A CutFEM method for two-phase flow problems

TL;DR

This paper introduces a novel CutFEM approach for two-phase Navier-Stokes flows, combining stabilization techniques, fictitious domains, and curvature smoothing to improve accuracy and robustness in microfluidic simulations.

Contribution

It develops a unified stabilization framework and extended fictitious domains, enhancing the accuracy and robustness of CutFEM for two-phase flow simulations.

Findings

Effective stabilization of advection and pressure-velocity coupling.

Improved accuracy with extended fictitious domains.

Robust interface handling with curvature smoothing.

Abstract

In this article, we present a cut finite element method for two-phase Navier-Stokes flows. The main feature of the method is the formulation of a unified continuous interior penalty stabilisation approach for, on the one hand, stabilising advection and the pressure-velocity coupling and, on the other hand, stabilising the cut region. The accuracy of the algorithm is enhanced by the development of extended fictitious domains to guarantee a well defined velocity from previous time steps in the current geometry. Finally, the robustness of the moving-interface algorithm is further improved by the introduction of a curvature smoothing technique that reduces spurious velocities. The algorithm is shown to perform remarkably well for low capillary number flows, and is a first step towards flexible and robust CutFEM algorithms for the simulation of microfluidic devices.