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arXiv · 1806.10156

A CutFEM method for two-phase flow problems

Susanne Claus·Pierre Kerfriden
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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.

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Susanne Claus, Pierre Kerfriden. 2018-06-26. A CutFEM method for two-phase flow problems. https://doi.org/10.1016/j.cma.2019.01.009

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