Piecewise parabolic method for compressible multi-fluid flows with van der Waals equation of state

In a compressible fluid-mixture model based on volume fraction, a high-order piecewise parabolic method (PPM) is employed to solve multi-fluid flows characterized by the van der Waals equation of state. A double shock approximation is used in the Riemann solver. Simulation on a pure interface problem indicates that the pressure and velocity profiles do not show any spurious oscillation at the contact discontinuity and the numerical diffusion is limited within two or three cell grids. It shows that the method deals with such physical problems as contact discontinuity, shock, multi-dimensional slip line efficiently.