Cell-centered Lagrange+Remap numerical strategy for a multi-material multi-velocity model

The present work is devoted to the numerical approximation of multi-material flows. The so-called 6-equation system is considered where each material has its own velocity but shares the same pressure with the rest of the mixture. This model is a necessary building block as dissipation is completely removed outside of shocks. A numerical scheme is then presented and extends the classical “Lagrange+Remap” strategy to a multi-velocity setting. Entropy considerations are the focal point of its derivation as a mean of stabilizing results, ensuring thermodynamical consistency and selecting shocks of interest. Finally the scheme’s robustness and ability to deal with the inner stiffness of contrasted mixtures are evaluated on several test cases.