M. Schäfer, B. Karasözen, Ö. Uğur, K. Yapıcı, Derivative Free Optimization of Stirrer Configurations, in: Proceedings of The Sixth European Conference on Numerical Mathematics and Advanced Applications, ENUMATH 2005, USC, Santiago de Compostela, Spain, 2005, Springer-Verlag, 2006, pp. 1031-1039.

Numerical Mathematics and Advanced Applications (Springer)
edited by Bermúdez de Castro, A.; Gómez, D.; Quintela, P.; Salgado, P.
ISBN: 978-3-540-34287-8

Abstract

In the present work a numerical approach for the optimization of stirrer configurations is presented. The methodology is based on a parametrized grid generator, a flow solver, and a mathematical optimization tool, which are integrated into an automated procedure. The grid generator allows the parametrized generation of block-structured grids for the stirrer geometries. The flow solver is based on the discretization of the incompressible Navier-Stokes equations by means of a fully conservative finite-volume method for block-structured, boundary-fitted grids. As optimization tool the two approaches DFO and CONDOR are considered, which are implementations of trust region based derivative-free methods using multivariate polynomial interpolation. Both are designed to minimize smooth functions whose evaluations are considered expensive and whose derivatives are not available or not desirable to approximate. An exemplary application for a standard stirrer configuration illustrates the functionality and the properties of the proposed methods also involving a comparison of the two optimization algorithms.