A finite difference real ghost fluid method on moving meshes with corner-transport upwind interpolation

The real ghost fluid method (RGFM) [Wang CW, Liu TG, Khoo BC. A real-ghost fluid method for the simulation of multi-medium compressible flow. SIAM J Sci Comput 2006;28:278–302] has been shown to be more robust than previous versions of GFM for simulating multi-medium flow problems with large density and pressure jumps. In this paper, a finite difference RGFM is combined with adaptive moving meshes for one- and two-dimensional problems. A high resolution corner-transport upwind (CTU) method is used to interpolate approximate solutions from old quadrilateral meshes to new ones. Unlike the dimensional splitting interpolation, the CTU method takes into account the transport across corner points, which is physically more sensible. Several one- and two-dimensional examples with large density and pressure jumps are computed. The results show the present moving mesh method can effectively reduce the conservative errors produced by GFM and can increase the computational efficiency.