Summary: The original ghost fluid method (GFM) developed by R. P. Fedkiw, T. Aslam, B. Merriman and S. Osher [J. Comput. Phys. 152, No. 2, 475–492 (1999; Zbl 0957.76052)] and the modified GFM (MGFM) developed by T. G. Liu, B. C. Khoo and K. S. Yeo [J. Comput. Phys. 190, No. 2, 651–681 (2003; Zbl 1076.76592)] 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 are treated via nonconservative 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.