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Adjoint Based Optimization of a Free Surface Flow for Film Casting
Author(s) -
Repke Sabine,
Marheineke Nicole
Publication year - 2010
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201010287
Subject(s) - free surface , formalism (music) , minification , flow (mathematics) , gradient descent , lagrangian , mathematical optimization , surface (topology) , stokes flow , mathematics , balanced flow , computer science , mathematical analysis , mechanics , physics , geometry , machine learning , artificial neural network , art , musical , visual arts
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)