Practical Techniques in Ghost Fluid Method for Compressible Multi-Medium Flows (Communications in Computational Physics, 2018)
The modified ghost fluid method (MGFM), due to its reasonable treatmentfor ghost fluid state, has been shown to be robust and efficient when applied to compressiblemulti-medium flows. Other feasible definitions of the ghost fluid state, however,have yet to be systematically presented. By analyzing all possible wave structuresand relations for a multi-medium Riemann problem, we derive all the conditions to definethe ghost fluid state. Under these conditions, the solution in the real fluid regioncan be obtained exactly, regardless of the wave pattern in the ghost fluid region. Accordingto the analysis herein, a practical ghost fluid method (PGFM) is proposed tosimulate compressible multi-medium flows. In contrast with the MGFM where threedegrees of freedom at the interface are required to define the ghost fluid state, only onedegree of freedom is required in this treatment. However, when these methods provedcorrect in theory are used in computations for the multi-medium Riemann problem,numerical errors at the material interface may be inevitable. We show that these errorsare mainly induced by the single-medium numerical scheme in essence, rather thanthe ghost fluid method itself. Equipped with some density-correction techniques, thePGFM is found to be able to suppress these unphysical solutions dramatically.