Efficient numerical approximation of compressible multi-material flow for unstructured meshes

We consider the numerical approximation of multi-dimensional multi-material flows. This is a difficult topic related to the numerical smearing of contact discontinuities (or material interfaces or slip lines). Any Eulerian scheme will produce an artificial mixing zone. In this artificial mixture, the computation of thermodynamical variables (pressure, sound speed, temperature, …) is difficult to achieve correctly. For the stiff cases considered in this paper, with solid-liquid-gas interfaces, small errors on the thermodynamical variables lead to the blow up of the computation in many cases. In this paper, we review and explain this problem, then we propose solutions for 1D and 2D flows. Contrarily to front-tracking techniques, our schemes use the same formulation everywhere on the mesh. We provide several examples with the stiffened gas equation of state (EOS): inert materials (water-air), and chemically reactive materials (solid explosive-Plexiglass-air).