The simulation of compressible multi-fluid flows by a GRP-based energy-splitting method

Abstract

This paper serves to simulate compressible multi-fluid flows using an energy-splitting method based on the generalized Riemann problem (GRP) solver. The emphasis is put on two-dimensional problems to address the fundamental role of transversal effect in the construction of numerical fluxes, which exhibits the genuine multi-dimensionality of the underlying numerical schemes. In contrast with the popularly-used methods of line which use exact or approximate Riemann solvers, the GRP solver, as the discontinuous version of the Lax–Wendroff method, takes the temporal-spatial coupling process to include the transversal effect. Combined with the energy-splitting technique developed earlier in Lei and Li [24], the resolution of flow fields around material interfaces is improved significantly.