ISBN 9783843901413

978-3-8439-0141-3, Reihe Mathematik

Sabine Repke
Adjoint-Based Optimization Approaches for Stationary Free Surface Flows

115 Seiten, Dissertation Technische Universität Kaiserslautern (2011), Softcover, A5

Zusammenfassung / Abstract

This work deals with the optimal control of a free surface Stokes flow, where the free surfaces respond to an applied outer pressure. Typical applications are fiber spinning or thin film manufacturing. We present two different PDE-constrained optimization problems that differ in the treatment of the free boundary as either state variable or control variable. In both cases we model the free boundary as the graph of a function. For the control-approach the existence of a minimizer is proved. For the two minimization problems we derive the necessary optimality conditions with help of the Lagrange technique. Moreover, the existence of Lagrange multipliers is established. The numerical approaches for solving the free surface Stokes flow as well as the corresponding adjoint system and different optimization methods like the steepest descent, the nonlinear conjugate gradient and a quasi Newton method are presented. For each optimization approach we compare the different optimization methods with respect to efficiency and number of required optimization iterations. Furthermore, the independence of the spacial grid is shown and a parameterstudy is performed. Finally, numerical results for the two strategies are compared with respect to accuracy and efficiency.