Understanding and predicting multiphase flows is of great relevance due to the ubiquitous nature of such flows in both nature and in many industrial applications. Rapid development of high speed computers and problem-specific algorithms in the last 2 decades has enabled the study of multiphase flows through numerical simulations. In this paper, we give a brief overview of different methods used in direct numerical simulations of two-phase flows. In particular, we focus on the volume of fluid (VOF) method used for locating and advecting the interface. VOF method is a mesh based interface capturing method in which a scalar function called void fraction field (which is the ratio of tracked fluid to the cell volume) is advected in order to track the interface position. A geometric VOF algorithm is detailed in this work. which strikes a balance between accuracy, ease of implementation and volume conservation on a structured grid. Another challenge in two-phase flow simulations is the inclusion of surface tension forces accurately. Here, we give a brief overview of Eulerian surface tension models and detail an approach balancing computational cost, curvature estimation and imposed timestep restriction. Finally, we discuss the most recent advances in VOF methods and outline the various numerical challenges we expect to encounter.

由于多相流在自然界和许多工业应用中普遍存在，因此理解和预测多相流具有重要意义。过去 20 年来，高速计算机和针对特定问题的算法的快速发展使得通过数值模拟研究多相流成为可能。在本文中，我们简要概述了两相流直接数值模拟中使用的不同方法。我们特别关注用于定位和平流界面的流体体积（VOF）方法。 VOF 方法是一种基于网格的界面捕获方法，其中平流传输称为空隙分数场（即跟踪流体与单元体积的比率）的标量函数以跟踪界面位置。本文详细介绍了几何 VOF 算法。它在结构化网格上的准确性、易于实施性和体积保护之间取得了平衡。两相流模拟的另一个挑战是准确地包含表面张力。在这里，我们简要概述了欧拉表面张力模型，并详细介绍了一种平衡计算成本、曲率估计和施加的时间步长限制的方法。最后，我们讨论 VOF 方法的最新进展，并概述我们预计会遇到的各种数值挑战。