Abstract
A weakly compressible scheme for low-Mach number gas-liquid two-phase flows have been developed for a fullexplicit time integration to avoid solving Poisson equation. We introduce the fractional splitting method and directional splitting method to solve Euler equation which an efficient semi-Lagrangian scheme is applicable to. To describe the gas-liquid interface the conservative Allen-Cahn equation, which is one of the phase-field models, combined with the continuum equation is introduces. The accuracy of numerical results of two-phase flow strongly depends on the mesh resolution near the interface. The AMR (Adaptive Mesh Refinement) method greatly reduces the computational cost, since it is possible to assign high-resolution mesh to the region around the moving interface. We have developed a code to solve the equation in a manner of the tree-based AMR. Fractional step method and the directional splitting method helps to reduce the implementation difficulties of AMR method. We successfully carried out some violent two-phase flow simulation and flow including very thin liquid film by using the method which is combined weakly compressible scheme with AMR method.
