A CutFEM method for two-phase flow problems

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 the stabilisation of the advection and the pressure–velocity coupling, on the one hand, and the stabilisation of the cut region on the other hand. 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 domains. 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 flows in microfluidic devices.