The singular limits of the Riemann solutions as pressure vanishes for a reduced two-phase mixtures model with non-isentropic gas state

Abstract

We study the cavitation and concentration phenomena of the Riemann solutions for a reduced two-phase mixtures model with non-isentropic gas state in vanishing pressure limit. We solve the Riemann problem by constructing the regions in (p, u, s) coordinate system. Then we obtain the limiting behaviors of the Riemann solutions and the formation of δ-shock waves and vacuum as pressure vanishes. We conclude that, as pressure vanishes, the limit of Riemann solutions is the Riemann solutions of the reduced 2-dimensional pressureless gas dynamics model. Finally, we present numerical simulations which are consistent with our theoretical analysis.