E. Franquet and V. Perrier, Runge???Kutta discontinuous Galerkin method for the approximation of Baer and Nunziato type multiphase models, Journal of Computational Physics, vol.231, issue.11
DOI : 10.1016/j.jcp.2012.02.002
URL : https://hal.archives-ouvertes.fr/hal-00684427

X. Zhang, Y. Xia, and C. Shu, Maximum-Principle-Satisfying and Positivity-Preserving High Order Discontinuous Galerkin Schemes for??Conservation Laws on Triangular Meshes, Journal of Scientific Computing, vol.229, issue.1, pp.29-62, 2012.
DOI : 10.1007/s10915-011-9472-8

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.457-4926236, 1999.
DOI : 10.1006/jcph.1999.6236

W. J. Rider and D. B. Kothe, Reconstructing Volume Tracking, Journal of Computational Physics, vol.141, issue.2, pp.112-1525906, 1998.
DOI : 10.1006/jcph.1998.5906
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.27.8649

T. Y. Hou and P. G. Lefloch, Why nonconservative schemes converge to wrong solutions: error analysis, Mathematics of Computation, vol.62, issue.206, pp.497-530, 1994.
DOI : 10.1090/S0025-5718-1994-1201068-0

C. Wang and C. Shu, An interface treating technique for compressible multi-medium flow with Runge???Kutta discontinuous Galerkin method, Journal of Computational Physics, vol.229, issue.23, 2010.
DOI : 10.1016/j.jcp.2010.08.012

S. Rhebergen, O. Bokhove, J. J. Van, and . Vegt, Discontinuous Galerkin finite element methods for hyperbolic nonconservative partial differential equations, Journal of Computational Physics, vol.227, issue.3, 2008.
DOI : 10.1016/j.jcp.2007.10.007
URL : http://doc.utwente.nl/62115/1/rhebergenBokhovevdVegt2008.pdf

M. Dumbser, A. Hidalgo, M. Castro, C. Parés, and E. F. Toro, FORCE schemes on unstructured meshes II: Non-conservative hyperbolic systems, Computer Methods in Applied Mechanics and Engineering, vol.199, issue.9-12, pp.9-12, 2010.
DOI : 10.1016/j.cma.2009.10.016
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.154.2589

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
DOI : 10.1016/S0021-9991(03)00011-1

M. Baer and J. Nunziato, A two-phase mixture theory for the deflagration-to-detonation transition (ddt) in reactive granular materials, International Journal of Multiphase Flow, vol.12, issue.6, pp.861-889, 1986.
DOI : 10.1016/0301-9322(86)90033-9

G. Dal-maso, P. G. Lefloch, and F. Murat, Definition and weak stability of nonconservative products, J. Math. Pures Appl, vol.74, issue.96, pp.483-548, 1995.

N. Andrianov and G. Warnecke, The Riemann problem for the Baer???Nunziato two-phase flow model, Journal of Computational Physics, vol.195, issue.2, pp.434-464, 2004.
DOI : 10.1016/j.jcp.2003.10.006

D. Drew and S. Passman, Theory of multicomponent fluids, of Applied Mathematical Sciences, 1999.
DOI : 10.1007/b97678

B. Cockburn and C. Shu, Runge-Kutta discontinuous Galerkin methods for convection-dominated problems, J. Sci. Comput, vol.16, issue.3, p.1012873910884, 2001.
DOI : 10.1007/978-3-662-03882-6_2

X. Zhang and C. Shu, On maximum-principle-satisfying high order schemes for scalar conservation laws, Journal of Computational Physics, vol.229, issue.9, 2010.
DOI : 10.1016/j.jcp.2009.12.030

X. Liu and S. Osher, Nonoscillatory High Order Accurate Self-Similar Maximum Principle Satisfying Shock Capturing Schemes I, SIAM Journal on Numerical Analysis, vol.33, issue.2, pp.760-779, 1996.
DOI : 10.1137/0733038
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.22.7962

A. Bermudez and M. E. Vazquez, Upwind methods for hyperbolic conservation laws with source terms, Computers & Fluids, vol.23, issue.8, pp.1049-107110, 1994.
DOI : 10.1016/0045-7930(94)90004-3

Y. Xing and C. Shu, High order well-balanced finite volume WENO schemes and discontinuous Galerkin methods for a class of hyperbolic systems with source terms, Journal of Computational Physics, vol.214, issue.2, 2006.
DOI : 10.1016/j.jcp.2005.10.005

S. T. Zalesak, Fully multidimensional flux-corrected transport algorithms for fluids, Journal of Computational Physics, vol.31, issue.3, pp.335-362, 1979.
DOI : 10.1016/0021-9991(79)90051-2