Runge-Kutta Discontinuous Galerkin Method with Front Tracking Method for Solving the Compressible Two-Medium Flow on Unstructured Meshes (Advances in Applied Mathematics and Mechanics, 2018)
In this paper, we extend using the Runge-Kutta discontinuous Galerkinmethod together with the front tracking method to simulate the compressible two-mediumflow on unstructured meshes. A Riemann problem is constructed in the normaldirection in the material interfacial region, with the goal of obtaining a compact,robust and efficient procedure to track the explicit sharp interface precisely. Extensivenumerical tests including the gas-gas and gas-liquid flows are provided to show theproposed methodologies possess the capability of enhancing the resolutions nearbythe discontinuities inside of the single medium flow and the interfacial vicinities of thetwo-medium flow in many occasions.