Finite Element Techniques for the Numerical Simulation of Two-Phase Flows with Mass Transport

We consider a standard sharp interface model for the fluid dynamics in a twophase incompressible flow, combined with a convection-diffusion model for solute transport. Some important numerical challenges related to these models are discussed. We present a finite element discretization method for the solute transport model. The method is based on an Eulerian approach, i.e. computational grids are not aligned to the interface and do not follow the interface motion. The interface motion is described using the level-set technique. We treat three numerical techniques, namely the extended finite element method (XFEM) for the approximation of discontinuities, the Nitsche-method for a convenient handling of interface conditions (e.g., Henry condition) and the space-time finite element technique. The basic underlying ideas are explained. These techniques are combined and result in the space-time Nitsche-XFEM that is used for the discretization of a two-phase solute transport problem. Properties of this method are discussed. Results of numerical experiments with this method are presented.