Computation of Multiphase Mixture Flows using RoeM and AUSMPW+ Schemes

Abstract

RoeM[1] and AUSMPW+[2] schemes, originally developed for the robust and accurate simulation of single phase gas dynamics, are extended to the compressible gas-liquid two-phase flows. We adopted homogeneous equilibrium model(HEM) using mass fraction to describe different two phases. In the Eulerian-Eulerian framework, HEM assumes dynamic and thermal equilibrium of the two phases in the same computational mesh. We derived new pressure weighting function from the mixture equation of state(EOS) to construct the new shock discontinuity sensing term(SDST), which is commonly used in RoeM and AUSMPW+ for the stable numerical flux calculation. The developed two-phase versions of RoeM and AUSMPW+ are applied on several air-water two-phase test problems. In spite of the large discrepancy of material properties such as density, enthalpy, and speed of sound, the numerical results show that both schemes provide very satisfactory solutions.