Optimal Boundary Control Problems Related to High-Lift Configurations

We investigate two control problems related to the aerodynamic optimization of flows around airfoils in high-lift configurations. The first task is the steady state maximization of lift subject to restrictions on the drag. This leads to a boundary control problem for the 2D stationary Navier-Stokes equations with constrained control functions belonging to L2(G)\textbf{L}^2(\Gamma) under an integral state constraint. We derive optimality conditions and treat the problem numerically by direct solution of the associated nonsmooth optimality system. The second part is based on a k-ω-Wilcox98 turbulence model. To deal with the curse of dimension and the nonlinearity of the system, we discuss a reduced-order model by adapting a small system of ODEs to solutions computed with the full model.