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@PHDTHESIS{Balan:669026,
      author       = {Balan, Aravind},
      othercontributors = {May, Georg and Müller, Siegfried},
      title        = {{A}djoint-based $hp$-adaptivity on anisotropic meshes for
                      high-order compressible flow simulations},
      school       = {Rheinisch-Westfälische Technische Hochschule Aachen},
      type         = {Dissertation},
      address      = {Aachen},
      reportid     = {RWTH-2016-07184},
      pages        = {1 Online-Ressource (120 Seiten) : Illustrationen,
                      Diagramme},
      year         = {2016},
      note         = {Veröffentlicht auf dem Publikationsserver der RWTH Aachen
                      University; Dissertation, Rheinisch-Westfälische Technische
                      Hochschule Aachen, 2016},
      abstract     = {High-order numerical methods such as Discontinuous
                      Galerkin, Spectral Difference, and Flux Reconstruction etc,
                      which use polynomials that are local to each mesh element to
                      represent the solution field, are becoming increasingly
                      popular in solving convection-dominated flows. This is due
                      to their potential in giving accurate results more
                      efficiently than lower order methods such as the classical
                      Finite Volume methods. In most engineering applications, we
                      are more interested in some specific scalar quantities
                      rather than the full flow details. In the case of
                      aerodynamic flow simulations, these quantities can be lift
                      or drag coefficient. To get accurate values for such target
                      functional quantities, adjoint-based error estimators, along
                      with a high-order solver, have been found to be quite
                      useful. They can identify the mesh elements that contribute
                      the most to the error, and adapting these elements should
                      result in a more accurate target functional. To adapt a mesh
                      element, one can either do mesh refinement (h-adaptation) or
                      polynomial space enrichment (p-adaptation) or both
                      (hp-adaptation). Of these, hp-adaptation offers the most
                      efficient way for adaptation, since one can locally choose
                      between mesh refinement or polynomial space enrichment based
                      on what is more efficient in resolving the local solution
                      features. We present efficient adjoint-based hp-adaptation
                      methodologies on isotropic and anisotropic meshes for the
                      recently developed high order Hybridized Discontinuous
                      Galerkin scheme for (nonlinear) convection-diffusion
                      problems, including the compressible Euler and Navier-Stokes
                      equations. hp-adaptation on isotropic meshes is based on the
                      spatial error distribution for a given target functional
                      given by the adjoint error estimator and the solution
                      regularity given by a regularity indicator. For anisotropic
                      meshes, we extend the refinement strategy based on an
                      interpolation error estimate, due to Dolejsi, by
                      incorporating an adjoint-based error estimate. Using the two
                      error estimates we determine the size and the shape of the
                      triangular mesh elements on the desired mesh to be used for
                      the subsequent adaptation steps. This is done using the
                      concept of mesh-metric duality, where the metric tensors can
                      encode information about mesh elements, which can be passed
                      to a metric-conforming mesh generator to generate the
                      required anisotropic mesh. The effectiveness of the
                      adaptation methodology is demonstrated using numerical
                      results: for a scalar convection-diffusion case with a
                      strong boundary layer; inviscid subsonic, transonic and
                      supersonic flows and viscous subsonic flow around a NACA0012
                      airfoil.},
      cin          = {080003 / 419720},
      ddc          = {620},
      cid          = {$I:(DE-82)080003_20140620$ / $I:(DE-82)419720_20140620$},
      typ          = {PUB:(DE-HGF)11},
      urn          = {urn:nbn:de:hbz:82-rwth-2016-071848},
      url          = {https://publications.rwth-aachen.de/record/669026},
}