A Numerical Method on Eulerian Grids for Two-Phase Compressible Flow (Advances in Applied Mathematics and Mechanics, 2018)
We develop a numerical method to simulate a two-phase compressible flowwith sharp phase interface on Eulerian grids. The scheme makes use of a level set todepict the phase interface numerically. The overall scheme is basically a finite volumescheme. By approximately solving a two-phase Riemann problem on the phase interface,the normal phase interface velocity and the pressure are obtained, which is usedto update the phase interface and calculate the numerical flux between the flows oftwo different phases. We adopt an aggregation algorithm to build cell patches aroundthe phase interface to remove the numerical instability due to the breakdown of theCFL constraint by the cell fragments given by the phase interface depicted using thelevel set function. The proposed scheme can handle problems with tangential slipingon the phase interface, topological change of the phase interface and extreme contrastin material parameters in a natural way. Though the perfect conservation of the mass,momentum and energy in global is not achieved, it can be quantitatively identified inwhat extent the global conservation is spoiled. Some numerical examples are presentedto validate the numerical method developed.