Runge-Kutta discontinuous Galerkin methods for compressible two-medium flow simulations: One-dimensional case

The Runge-Kutta discontinuous Galerkin (RKDG) method for solving hyperbolic conservation laws is a high order finite element method, which utilizes 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 the RKDG finite element method for compressible two-medium flow simulation with conservative treatment of the moving material interfaces. Numerical results for both gas-gas and gas-water flows in one-dimension are provided to demonstrate the characteristic behavior of this approach.

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