Gas-liquid two-phase flows simulation based on weakly compressible scheme with interface-adapted AMR method

Abstract

A weakly compressible scheme using the interface-adapted adaptive mesh refinement (AMR) method is proposed for simulating low Mach number gas-liquid two-phase flows in large-scale and high-resolution simulations. A pressure evolution equation is derived from the iso-thermal process and low-Mach-number assumptions. We solve the Navier-Stokes equation and the pressure equation explicitly including acoustic waves. In the conventional semi-implicit method to solve incompressible two-phase flows, the computational cost of the linear solver increases as the problem size becomes larger. The conservative phase-field equation was solved using the finite volume method (FVM) to capture the gas-liquid interface while conserving the total mass of each phase. We developed GPU code for a tree-based AMR that greatly reduces the computational cost of assigning a high-resolution mesh around the moving interface region. The data structure of the memory pool has extra space allocated to prevent frequent memory allocations and deallocations. Results for the two-phase flow benchmark problems, 2D rising-bubble and dam-breaking onto dry floor problem, are in good agreement with the results of incompressible solvers. The two-phase flow simulation of the dam-breaking onto a wet floor problem maintained the shape interface regardless of whether the AMR method was used or not. We have computed a two-dimensional soap bubble growing from 16mm to 120mm in diameter with about 0.9 million total cells. The final thickness of the liquid film was about 0.1mm with the finest cell size being 0.0195mm, equivalent to 8,192×8,192 uniform cells. This computation showed that high-resolution two-phase flow simulation with the explicit scheme and AMR method reproduced the behavior of the thin liquid film.