A HLLC-type finite volume method for incompressible two-phase flows

A finite volume method based on the artificial compressibility scheme has been developed to simulate incompressible two-phase flows. In this method, the level set equation, used to capture the interface between two phases, is solved by coupling with the Navier-Stokes equations. The HLLC approximate Riemann solver, capable of resolving contact discontinuity accurately, is proposed to compute the intercell flux. In order to solve the interface flow accurately and efficiently, the high-order WENO reconstruction and the matrix-free implicit dual-time stepping method are applied in this study. Several classical cases, including a Rayleigh-Taylor instability problem, a broken dam problem and two bubble-rising problems are studied. The capability of the present scheme in simulating interface flows is validated by comparison with experimental data or reported results. (C) 2020 Elsevier Ltd. All rights reserved.