We develop an efficient, robust and high accuracy framework for the direct numerical simulation of incompressible multiphase flow. This approach combines a high accuracy interfacial jump capturing method with a topology preserving interface tracking method in a semi-implicit setting. With the help of a composite solution for the individual fluid phases within the interfacial cells, the interfacial jump capturing method provides a 2nd order accurate solution and leads to a symmetric coefficient matrix. The method is fully integrated with a high accuracy, topology preserving level set based interface model that allows the accurate translation of the jump conditions between the interface and the grid cells. These two methods of interfacial jump capturing and topology preserving interface tracking are implemented within a semi-implicit solution framework to reduce the simulation cost for viscous flow applications. We solve a variety of 2D and 2D axisymmetric test problems to both verify and validate the new framework.

我们为不可压缩多相流的直接数值模拟开发了一个高效、稳健和高精度的框架。这种方法在半隐式设置中结合了高精度界面跳跃捕获方法和拓扑保留界面跟踪方法。在界面单元内各个流体相的复合解的帮助下，界面跳跃捕获方法提供了二阶精确解并导致对称系数矩阵。该方法与高精度、基于拓扑保持水平集的界面模型完全集成，允许界面和网格单元之间的跳跃条件的准确转换。这两种界面跳跃捕获和拓扑保持界面跟踪方法在半隐式解决方案框架内实现，以降低粘性流应用的仿真成本。我们解决了各种 2D 和 2D 轴对称测试问题，以验证和验证新框架。