A GRP-based high resolution ghost fluid method for compressible multi-medium fluid flows I: One-dimensional case

Abstract

This paper proposes a generalized Riemann problem (GRP)-based high resolution ghost fluid method (GFM) for the simulation of 1-D multi-medium compressible fluid flows. A kind of linearly distributed ghost fluid states is defined via a local double-medium generalized Riemann problem (GRP) at the material interface. The advantages of the GRP-based GFM over the RP-based GFM (MGFM) are reflected in the following aspects: (i) The GRP-based GFM can maintain the continuity of the material derivatives of the pressure across material interfaces, so that the pressure mismatch in the RP-based GFM (MGFM) can be eliminated dramatically, even for long time computation. (ii) The initial data for the associated Riemann problem of the local double-medium GRP are second-order approximation for the fluid states at material interfaces, and the initial data for the local double-medium GRP are also second-order approximation for the fluid states near material interfaces, so that the numerical accuracy are increased greatly. (iii) The GRP-based GFM can reflect the thermodynamical properties of different mediums, which have fundamental importance for the study of compressible fluid flow, so that the overheating errors in the RP-based GFM (MGFM) can be suppressed. Several typical numerical examples display the excellent performance of our new method.