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.