A Comparison Study of Numerical Methods for Compressible Two-Phase Flows (Advances in Applied Mathematics and Mechanics, 2018)
In this article a comparison study of the numerical methods for compressibletwo-phase flows is presented. Although many numerical methods have been developedin recent years to deal with the jump conditions at the fluid-fluid interfacesin compressible multiphase flows, there is a lack of a detailed comparison of thesemethods. With this regard, the transport five equation model, the modified ghost fluidmethod and the cut-cell method are investigated here as the typical methods in thisfield. A variety of numerical experiments are conducted to examine their performancein simulating inviscid compressible two-phase flows. Numerical experiments includeRichtmyer-Meshkov instability, interaction between a shock and a rectangle $SF_6$ bubble,Rayleigh collapse of a cylindrical gas bubble in water and shock-induced bubblecollapse, involving fluids with small or large density difference. Based on the numericalresults, the performance of the method is assessed by the convergence order of themethod with respect to interface position, mass conservation, interface resolution andcomputational efficiency.