A finite volume WENO scheme for immiscible inviscid two-phase flows

Abstract

This article presents a two-phase finite volume (FV) method based on the concept of equilibrium volume fraction for simulating inviscid two-phase flows. A reduced three-equation hyperbolic system is adopted as the governing equations, which is closed with a barotropic equation of state for both phases. A modified weighted essentially non-oscillatory (WENO) scheme is proposed for reconstructing the fluid state at cell-interfaces, which can avoid strictly pressure or velocity oscillations near material interfaces in the test-case of the advection of an isolated interface, while retaining the convergence order of the WENO scheme in 1D and 2D cases. Besides, with the generalized Riemann invariants (GRI), the eigenstructure of the hyperbolic system is analyzed and an approximate Riemann flux solver is proposed based on the linearization of the GRI. The semi-discrete system is explicitly integrated in time by means of the classical 4th-order Runge-Kutta (RK4) scheme. The proposed scheme is validated in a series of two-phase test-cases, such as advection of a two-phase vortex, linear sloshing, long-time wave propagation and dam-break flows, for which good agreements are obtained with the references.