Explicit Solver for Large-Scale Incompressible Gas-Liquid Two-Phase Flow Simulations

Abstract

Incompressible flows have much lower flow speeds to compare with the sound speed and called low Mach number flows. So far, we have simulated incompressible flows by using semi-implicit solvers, in which we iteratively compute the linear equation derived from the pressure Poisson equation. In the case of incompressible gas-liquid two-phase flows, the sparse matrix would be very stiff with non-zero elements changing largely from the gas density to the liquid density at the interface. Even if we use a sophisticated Krylov sub-space iteration solver with the multi-grid preconditioner, the convergence becomes poor for large-scale problems. We have developed a weakly compressible gas-liquid two-phase solver based on fully-explicit time integration of compressible Navier-Stokes equation. For several benchmark problems, the results of the weakly compressible solver are in good agreement with those of the semi-implicit incompressible solver. Since the weakly compressible solver uses a local stencil access, it is possible to implement AMR (Adaptive Mesh Refinement) method with less programming cost. Fine meshes are assigned near the gas-liquid interface and we efficiently compute a liquid film generated by a spoon and a growing soap bubble with the AMR two-phase flow solver.