Extension of AUSM-type fluxes: from single-phase gas dynamics to multi-phase cryogenic flows at all speeds

Despite their simple formulations, advection upstream splitting method (AUSM)-type flux schemes treat linear and nonlinear waves of complex flow fields in a robust and accurate manner. This paper presents the progress of AUSM-type fluxes augmented with pressure-based weight functions introduced by the authors and their colleagues. Starting from a flux designed for single-phase gas dynamics (AUSMPW+), its extensions to capture multi-phase flow physics with phase transition (AUSMPW+_N) have been carried out. The accuracy of the computed results by the AUSMPW+_N scheme for multi-phase flows is then further improved by introducing a simple phase interface-sharpening procedure, which scales the volume fraction in a mass-conserving manner. Various all-speed compressible tests ranging from interactions between a shock and phase interfaces, two- and three-dimensional interface-only problems, to a cryogenic three-component flow with phase change are computed to demonstrate the effectiveness of the proposed method.