A CutFEM method for two-phase flow problems
This work addresses the challenge of simulating two-phase flows with moving interfaces, particularly for microfluidic applications, but the results are limited to low capillary numbers.
The paper presents a cut finite element method for two-phase Navier-Stokes flows, featuring unified stabilization and curvature smoothing. The algorithm performs well for low capillary number flows, aiming to enable simulation of microfluidic devices.
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.