In this work, a finite element method (FEM) is introduced to simulate surface tension dominated flow of two immiscible fluids. The method proposes an enriched space, created by standard FEM shape functions for capturing both strong and weak pressure discontinuities. Discontinuities are captured by adding one additional degree of freedom per each node of the elements cut by the interface. The method captures strong pressure discontinuity at the interface of a spherical droplet as well as its capability in handling large pressure gradient discontinuity in a hydrostatic liquid–gas container, accurately. Furthermore, by simulating the oscillations of a prolate droplet, the mass conservation property of the method and the effect of the smoothing procedure on the result are assessed. Finally, the method is tested by simulating the rising gas bubble inside a liquid domain.
Two-phase incompressible fluid flows with surface tension
