Optimal Vortex Reduction for Instationary Flows Based on Translation Invariant Cost Functionals

An efficient numerical realization of a cost functional for vortex reduction for unsteady flows described by the Navier-Stokes equations based on space-time finite element discretization is presented and it is demonstrated that the choice of cost functionals has a significant effect on the reduction of vortices.

Abstract

We consider the problem of an appropriate choice of a cost functional for vortex reduction for unsteady flows described by the Navier–Stokes equations. This choice is directly related to a physically correct definition of a vortex. Therefore, we discuss different possibilities for the cost functional and analyze the resulting optimal control problems. Moreover, we present an efficient numerical realization of this concept based on space-time finite element discretization and demonstrate its behavior in some numerical experiments. It is demonstrated that the choice of cost functionals has a significant effect on the reduction of vortices.