A Comparison Study of Numerical Methods for Compressible Two-Phase Flows

Abstract

In this article a comparison study of the numerical methods for compressible two-phase flows is presented. Although many numerical methods have been developed in recent years to deal with the jump conditions at the fluid-fluid interfaces in compressible multiphase flows, there is a lack of a detailed comparison of these methods. With this regard, the transport five equation model, the modified ghost fluid method and the cut-cell method are investigated here as the typical methods in this field. A variety of numerical experiments are conducted to examine their performance in simulating inviscid compressible two-phase flows. Numerical experiments include Richtmyer-Meshkov instability, interaction between a shock and a rectangle SF6 bubble, Rayleigh collapse of a cylindrical gas bubble in water and shock-induced bubble collapse, involving fluids with small or large density difference. Based on the numerical results, the performance of the method is assessed by the convergence order of the method with respect to interface position, mass conservation, interface resolution and computational efficiency.

A simplified lattice Boltzmann flux solver for multiphase flows with large density ratio

“…Multiphase flows have drawn more and more attentions due to their crucial role in the nature and engineering applications 1,2 . Apart from the experimental methods, 3 numerical study is an alternative way to explore the mechanism of the multiphase problems considering its low cost and great convenience 4 . To simulate complex multiphase flows, researchers have proposed many numerical methods, including volume of fluid model, 5 level set method, 6 front tracking approach 7 and the diffuse interface theory 8 .…”