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

摘要

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 L2 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.