Speaker
Dennis Trautwein, University of Regesburg
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).