Runge-Kutta discontinuous Galerkin method with front tracking method for solving the compressible two-medium flow

The Runge-Kutta discontinuous Galerkin method together with the front tracking method for solving the compressible two-medium flow is presented. The fluid interface boundary condition is defined via a non-conservative method based on the real ghost fluid method. A Riemann problem is constructed in the normal direction of the interface, the corresponding Riemann solutions are used to determine the motion of the interface and obtain the ghost fluid states directly. Extensive numerical tests including the gas-gas and gas-liquid flows are provided to illustrate that the proposed methods possess the capability of enhancing the resolutions nearby the discontinuities in the single medium and material interfacial vicinities.