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Derivative Free Optimization of Stirrer Configurations

In: Numerical Mathematics and Advanced Applications

Author

Listed:
  • M. Schäfer

    (Darmstadt University of Technology, Department of Numerical Methods in Mechanical Engineering)

  • B. Karasözen

    (Middle East Technical University, Department of Mathematics and Institute of Applied Mathematics)

  • Ö. Uğur

    (Middle East Technical University, Institute of Applied Mathematics)

  • K. Yapıcı

    (Middle East Technical University, Department of Chemical Engineering)

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.

Suggested Citation

  • M. Schäfer & B. Karasözen & Ö. Uğur & K. Yapıcı, 2006. "Derivative Free Optimization of Stirrer Configurations," Springer Books, in: Alfredo Bermúdez de Castro & Dolores Gómez & Peregrina Quintela & Pilar Salgado (ed.), Numerical Mathematics and Advanced Applications, pages 1031-1039, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-34288-5_103
    DOI: 10.1007/978-3-540-34288-5_103
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