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Vortex control of instationary channel flows using translation invariant cost functionals

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Abstract

The use of translation invariant cost functionals for the reduction of vortices in the context of shape optimization of fluid flow domains is investigated. Analytical expressions for the shape design sensitivity involving different cost functionals are derived. Instationary channel flow problems with a bump and an obstacle as possible control boundaries are taken as test examples. Numerical results are provided in various graphical forms for relatively low Reynolds numbers. Striking differences are found for the optimal shapes corresponding to the different cost functionals, which constitute different quantification of a vortex.

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Authors and Affiliations

  1. Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences, Altenbergerstraße 69, 4040, Linz, Austria

    H. Kasumba

  2. Institut für Mathematik und Wissenschaftliches Rechnen, Karl-Franzens-Universität Graz, Heinrichstraße 36, 8010, Graz, Austria

    K. Kunisch

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  1. H. Kasumba
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  2. K. Kunisch
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Correspondence to K. Kunisch.

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Kasumba, H., Kunisch, K. Vortex control of instationary channel flows using translation invariant cost functionals. Comput Optim Appl 55, 227–263 (2013). https://doi.org/10.1007/s10589-012-9516-5

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  • DOI: https://doi.org/10.1007/s10589-012-9516-5

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