Simulations of Compressible Two-Medium Flow by Runge-Kutta Discontinuous Galerkin Methods with the Ghost Fluid Method (Communications in Computational Physics, 2018)
The original ghost fluid method (GFM) developed in [13] and the modified GFM (MGFM) in [26] have provided a simple and yet flexible way to treat two-medium flow problems. The original GFM and MGFM make the material interface”invisible” during computations and the calculations are carried out as for a singlemedium such that its extension to multi-dimensions becomes fairly straightforward.The Runge-Kutta discontinuous Galerkin (RKDG) method for solving hyperbolic conservation laws is a high order accurate finite element method employing the usefulfeatures from high resolution finite volume schemes, such as the exact or approximateRiemann solvers, TVD Runge-Kutta time discretizations, and limiters. In this paper,we investigate using RKDG finite element methods for two-medium flow simulationsin one and two dimensions in which the moving material interfaces are treated via nonconservative methods based on the original GFM and MGFM. Numerical results forboth gas-gas and gas-water flows are provided to show the characteristic behaviors ofthese combinations.