Simulations of compressible two-medium flow by Runge-Kutta discontinuous Galerkin methods with ghost fluid method

Abstract

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 single medium 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 useful features from high resolution finite volume schemes, such as the exact or approximate Riemann solvers, TVD Runge-Kutta time discretizations, and limiters. In this paper, we investigate using RKDG finite element methods for two-medium flow simulations in one and two dimensions in which the moving material interfaces is treated via non-conservative methods based on the original GFM and MGFM. Numerical results for both gas-gas and gas-water flows are provided to show the characteristic behaviors of these combinations. © 2008 Global-Science Press.