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.

中文翻译：

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流体动力学耦合三分量守恒 Allen–Cahn 相场模型的快速稳定的尺寸分裂模拟

在本研究中，开发了一种有效的维数分裂方法来求解三分量守恒艾伦-卡恩模型和不可压缩纳维-斯托克斯方程的耦合系统。该方法将数值离散系统完全解耦，将高维问题的计算转化为一维问题，大大降低了二维和三维的高计算成本。通过在MAC交错网格上采用方向分裂压力校正方法和交替方向隐式（ADI）方案，可以通过矩阵乘法完成实际计算，这进一步允许我们采用并行运算来计算加速度。为了保证长时间模拟的稳定性，引入了一种新颖的后处理方法来强制数值解的物理属性，例如最大束缚原理（MBP）、质量守恒和无体积泄漏条件。数值测试结果表明，所提出的数值算法能够提供稳定的二阶解。进行了大量的仿真来验证所提出的方法在模拟和探索三相流行为方面的有效性。