Commun. Comput. Phys.,
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Volume 3.

Simulations of Compressible Two-Medium Flow by Runge-Kutta Discontinuous Galerkin Methods with the Ghost Fluid Method

Jianxian Qiu 1*, Tiegang Liu 2, Boo Cheong Khoo 3

1 Department of Mathematics, Nanjing University, Nanjing, Jiangsu 210093, China.
2 Institute of High Performance Computing, #01-01 The Capricorn, Singapore Science Park II, Singapore 117528, Singapore; and Department of Mathematics, Beijing University of Aeronautics and Astronautics, Beijing, China.
3 Department of Mechanical Engineering, National University of Singapore, Singapore 119260, Singapore; and Singapore-MIT Alliance, 4 Engineering Drive 3, National University of Singapore, Singapore 117576, Singapore.

Received 21 Mar 2007; Accepted (in revised version) 31 May 2007
Available online 23 October 2007


The original ghost fluid method (GFM) developed in \cite{FAMO} and the modified GFM (MGFM) in \cite{LKY3} 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.

AMS subject classifications: 65M60, 65M99, 35L65

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Key words: Runge-Kutta discontinuous Galerkin method, WENO scheme, ghost fluid method, approximate Riemann problem solver.

*Corresponding author.
Email: (J. Qiu), (T. Liu), (B. C. Khoo)

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