A mixer design for the pigtail braid

The stirring of a body of viscous fluid using multiple stirring rods is known to be particularly effective when the rods trace out a path corresponding to a nontrivial mathematical braid. The optimal braid is the so-called "pigtail braid", in which three stirring rods execute the usual "over-under" motion associated with braiding plaiting) hair. We show how to achieve this optimal braiding motion straightforwardly: one stirring rod is driven in a figure-of-eight motion, while the other two rods are baffles, which rotate episodically about their common centre. We also explore the extent to which the physical baffles may be replaced by flow structures (such as periodic islands).

Error estimation and adaptive mesh refinement for aerodynamic flows

This lecture course covers the theory of so-called duality-based a posteriori error estimation of DG finite element methods. In particular, we formulate consistent and adjoint consistent DG methods for the numerical approximation of both the compressible Euler and Navier-Stokes equations; in the latter case, the viscous terms are discretized based on employing an interior penalty method. By exploiting a duality argument, adjoint-based a posteriori error indicators will be established. Moreover, application of these computable bounds within automatic adaptive finite element algorithms will be developed. Here, a variety of isotropic and anisotropic adaptive strategies, as well as $hp$-mesh refinement will be investigated.