Pressure XFEM for two-phase incompressible flows with application to 3D droplet problems

Abstract

We consider the numerical simulation of 3D two-phase flow problems using finite element methods on adaptive multilevel tetrahedral grids and a level set approach for interface capturing. The approximation of the discontinuous pressure in standard finite element spaces yields poor results with an error of order 0.5 w.r.t. the L 2 norm. Second order approximations can be achieved by the introduction of an extended finite element space (XFEM) adding special basis functions incorporating a jump at the interface. A simple stabilization strategy for the XFEM basis is presented which also offers this optimal approximation property. © 2011 Springer-Verlag Berlin Heidelberg.