Efficient reduction of vertex clustering using front tracking with surface normal propagation restriction

A significant computational expense and source of numerical errors in front tracking is the remeshing of the triangulated front, required due to distortion and compaction of the front following the Lagrangian advection of its vertices. Additionally, in classic front tracking, the remeshing of the front mesh is required not only due to the deformation of the front shape, but also because the vertices of the front are translated in the direction tangential to the front, induced by the front advection. We present the normal-only advection (NOA) front-tracking method with the aim of preventing the tangential motion of the front vertices and the associated vertex clustering, in order to reduce the number of remeshing operations required to retain a high-quality triangulated interface. To this end, we reformulate the velocity used to advect the front at each discrete front-vertex position. The proposed method is validated and tested against the classic front-tracking method, comparing volume conservation, shape preservation, computational costs, and the overall need for front remeshing, as well as experimental results for canonical interfacial flows. The presented results demonstrate that the NOA front-tracking method leads to a typical reduction of remeshing operations by 80% or more compared to the classic front-tracking method for well-resolved cases, and results in a smoother front mesh, which is essential for an accurate representation of the geometrical properties of the front. The volume conservation error is reduced by approximately one order of magnitude with the proposed method compared to the classic front-tracking method, at a similar computational cost.