Tracking discontinuities in shallow water equations and ideal magnetohydrodynamics equations via Ghost Fluid Method

Existing Ghost Fluid Method (GFM) works well for most gas flows but still leaves much room for further improvement in other applications. In the spirit of GFM, we propose a new GFM to track discontinuities in shallow water equations and ideal magnetohydrodynamics (MHD) equations: a new GFM is designed for tracking shock wave in shallow water equations; then the GFM is extended to treat contact discontinuity in ideal MHD equations where the interface moves with the entropy wave speed. In this paper, the zero contour of a level set function is used to specify the location of discontinuities, and the GFM implicitly captures the boundary conditions at the interface by the construction of a ghost fluid. The numerical results show the desired accuracy and robustness of our new GFM.