Level Set Methods for Two-Phase Flows with FEM

Abstract: Two-phase flows is a branch of multiphase flows. The aim of the project is to implement two different level set methods and analyse and compare the numerical results. The level set method is used in order to represent the behaviour of the interface between two incompressible fluids in a flow. Reinitialization is a method to straighten a distorted shape of the level set function that might be caused by the numerical solution of the convection equation and/or by the complicated fluid velocity fields. The main purpose of reinitialization is to preserve the level set function, and thus the shape of the interface as much as possible throughout the simulation. In  order to avoid the oscillations, the stationary weak form is approximated with Galerkin Least Squares (GLS) finite element instead of standard finite element approximation. In order to create the velocity field of the incompressible fluid for the benchmark case, the Stokes equations are solved. The stability has to be measured carefully as it has imbalance between space stability and time stability as well as with the reinitialization. The convergence rates in the numerical results for the both experiment and benchmark cases show that reinitializations usually give a better result. Further researches for this paper could be using another FEM stabilization method, which is other than GLS, in order to solve the stabilization problem in 2D.