3d Two-phase Flow Simulations with the Extended Finite Element Method (xfem)

Abstract. Based on a validated two-dimensional XFEM code for two-phase flows, this work deals with the extension of this code to three spatial dimensions using structured hexahedral meshes. Surface tension effects are considered, resulting in a discontinuous pressure field. The treatment of hexahedral elements which are cut by the interface is shown. In contrast to linear tetrahedral elements, the discontinuity inside trilinear hexahedral elements is in general not linear but curved. As the XFEM introduces discontinuous functions in the approximation space the hexahedral elements need to be subdivided for integration purposes. Moreover, it is shown how integration points can be placed on the discontinuity itself, which is important for the evaluation of the surface-tension term. Numerical results show the correct prediction of the surface tension and the resulting jump in the pressure field is captured accurately.