Tracking discontinuities in shallow water equations and ideal magnetohydrodynamics equations via ghost fluid method

  • Authors:

  • Li Cai;Jian-Hu Feng;Wen-Xian Xie;Jun Zhou

  • Affiliations:

  • College of Astronautics, Northwestern Polytechnical University, Shaanxi, PR China;College of Science Chang'an University, Shuanxi, PR China;School of Science Northwestern Polytechnical University, Shaanxi, PR China;College of Astronautics, Northwestern Polytechnical University, Shaanxi, PR China

  • Venue:
  • Applied Numerical Mathematics
  • Year:
  • 2006

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Abstract

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.