Exact and approximate Riemann solvers at phase boundaries

Abstract

We present an exact as well as two new approximate Riemann solvers for phase boundaries in compressible multiphase flow without mass transfer governed by the Euler equations. These Riemann solvers are designed for the simulation of compressible tow-phase flow in the framework of a sharp interface approach. The focus lies thereby on the accuracy as well as on the computational efficiency of the Riemann solvers. Furthermore, the approximate Riemann solvers are suitable for general equations of state, which do not have to be given in a closed analytical form and can include surface tension effects at the phase boundaries. Numerical tests in the form of two-phase shock-tube problems and droplet-shock interactions conclude the presentation.