Simulating compressible two-phase flows with sharp-interface discontinuous Galerkin methods based on ghost fluid method and cut cell scheme

Abstract

A sharp-interface Runge-Kutta discontinuous Galerkin method with the combination of Ghost Fluid Method and Cut Cell approach is developed to simulate compressible two-medium flows with free interfaces. In this approach, the material interface is explicitly described by a simple cut line, and is implicitly evolved with Level Set method. Around the small cells which appear when the regular cells are passed by the interface, some ghost fluids are stored in these cells. The small cells are updated by an improved real-ghost mixing method to avoid the complicated cell-merge approach and the topological change difficulty encountered in our previous work. Under the DG frame, the improved mixing method can avoid the excessive numerical dissipation which is caused by the original mixing method presented in the previous work. The Runge-Kutta discontinuous Galerkin method is applied to calculate the flow field, and the HLL-type approximate Riemann solver is applied for the face flux. The adaptive mesh refinement technology is also adapted to reduce computing costs. Various numerical examples are tested to show the robustness and capability of the presented method.