Piecewise parabolic method for compressible multi-fluid flow with Mie-Grneisen equation of state

A compressible fluid-mixture model based on the volume fraction is introduced and a high-order piecewise parabolic method (PPM) is employed to solve the multi-fluid flow which are characterized by the Mie-Grneisen equation of state. The double shock approximation and two level iteration algorithm are used to solve the Riemann problem for general equation of state. A new high resolution scheme is proposed for the mixed type multi-fluid model, which satisfies the principle of oscillation-free for pressure and velocity near the interface between different fluids. For a pure interface problem, the proposed scheme is oscillation-free, and the numerical results also validate that there is no any spurious oscillation in the pressure as well as in velocity profiles on the contact discontinuity while numerical diffusion is limited in two or three cell grids, which is much better than state of the art algorithms. Some numerical experiments and comparisons are presented, and the numerical results show that the new method can simulate the complicated compressible multi-fluid problem such as high pressure ratio Riemann problem, shock-interface interaction and so on.