A robust WAF-HLL scheme for the compressible two-pressure two-velocity multiphase flow model

Abstract

In this paper we have developed a robust WAF-HLL scheme for the compressible two-pressure two-velocity six-equation two-fluid model by improving the earlier WAF-HLL scheme (Yeom and Chang, 2010b) that was also proposed by the authors. The earlier scheme has, however, shown spurious oscillations and instabilities across the shock wave for some severe two-phase flow problems because the WAF (Weighted Average Flux) procedure was applied to the single numerical flux that consists of the gas and the liquid phases. The main idea of the new WAF-HLL scheme is to split the numerical flux of the overall two-phase flow into two phasic components for the gas phase and the liquid phase before we apply the WAF procedure to each of the two phasic numerical fluxes. The present scheme has become numerically very robust as we have removed the oscillations. Furthermore, it makes use of the quadrilateral unstructured grid for more flexibility to deal with complex flow geometry. We demonstrate by solving several two-phase benchmark problems that the new WAF-HLL scheme is significantly more robust than the earlier WAF-HLL scheme, while having accuracy comparable to the earlier one.