A Unified Algorithm for Interfacial Flows with Incompressible and Compressible Fluids

Abstract

AbstractThe majority of available numerical algorithms for interfacial two-phase flows either treat both fluid phases as incompressible (constant density) or treat both phases as compressible (variable density). This presents a limitation for the prediction of many two-phase flows, as treating both phases as compressible is computationally expensive due to the very stiff pressure–density–temperature coupling of liquids. A framework with the capability of treating one phase compressible and the other phase incompressible, therefore, has a significant potential to improve the computational performance and still capture all important physical mechanisms. We propose a numerical algorithm that can simulate interfacial flows in all Mach number regimes, from \(M=0\) to \(M > 1\), including interfacial flows in which compressible and incompressible fluids interact, within the same pressure-based framework and conservative finite-volume discretisation. For interfacial flows with only incompressible fluids or with only compressible fluids, the presented algorithm reduces to numerical frameworks that have already been presented in the literature. Representative test cases are used to validate the proposed algorithm, including mixed compressible–incompressible interfacial flows with acoustic waves, shock waves and rarefaction fans.