Dennis Trautwein: Parametric finite element approximation of two-phase Navier–Stokes flow with viscoelasticity

Abstract

We present a parametric finite element approximation of two-phase Navier–Stokes flow with viscoelasticity. The free boundary problem is given by the viscoelastic Navier–Stokes equations in the two phases, which are connected with jump conditions across the interface. The elasticity in the fluids is described with the Oldroyd-B model. We approximate a variational formulation for the mean curvature of the interface and for the interface evolution with a parametric finite element method which can be fitted or unfitted. The two-phase Navier–Stokes–Oldroyd-B system in the bulk regions is discretized in a way that guarantees unconditional solvability and energy-stability for the coupled bulk-interface system. In the end, we show the applicability of our method with numerical results. This presentation is based on a joint work with Harald Garcke (University of Regensburg, Germany) and Robert Nürnberg (University of Trento, Italy).