Speaker
Arnold Reusken, RWTH Aachen
Abstract
In this presentation we consider a Navier-Stokes type system, posed on a smooth
closed stationary or evolving two-dimensional surface embedded in three
dimensional space. We briefly address modeling aspects related to this system. We
introduce the so-called tangential surface Navier-Stokes equations and discuss a
well-posed weak variational formulation of this PDE system that forms the basis for
finite element discretization methods. Furthermore we explain the basic ideas of an
unfitted finite element method, known as TraceFEM, that is used in our numerical
simulation of the tangential surface Navier-Stokes system. Results of numerical
experiments with this method are presented that illustrate how lateral flows are
induced by smooth deformations of a material surface. We also briefly address some recent work
related the full surface Navier-Stokes system.