A marching cubes based method for topology changes in three-dimensional two-phase flows with front tracking

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.