Optimization and Computational Fluid Dynamics - Department of ...

Chapter 3
Mathematical Aspects of CFD-based
Optimization
Hans Georg Bock and Volker Schulz
Abstract There exist several computational strategies of different efficiency
for the solution of model-based optimization problems – particularly, in the
case of models based on challenging CFD problems. Applied mathematics
provides means for their analysis and for advice on their proper usage.
In this chapter, methods are mainly analyzed based on the explicit treatment
of the underlying CFD-problem as a constraint of a nonlinear optimization
problem, thus providing the potential for high computational efficiency.
Methods of this form are termed optimization boundary value problem methods,
simultaneous optimization methods or one-shot optimization methods.
The necessary conditions of optimality play a key structural role in devising
those strategies. Special attention is given to the following issues: modular
sequential quadratic programming with approximate linear solvers, preconditioning
of the Karush-Kuhn-Tucker (KKT) system and multigrid optimization
in the case of stationary problems. In the case of unsteady problems, we
will concentrate on time-domain decomposition such as by multiple shooting,
and on algorithmic developments for real-time optimization. The aim of
the presentation is to give a survey on advanced and fast methods for optimization
within a CFD framework. For details, the reader is referred to the
relevant literature.
Hans Georg Bock
Interdisciplinary Center for Scientific Computing (IWR),
University of Heidelberg, Germany
(e-mail: Bock@iwr.uni-heidelberg.de)
Volker Schulz
Department of Mathematics, University of Trier, Germany
(e-mail: Volker.Schulz@uni-trier.de)
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