A discontinuous Galerkin method for the simulation of compressible gas-gas and gas-water two-medium flows

In this paper, we develop a new discontinuous Galerkin method for the simulation of shocks and interfaces in compressible gas-gas and gas-water two-medium flows by solving the γ-based model. The spatial discretization is carefully designed to possess the following features: discrete conservation in terms of the total mass, total momentum and total energy; high-order accuracy and consistency for smooth flows; free of oscillations at an isolated material interface. In order to handle potential discontinuities arising in the simulation, a nonlinear limiter based on the weighted essentially non-oscillatory (WENO) strategy is employed to suppress numerical oscillations and to preserve high order of accuracy in regions of smooth flows. The WENO reconstruction is imposed on suitably selected quantities, rather than the conserved ones. In case for discontinuities with large pressure ratio, low density and dramatic change of material property where unphysical variables may be encountered, a posteriori solution correction on the subcell level is locally adopted to enhance the robustness. A series of typical test cases for both one- and two-dimensional problems are provided to demonstrate the performance of the proposed method.