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Adjoint-Based Error Estimation and Mesh Refinement in an Adjoint-Based Airfoil Shape Optimization of a Transonic Benchmark Problem

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New Results in Numerical and Experimental Fluid Mechanics X

Part of the book series: Notes on Numerical Fluid Mechanics and Multidisciplinary Design ((NNFM,volume 132))

Abstract

In this article, we apply a new airfoil shape optimization algorithm based on adaptive higher order Discontinuous Galerkin methods with discretization error control to a 2D benchmark problem of the AIAA Design Optimization Discussion Group. Each flow solution in the optimization process is computed on a sequence of goal-oriented h- or hp-refined meshes until the estimation of the discretization error in a given target quantity (like the drag coefficient) is below a prescribed error tolerance. Furthermore, the optimization is driven by the Sequential Quadratic Programming (SQP) algorithm and the corresponding gradient of the objective function is evaluated via the adjoint approach. Finally, the effect of the discretization error on the quality of the optimized airfoil shapes is investigated.

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Authors and Affiliations

  1. DLR, Lilienthalplatz 7, 38108, Braunschweig, Germany

    Ding Li & Ralf Hartmann

Authors
  1. Ding Li
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  2. Ralf Hartmann
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Corresponding author

Correspondence to Ralf Hartmann .

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Editors and Affiliations

  1. Ins. für Aerodynamik & Strömungstechnik, Deutsches Zentrum für Luft- und Raumfahr, Göttingen, Germany

    Andreas Dillmann

  2. Airbus Deutschland, Bremen, Bremen, Germany

    Gerd Heller

  3. Institut für Aerodynamik und Gasdynamik, Universität Stuttgart, Stuttgart, Germany

    Ewald Krämer

  4. Inst. für Aerodynamik & Strömungstechnik, Deutsches Zentrum für Luft- und Raumfahr, Göttingen, Niedersachsen, Germany

    Claus Wagner

  5. Technische Universität München, Lehrstuhl für Aerodynamik & Strömungsm, Garching, Bayern, Germany

    Christian Breitsamter

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Li, D., Hartmann, R. (2016). Adjoint-Based Error Estimation and Mesh Refinement in an Adjoint-Based Airfoil Shape Optimization of a Transonic Benchmark Problem. In: Dillmann, A., Heller, G., Krämer, E., Wagner, C., Breitsamter, C. (eds) New Results in Numerical and Experimental Fluid Mechanics X. Notes on Numerical Fluid Mechanics and Multidisciplinary Design, vol 132. Springer, Cham. https://doi.org/10.1007/978-3-319-27279-5_47

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  • DOI: https://doi.org/10.1007/978-3-319-27279-5_47

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-27278-8

  • Online ISBN: 978-3-319-27279-5

  • eBook Packages: EngineeringEngineering (R0)

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