Three-dimensional Edge-based Interface Tracking (EBIT) Method for Multiphase-flows Simulation with Surface Tension

We present a novel Front-Tracking method called Edge-Based Interface Tracking (EBIT) method for multiphase-flows simulation. In the EBIT method, the marker points are located on the grid edges, and the connectivity of markers is implicitly described by a local data structure called Color Vertex, which makes this method suitable for parallelization. Furthermore, the Front-Tracking feature of the EBIT method facilitates its coupling with a boundary model for multiscale computations. In the EBIT method, the marker is advected by a split method. From the position of marker points, we can easily compute the volume fractions. Then the coupling with the Navier-Stokes equations is similar to that in the VOF method.

In this paper, we extend the 2D EBIT method to 3D for a cuboid volume grid. By decomposing a 3D advection along one direction into four 2D advection problems on the corresponding faces of a cubic cell, we can resuse most of the algorithms developed for the 2D EBIT method, which makes the extension to 3D relatively straightforward. The 3D EBIT method on an Octree grid is implemented inside the platform Basilisk. To validate the solver, we conduct several test cases: (1) Translation, (2) Single vortex, (3) Oscillating droplet, (4) Rising bubble, and compare the results with those by the VOF method.