2001.
[25] R. Saurel، F. Petitpas، and R. A. Berry. “Simple and efficient relaxation methods for interfaces separating compressible fluids، cavitating flows and shocks in multiphase mixtures”. J. Comput. Phys. 228(5), pp: 1678–1712، 2009.
[26] G. Allaire، S. Clerc، and S. Kokh. “A five-equation model for the simulation of interfaces between compressible fluids”. J. Comput. Phys. 181, pp: 577–616، 2002.
[27] Murrone and H. Guillard. “A five-equation reduced model for compressible two- phase flow problems”. J. Comput. Phys. 202(2), pp: 664–698، 2005.
[28] J.J. Kreeft، B. Koren. “A new formulation of Kapila’s five-equation model for compressible two-fluid flow، and its numerical treatment”. J. Comput. Phys. 229, pp: 6220–6242, 2010.
[29] S. Qamar، M. Ahmed. “A high order kinetic flux-vector splitting method for the reduced five-equation model of compressible two-fluid flows”. J. Comput. Phys.228, pp: 9059-9078, 2009.
[30] S. Koch، F. Lagoutière. “An anti-diffusive numerical scheme for the simulation of interfaces between compressible fluids by means of a five-equation model”. 229, pp: 2773-2809, 2010.
[31] M. Baer and J. Nunziato. “A two-phase mixture theory for the deflagration-to-detonation transition (DDT) in reactive granular materials.” Int. J. Multiphase Flows،12,pp:861–889، 1986.
[32] E. F. Toro. “Riemann Solvers and Numerical Methods for Fluid Dynamics”. Springer، Berlin، 1999.
[33] S. F. Davis. “Simplified second-order Godunov-type methods”. SIAM J. Sci. Statist.Comput. 9, pp: 445–473، 1998.
[34] J.F.Haas، B.Sturtevant، “Interaction of weak shock waves with cylindrical and spherical gas in homogeneities”، Journal of Fluid Mechanics 181, pp: 41-76, 1987.
[35] Marquina، P. Mulet. “A flux-split algorithm applied to conservative models for multicomponent compressible flows”. J. Comput. Phys. 185 120-138, 2003.
[36] J.J. Quirk، S. Karni، "On the dynamics of a shock-bubble interaction"، Journal of Fluid Mechanics 318, pp: 129–163, 1996.
[37] C. Wang، C.-W. Shu. “An interface treating technique for compressible multi-medium flow with Runge–Kutta discontinuous Galerkin method”. J. Comput. Phys. 229, pp: 8823–8843, 2010.
[38] J.W. Banks et al. “A high-resolution Godunov method for compressible multi-material flow on overlapping grids”. J. Comput. Phys. 223,pp: 262–297,2007.
[39] R.R. Nourgaliev، T.N. Dinh، T.G. Theofanous.”Adaptive characteristics-based matching for compressible multifluid dynamics”. J. Comput. Phys. 213, pp: 500–529, 2006.
[40] S.K. Sambasivan، H.S. UdayKumar. “Sharp interface simulations with Local Mesh Refinement for multi-material dynamics in strongly shocked flows”. Computers & Fluids 39, pp: 1456–1479, 2010.