Front tracking with surface normal propagation restriction

The modelling of interfacial flows with the front tracking method comes along with potential computational expenses and difficulties. One of the main computational expenses, and a source of numerical error is the remeshing of the front mesh due to its distortion and compaction during the advection of the front vertices. Classical remeshing operations are error-prone and do not strictly conserve the volume of the interacting bulk phases or preserve the shape of the interface. Mitigating or eliminating these inaccuracies requires additional and potentially computationally expensive methods.

The aim of the presented method is to overcome tangential front vertex movement and vertex clustering
in order to prevent, or at least reduce or postpone front remeshing. For the proposed front tracking method, the suppression of vertex movement tangential to the front is achieved by a reformulation of the surface velocity vector at each discrete front vertex position. The front vertices are no longer moved with the interpolated fluid velocity as in the classical front tracking advection, but the new velocity vector is composed of the sum of the center-of-mass velocity of the body enclosed by the front mesh plus a vertex velocity relative to the center of mass velocity. This velocity relative to the center of mass velocity is decomposed into a surface tangential and surface normal component from which only the surface normal velocity component is used for front vertex advection to cancel tangential vertex movement. This new front tracking method is tested using canonical test-cases, such as a rising bubble in an otherwise quiescent flow, shown in Figure 1, or a droplet in shear flow, focusing on mass conservation, shape preservation and the computational costs.