Compressible solver for two-phase flows with sharp interface and capillary effects preserving accuracy in the low Mach regime

Abstract

We present a sharp interface approach for compressible two-phase flows that preserves its accuracy in the low Mach regime. The interface between both fluids is captured by a Level Set function via the Ghost Fluid method. In the low Mach regime, classic Finite Volume compressible solvers lose accuracy on quadrangle or hexahedral meshes and a low Mach correction is then necessary to reduce the numerical dissipation. The sharp interface that separates both fluids, may induce an important jump in the medium properties that induces additional challenges for the design of a numerical scheme. Indeed, the well-known low Mach fixes in the literature could lead to significant truncation errors when the flow involves large density and sound speed ratios between both phases. To preserve the accuracy of the numerical method, we propose a specific low Mach fix for this interface problem that yields a uniform truncation error with respect to the Mach number. Numerical results show significant evidances of the efficiency and accuracy of the proposed low Mach correction.