An enriched finite element method and level sets for axisymmetric two-phase flow with surface tension

A nite element method for axisymmetric two-phase ow problems is presented. The method uses an enriched nite element formulation, in which the interface can move arbitrarily through the mesh without remeshing. The enrichment is implemented by the extended nite element method (X-FEM) which models the discontinuity in the velocity gradient at the interface by a local partition of unity. It provides an accurate representation of the velocity eld at interfaces on an Eulerian grid that is not conformal to the weak discontinuity. The interface is represented by a level set which is also used in the construction of the element enrichment. Surface tension e ects are considered and the interface curvature is computed from the level set eld. The method is demonstrated by several examples