A combined finite volume discontinuous galerkin approach for the sharp-interface tracking in multi-phase flow

Abstract

In this paper, a numerical method for the simulation of compressible two-phase flows is presented. The multi-scale approach consists of several components that allow to sharply resolve the discontinuous nature of multi-phase flow: A discontinuous Galerkin solver for the macroscopic scales of the flow, a microscale Riemann solver at the interface that supplies the necessary interfacial jump conditions, a ghost-fluid based coupling of the interfacial conditions to the flow, and a level-set interface tracking formalism. To be able to locally guarantee a sharp and stable resolution at the interface, a finite volume technique on an adaptive subcell refinement is applied. The capabilities of the method are demonstrated for a three-dimensional shock-droplet interaction problem.