Open Access
Error estimation and adjoint-based refinement for multiple force coefficients in aerodynamic flow simulations
Ralf Hartmann
- 01 Jul 2008
TL;DR: In this paper, an overview of recent developments on adaptive higher order Discontinuous Galerkin discretizations for the use in computational aerodynamics at the DLR in Braunschweig is given.
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Abstract: In this talk we give an overview of recent developments on adaptive higher order Discontinuous Galerkin discretizations for the use in computational aerodynamics at the DLR in Braunschweig. In particular, this includes some of the most recent developments and results achieved in the EU project ADIGMA. Important quantities of interest in aerodynamic flow simula tions are the aerodynamic force coefficients including the pressure induced and the viscous stress induced drag, lift and moment coefficients, respectively. A posteriori error estimation and goal-oriented (adjoint-based) refine ment approaches have been developed for the accurate and efficient computation of single target quantities. These approaches are based on computing an adjoint solution related to each of the specific target quantities under consideration. The resulting goal-oriented adaptively refined me shes are specifically tailored to the accurate computation of the target quantity under consideration.
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References
deal.II—A general-purpose object-oriented finite element library
TL;DR: The paper presents a detailed description of the abstractions chosen for defining geometric information of meshes and the handling of degrees of freedom associated with finite element spaces, as well as of linear algebra, input/output capabilities and of interfaces to other software, such as visualization tools.
An optimal order interior penalty discontinuous Galerkin discretization of the compressible Navier-Stokes equations
Ralf Hartmann,Paul Houston +1 more
TL;DR: A new symmetric version of the interior penalty discontinuous Galerkin finite element method for the numerical approximation of the compressible Navier-Stokes equations is proposed, showing the optimality of the proposed method when the error is measured in terms of both the L"2-norm and for certain target functionals.
186
Goal-Oriented A Posteriori Error Estimation for Multiple Target Functionals
Ralf Hartmann,Paul Houston +1 more
- 01 Jan 2003
TL;DR: In many applications the quantities of interest are a series of target functionals of the solution to the governing system of partial differential equations rather than the solution itself, for example, in the field of aerodynamics.
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The importance of adjoint consistency in the approximation of linear functionals using the discontinuous Galerkin finite element method
Kathryn Harriman,David J. Gavaghan,Endre Süli +2 more
- 01 Jul 2004
TL;DR: In this article, a discontinuous Galerkin finite element method with interior penalty is used to compute the solution to an elliptic partial differential equation and a linear functional of this solution can be evaluated.
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Error estimation and adjoint based refinement for an adjoint consistent DG discretisation of the compressible Euler equations
TL;DR: The effect of adjoint consistency on the accuracy of the flow solution, the smoothness of the discrete adjoint solution and the a posteriori error estimation with respect to aerodynamical force coefficients on locally refined meshes is demonstrated.