Nitsche-XFEM for a transport problem in two-phase incompressible flows

We consider the transport of a dissolved species in a divergence-free immiscible incompressible two-phase flow modeled by a convection diffusion equation. The so-called Henry interface condition leads to a jump condition for the concentration at the interface between the two phases. This discontinuity of the solution render the numerical solution on unfitted meshes difficult. Furthermore time discretization on moving interfaces and handling typically convection dominant situations makes the overall problem delicate. We propose a numerical method using extended finite elements and a Nitsche-type technique combined with streamline diffusion stabilization. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)