Contact preserving Riemann solver for incompressible two-phase flows

Abstract

In numerical simulation of multi-fluid flows, it is very crucial to accurately capture the interface separating the fluids, which has the properties of a contact wave. Since HLLC (Harten Lax van-Leer with contact) formulation has the ability to model contact waves exactly, a novel HLLC-type Riemann solver is proposed for calculation of convective flux in a system where the incompressible-Navier–Stokes equations are tightly coupled with the volume of fluid (VOF) equation. The efficacy of the new formulation is evaluated by solving various standard test problems involving two-fluid flows.