Adjoint-based Formulation for Shape Optimization Problems in Computational Fluid Dynamics

Sammanfattning: A continuous adjoint formulation for exterior optimization of Dirichlet data on the boundary for potential flow applications has been developed in this thesis. This has been performed by utilizing boundary integral methods for both the primal problem (Laplace’s equation) and for the corresponding adjoint equation (Poisson’s equation) on the unit disc. A considerable portion is devoted to the estimation of the boundary flux for Poisson’s equation. The boundary flux is the (unique) Riesz-representer that determines the search direction in descent methods where the optimal control problem is to reconstruct the Dirichlet data on the boundary in order to minimize a quadratic functional.