Fluid flow problems with a moving interface are found in many applications in physics and engineering. In these type of problems, apart from the unknown flow in the bulk domain, also the position of the free surface needs to be determined.
The goal of this thesis is to investigate front tracking finite element methods applied to two-phase incompressible Navier–Stokes flows. The front tracking
approach consists on seeking a parametrization of the unknown interface over a reference manifold. A novel variational formulation for the interface evolution is used. This formulation preserves, in general, the interface mesh quality over time. Moreover, being a fitted approach, the interface mesh is made up of faces of elements belonging to the bulk mesh.
Several fully discrete finite element approximations are derived and, wherever possible, stability and existence results are proved. In order to demonstrate the accuracy and robustness of the proposed algorithms, extensive numerical experiments are carried out, both in 2d and in 3d. A variety of finite element spaces are used. Smoothing and remeshing routines are applied to the bulk mesh to avoid heavily distorted simplicies.