Adjoint Based Optimization of a Free Surface Flow for Film Casting |
| |
| Authors: | Sabine Repke Nicole Marheineke |
| |
| Affiliation: | 1. Fraunhofer-Institut für Techno- und Wirtschaftsmathematik, Fraunhofer Platz 1, D-67663 Kaiserslautern;2. Technische Universität Kaiserslautern, Fachbereich Mathematik, Erwin-Schrödinger Str., D-67663 Kaiserslautern |
| |
| Abstract: | Motivated by the industrial process of film casting, we discuss an optimal control approach for a viscous free surface flow that is asymptotically described by 2d Stokes equations. The aim is to optimize the shape of the free boundaries by adjusting the ambient pressure. A PDE-constrained optimization problem is set up, where the free surfaces are described as graphs. The first-order optimality system is derived via the Lagrangian formalism. The resulting minimization problem is solved by a steepest descent method, where the gradient is expressed in terms of the adjoint variables. Numerical results are presented. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) |
| |
| Keywords: | |
|
|
