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Error Estimation and Anisotropic Mesh Refinement for Aerodynamic Flow Simulations

In: Numerical Mathematics and Advanced Applications 2009

Author

Listed:
  • Tobias Leicht

    (Institute of Aerodynamics and Flow Technology, Center for Computer Applications in Aerospace Science and Engineering, DLR (German Aerospace Center))

  • Ralf Hartmann

    (Institute of Aerodynamics and Flow Technology, Center for Computer Applications in Aerospace Science and Engineering, DLR (German Aerospace Center))

Abstract

Aerodynamic flow fields are dominated by anisotropic features at both boundary layers and shocks. Solution-adaptive local mesh refinement can be improved considerably by respecting those anisotropic features. Two types of anisotropy indicators are presented. Whereas the first one is based on polynomial approximation properties and needs the evaluation of second and higher order derivatives of the solution the second one exploits the inter-element jumps arising in discontinuous Galerkin methods and can easily be used with higher order discretizations and even hp-refinement. Examples for sub-, trans- and supersonic flows combining these anisotropic indicators with reliable residual or adjoint based error estimation techniques demonstrate the potential and limitations of this approach.

Suggested Citation

  • Tobias Leicht & Ralf Hartmann, 2010. "Error Estimation and Anisotropic Mesh Refinement for Aerodynamic Flow Simulations," Springer Books, in: Gunilla Kreiss & Per Lötstedt & Axel Målqvist & Maya Neytcheva (ed.), Numerical Mathematics and Advanced Applications 2009, pages 579-587, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-11795-4_62
    DOI: 10.1007/978-3-642-11795-4_62
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