Shock jump relations for multiphase mixtures with stiff mechanical relaxation

Examples of multiphase mixtures for which velocity and pressure relaxation are a stiff phenomenon are involved in many practical applications dealing with condensed phase mixtures, solid alloys, propellants and solid explosives, specific composite materials, micro- and nano-structured mixtures, etc. Shock relations for the mixture necessitate the determination of the volume fraction jump or any other thermodynamic variable jump. Examination of the shock dispersion mechanism suggests such jump relations. These relations are the phase Hugoniots which are compatible with the mixture energy equation. The corresponding model is conservative and symmetric. It fulfils the single-phase limit and guarantees volume fraction positivity. The shock relations are validated over a large set of experimental data and provide a remarkable agreement. R. Saurel, O. Le Métayer, J. Massoni and S. Gavrilyuk also belong to INRIA SMASH Project.