A CutFEM method for two-phase flow problems

Susanne Claus (1) , Pierre Kerfriden (1)

1 School of Engineering [Cardiff]

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.

Mots clés: cut finite element method; two-phase flow; micro-fluidic devices; level set technique; continuous interior penalty

Domaines: Mécanique des structures [physics.class-ph]

Susanne Claus, Pierre Kerfriden. A CutFEM method for two-phase flow problems. Computer Methods in Applied Mechanics and Engineering, 2019, 348, pp.185-206. ⟨10.1016/j.cma.2019.01.009⟩. ⟨hal-02059066⟩