Workshop on Numerical Methods and Analysis in CFD - Abstract
Schöberl, Joachim
In this talk we present discretization techniques for Stokes and Navier--Stokes equations based on H(div)-conforming finite elements for the velocity. One family of methods is based on hybridized discontinuous Galerkin (HDG) methods, the other one is a mixed formulation introducing the stress as a new variable. Since the obtained velocity approximation is exactly divergence free, we obtain stability for high Reynolds numbers. We compare energy dissipation for direct simulation (i.e. an implicit turbulence model) with various established methods for turbulence. H(div)-conformity allows the mapping of vector-fields by the Piola transform. Thus, the exact divergence free conditon is preserved under morphing of the domain. We show examples from fluid-structure interaction as well as model order reduction where this property is of advantage. The presented methods are available within the open source finite element package NGSolve.