The kinetic theory based gas-dynamical computational scheme, due to Prendergast and Xu, is generalized to the case of inhomogeneous materials consisting of initially spatially separated materials of different densities and temperatures. The Bhatnagar–Gross– Krook model of the Boltzmann equation is generalized to the case of two mass species. Cells in a finite volume representation are updated by means of fluxes across boundaries with adjacent cells in such a way as to satisfy the local conservation laws but to include viscous and thermally conducting effects. Applications to several test problems are given for the two-dimensional case. High Mach number shocks can be treated with the techniques developed.
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Kotelnikov et al. (1997) studied this question.
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