Title: A marching cubes based method for topology changes in three-dimensional two-phase flows with front tracking Show Chinese title

Title: 基于Marching Cubes算法的三维两相流前跟踪拓扑变化方法

Abstract: The handling of topology changes in two-phase flows, such as breakup or coalescence of interfaces, with front tracking is a well-known problem that requires an additional effort to perform explicit manipulations of the Lagrangian front. In this work, we present an approach that allows to perform topology changes with interfaces made of connected triangular elements. The methodology consists of replacing the fluid entities that undergo breakup/coalescence with the iso-surface corresponding to the indicator function value I = 0.5, which automatically returns the shape of the bodies after topology changes. The generation and triangulation of such surface is obtained by exploiting the marching cubes algorithm. Since we perform the reconstruction of the interface only for the bodies that experience breakup/coalescence, the increase in computational cost with respect to a classic front tracking scheme without topology changes is small. Using validation cases, we show that the proposed reconstruction procedure is second-order accurate for volume conservation and able to capture the physics of several two-phase flow configurations undergoing topology changes. The validation cases include the breakup of a droplet in simple shear flow and two rising bubbles in different regimes (peripheral and central breakups). Coalescence is tested by modelling the binary collision between two droplets. For the selected validation cases, an excellent agreement between the numerical results and experiments is observed. The proposed methodology is able to capture the details of such interfacial flows, by predicting accurately the coalescence/breakup dynamics, as well as the number, size and shapes of satellite droplets/bubbles after topology changes. Show Chinese abstract

Abstract: 两相流中拓扑变化（如界面的破裂或聚结）的处理是前向跟踪方法中的一个众所周知的问题，需要额外的努力来进行拉格朗日界面的显式操作。在本文中，我们提出了一种方法，允许使用由连接的三角形单元组成的界面来执行拓扑变化。该方法的核心是用指示函数值I=0.5对应的等值面替换经历破裂/聚结的流体实体，这会自动返回拓扑变化后物体的形状。这种表面的生成和三角化通过利用Marching Cubes算法实现。由于我们仅对经历破裂/聚结的物体进行界面重构，因此与没有拓扑变化的经典前向跟踪方案相比，计算成本的增加很小。通过验证案例，我们展示了所提出的重构程序对于体积守恒具有二阶精度，并且能够捕捉到几种经历拓扑变化的两相流构型的物理现象。验证案例包括简单剪切流中液滴的破裂以及不同模式（周边破裂和中心破裂）下的两个上升气泡。通过模拟两个液滴的二元碰撞来测试聚结。对于选定的验证案例，数值结果与实验观察之间表现出极好的一致性。所提出的方法能够准确预测聚结/破裂的动力学过程，以及拓扑变化后卫星液滴/气泡的数量、大小和形状，从而捕捉到这些界面流动的细节。