An improved HLLC-type solver for incompressible two-phase fluid flows

Abstract

In this paper, an HLLC-type contact preserving Riemann solver for incompressible two-phase flows using the artificial compressibility formulation is presented. This formulation is an improvement over the previous HLLC-VOF formulation (Bhat and Mandal, 2019). In this work, unlike the previous formulation, the variation of the volume fraction is taken into account when calculating the eigenvalues and eigenvectors. Hence, the equations for the intermediate states and the intermediate wave speed are closely-coupled with density variation during pseudo-time evolution of the solution. Additionally, an interface compression algorithm is used in tandem to ensure sharp interfaces. This modified Riemann solver (called HLLC-VOF-M) is found to be more robust and accurate compared to the older HLLC-VOF solver and the non-contact preserving HLL solver. Several test problems in two- and three-dimensions are solved to demonstrate and evaluate the efficacy of the solver on structured and unstructured meshes.