Computations of flows with interfaces using arbitrary Lagrangian Eulerian method

This work is devoted to the accurate simulation of incompressible two phase flows. The core of our methodology is the use of interface resolving meshes and the arbitrary Lagrangian-Eulerian (ALE) description of the fluid kinematics. Our numerical scheme is based on second order finite elements, a fractional step ? time discretisation, and a special approximation of the curvature to incorporate surface tension effects. We demonstrate the potential of the proposed numerical method by the simulation of a rising bubble and the Rayleigh-Taylor instability problem