An interface-sharpening method with adaptive mesh refinement for volume-of-fluid simulations of two-phase compressible flows

Abstract

We propose an interface-sharpening method for volume-of-fluid simulations of two-phase compressible flows. In the proposed method, sharpening of the interface between two phases is achieved by introducing a source term to the advection-reaction equation for the phase volume fraction. The inherent numerical diffusivity arising from the discretization of this equation is used to construct the source term. The resulting governing equations of the two-phase compressible flow are quasi-conservative and hyperbolic, with the phase volume fraction being bounded and free of spurious oscillations. The proposed method, called advection-reaction interface sharpening (ARIS), can be applied inline so that no post-processing of the phase volume fraction is required after each time step. The conservation equations for mass, momentum and energy are solved with a dimensional-splitting Monotone Upstream-centered Scheme for Conservation Laws (MUSCL). The interfacial resolution is improved by combining a fully-threaded-tree algorithm with adaptive mesh refinement. In validation tests performed on a variety of one- and two-dimensional benchmark flows, we find that ARIS can reduce the interface thickness to just three to four computational cells, improving the interfacial resolution without sacrificing computational efficiency. This study shows that ARIS can provide robust, quasi-conservative, oscillation-free and nearly sharp solutions of the phase volume fraction in various one- and two-dimensional interfacial flows, paving the way for extensions of this method to three-dimensional flows with more than two phases.