Comparison of Sharp and Diffuse Interface Methods for Radially Symmetric Compressible Multi-Medium Fluid Flows (Advances in Applied Mathematics and Mechanics, 2024)
The effects of non-physical mixing on interface development are still notreasonably evaluated when diffuse interface methods (DIMs) are employed to treatthe two-medium flows with immiscible interfaces, especially for compressible multi-medium flows with geometrical source terms. In this work, we simulate radially symmetric multi-medium flows employing the sharp interface methods (SIMs) and DIMsto evaluate their performance such as pressure dislocations, mass conservation, andconvergence. The $γ$-based model and the five-equation transport model are two common DIMs, which are extended to equations with geometrical source terms combinedwith discontinuous Galerkin (DG) methods. For the SIMs, we employ the classicalmodified ghost fluid method (MGFM) and its second-order extension (2nd-MGFM)developed recently. Numerical results exhibit that the 2nd-MGFM is more effective inmaintaining the interfacial pressure equilibrium relative to the MGFM. The DIMs canalways maintain the pressure continuity naturally and total mass conservation, whichis not available for SIMs. Further, under the premise of immiscible interfaces definedartificially, the DIMs cannot provide satisfactory single medium mass conservation,while the SIMs have a smaller mass error. In addition, compared to the other threemethods, the 2nd-MGFM has higher confidence for radially symmetric flows, matching the exact solution in sparser grids.