An enriched finite element/level-set method for simulating two-phase incompressible fluid flows with surface tension

Abstract

A finite element method is introduced to simulate surface tension dominated flow of two immiscible fluids featuring an enriched space for capturing both strong and weak pressure discontinuities. The proposed enriched finite element space is created utilizing the standard finite element shape functions. Discontinuities are captured by adding merely one additional degree of freedom per each node of the elements cut by the interface. Being local to the cut elements, these additional degrees of freedom are eliminated before assembling the global system of equations following a condensation procedure. The method is stabilized introducing a procedure for improving the conditioning of the enriched pressure contribution to the stiffness matrix in small-cut situations. An improved smoothing strategy based on an artificial diffusion equation is proposed to enhance the performance of the method on rather coarse meshes. A series of three-dimensional two-phase fluid flow benchmarks are solved to assess the performance of the method. Particular attention is paid to surface tension dominated cases. The method is verified by showing its accuracy in capturing 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. The method is further validated by simulating oscillations of a slightly disturbed spherical droplet. The mass conservation property of the method and the effect of the smoothing procedure on the result is assessed by simulating the oscillations of a prolate droplet. Ultimately, the method is tested in a more challenging setting by simulating the rising gas bubble inside a liquid domain.