Fast and stable dimension splitting simulations for the hydrodynamically coupled three-component conserved Allen–Cahn phase field model

Abstract

In this study, an efficient dimension splitting method is developed for solving the coupled system of three-component conserved Allen–Cahn model and incompressible Navier–Stokes equation. The proposed method completely decouples numerical discrete system and transforms the computing of high-dimensional problems into one-dimensional problems, which greatly minimizes high computational costs in two- and three-dimensions. Via employing the direction splitting pressure correction method and alternate direction implicit (ADI) scheme on MAC staggered grids, the practical computing can be accomplished by matrix multiplication, which further allows us to employ parallel operations for computing acceleration. To guarantee the long time simulation stability, a novel post-processing method is introduced to force the physical properties, such as the maximum bound principle (MBP), mass conservation, and no volume leakage conditions, of the numerical solution. Numerical test results show that the proposed numerical algorithm can provide stable and second-order solution. A large number of simulations are performed to verify the effectiveness of the proposed method in simulating and exploring the behavior of three-phase flows.