Comparison of derivative free Newton-based and evolutionary methods for shape optimization of flow problems
✍ Scribed by Zerrin Harth; Hongtao Sun; Michael Schäfer
- Publisher
- John Wiley and Sons
- Year
- 2007
- Tongue
- English
- Weight
- 707 KB
- Volume
- 53
- Category
- Article
- ISSN
- 0271-2091
- DOI
- 10.1002/fld.1304
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✦ Synopsis
Abstract
The object of this study is to investigate two derivative free optimization techniques, i.e. Newton‐based method and an evolutionary method for shape optimization of flow geometry problems. The approaches are compared quantitatively with respect to efficiency and quality by using the minimization of the pressure drop of a pipe conjunction which can be considered as a representative test case for a practical three‐dimensional flow configuration. The comparison is performed by using CONDOR representing derivative free Newton‐based techniques and SIMPLIFIED NSGA‐II as the representative of evolutionary methods (EM).
For the shape variation the computational grid employed by the flow solver is deformed. To do this, the displacement fields are scaled by design variables and added to the initial grid configuration. The displacement vectors are calculated once before the optimization procedure by means of a free form deformation (FFD) technique.
The simulation tool employed is a parallel multi‐grid flow solver, which uses a fully conservative finite‐volume method for the solution of the incompressible Navier–Stokes equations on a non‐staggered, cell‐centred grid arrangement. For the coupling of pressure and velocity a pressure‐correction approach of SIMPLE type is used. The possibility of parallel computing and a multi‐grid technique allow for a high numerical efficiency. Copyright © 2006 John Wiley & Sons, Ltd.