Assessment of Two Versions of Ghost Fluid Method for 2D Multi-Medium Compressible Flow

The main difficulty in computing multi-medium flow is how to treat the medium interface. The recently developed ghost fluid method (GFM) [1], which is implemented in conjunction with the level set method, provides unified computation of multi-medium flow without tracking the interface explicitly (here the original GFM in [1] is denoted as OGFM). The appealing features of GFM are its unified treatment of the whole flowfield, easy extension to multi-dimensions and maintenance of a relatively sharp interface without smearing. While OGFM could simulate some simple gas-gas flows, it encountered difficulties in computing gas-liquid flow because of breakdown of computation caused by the sensitivity of pressure to the variation of water density. Fedkiw et al made slight modification to his OGFM which used the normal velocity from the more stiffened and the pressure from the less stiffened as the interface velocity and pressure, respectively (this version is denoted as NGFM). However, it could only compute some simple gas-liquid flows. It was still problematic in computing shock-interface interaction problems in gas-liquid flows. Liu et al [2] developed a modified version of GFM which used a ghost fluid status provided by solving approximate Riemann problem (denoted as MGFM). More recently, Wang et al [3] further proposed a version named RGFM which defines both the real fluid next to the interface and the ghost fluid using solutions of a different set of approximate Riemann problem. In this paper, we assess MGFM and RGFM in one and two dimensional cases and revisit the technique to define the ghost fluid. The spatial discretization for the Euler equations is Harten’s second order TVD scheme and the WENO scheme. The computational effects associated with different sets of approximate Riemann problems are demonstrated for several 2D multi-medium flow problems, including air-helium shock interaction [1], underwater explosion, and underwater gas jet flow.