XFEM with hanging nodes for two-phase incompressible flow

This study develops the h-version of the Extended Finite Element Method (XFEM) applied to the simulation of two-fluid incompressible flow in two and three dimensions. A multilevel adaptive mesh refinement realized via hanging nodes on 1-irregular meshes is employed in the vicinity of the two-fluid interface. The sign-enrichment is used for the XFEM approximation which accurately accounts for the jump in the pressure field. The level-set method is used for the implicit representation of the interface. The Laplace–Beltrami technique is employed for the modelling of the surface tension, which avoids the explicit computation of the curvature. An emphasis of this work is on how the interplay between the interface movement (in terms of a time-dependent level-set function), the adaptive refinement and the enriched XFEM approximations, is realized. This study also demonstrates that the approximation of the normal vector to the interface, required for the computation of the surface tension, can have a significant impact on the accuracy of the solver. Several two- and three-dimensional test cases are investigated.