Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4646301 | Applied Numerical Mathematics | 2006 | 15 Pages |
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.