A stabilized finite element method using a discontinuous level set approach for solving two phase incompressible flows

A numerical method for the simulation of three-dimensional incompressible twophase flows is presented. The proposed algorithm combines an implicit pressure stabilized finite element method for the solution of incompressible two-phase flow problems with a level set method implemented with a quadrature-free Discontinuous Galerkin (DG) method [1]. The use of a fast contouring algorithm [2] permits us to localize the interface accurately. By doing so, we can compute the discontinuous integrals without neither introducing an interface thickness nor reinitializing the level set. The capability of the resulting algorithm is demonstrated with ”large scale” numerical examples (free surface flows : dam break, sloshing) and ”small scale” ones (two phase Poiseuille, Rayleigh-Taylor instability).