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Review of OutputBased Error Estimation and Mesh Adaptation in Computational Fluid Dynamics
"... Error estimation and control are critical ingredients for improving the reliability of computational simulations. Adjointbased techniques can be used to both estimate the error in chosen solution outputs and to provide local indicators for adaptive refinement. This article reviews recent work on th ..."
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Error estimation and control are critical ingredients for improving the reliability of computational simulations. Adjointbased techniques can be used to both estimate the error in chosen solution outputs and to provide local indicators for adaptive refinement. This article reviews recent work on these techniques for computational fluid dynamics applications in aerospace engineering. The definition of the adjoint as the sensitivity of an output to residual source perturbations is used to derive both the adjoint equation, in fully discrete and variational formulations, and the adjointweighted residual method for error estimation. Assumptions and approximations made in the calculations are discussed. Presentation of the discrete and variational formulations enables a sidebyside comparison of recent work in outputerror estimation using the finite volume method and the finite element method. Techniques for adapting meshes using outputerror indicators are also reviewed. Recent adaptive results from a variety of laminar and Reynoldsaveraged Navier–Stokes applications show the power of outputbased adaptive methods for improving the robustness of computational fluid dynamics computations. However, challenges and areas of additional future research remain, including computable error bounds and robust mesh adaptation mechanics. I.
Discontinuous Galerkin methods on hpanisotropic meshes II: A posteriori error analysis and adaptivity
 In preparation
"... We consider the a priori error analysis of hpversion interior penalty discontinuous Galerkin methods for second{order partial dierential equations with nonnegative characteristic form under weak assumptions on the mesh design and the local nite element spaces employed. In particular, we prove a pr ..."
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We consider the a priori error analysis of hpversion interior penalty discontinuous Galerkin methods for second{order partial dierential equations with nonnegative characteristic form under weak assumptions on the mesh design and the local nite element spaces employed. In particular, we prove a priori hperror bounds for linear target functionals of the solution, on (possibly) anisotropic computational meshes with anisotropic tensorproduct polynomial basis functions. The theoretical results are illustrated by a numerical experiment. 1
OutputDriven Anisotropic Mesh Adaptation for Viscous Flows Using Discrete Choice Optimization,” AIAA Paper
, 2010
"... This paper presents a mesh adaptation scheme for direct minimization of output error using a selection process for choosing the optimal refinement option from a discrete set of choices. The scheme is geared for viscous aerodynamic flows, in which solution anisotropy makes certain refinement options ..."
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Cited by 5 (2 self)
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This paper presents a mesh adaptation scheme for direct minimization of output error using a selection process for choosing the optimal refinement option from a discrete set of choices. The scheme is geared for viscous aerodynamic flows, in which solution anisotropy makes certain refinement options more efficient compared to others. No attempt is made, however, to measure the solution anisotropy directly or to incorporate it into the scheme. Rather, mesh anisotropy arises naturally from the minimization of a cost function that incorporates both an output error estimate and a count of the additional degrees of freedom for each refinement option. The method is applied to outputbased adaptive simulations of the laminar and Reynoldsaveraged compressible NavierStokes equations on bodyfitted meshes in two and three dimensions. Twodimensional results for laminar flows show a factor of 23 reduction in the degrees of freedom on the final adapted meshes when the discrete choice optimization is used compared to pure isotropic adaptation. Preliminary results on a wingbody configuration show that these savings improve in three dimensions and for higher Reynoldsnumber flows. I.
OutputBased Error Estimation and Mesh Adaptation in Computational Fluid Dynamics: Overview and Recent Results
"... Error estimation an control are critical ingredients for improving the reliability of computational simulations. Adjointbased techniques can be used to both estimate the error in chosen solution outputs and to provide local indicators for adaptive refinement. This article reviews recent work on the ..."
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Cited by 5 (1 self)
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Error estimation an control are critical ingredients for improving the reliability of computational simulations. Adjointbased techniques can be used to both estimate the error in chosen solution outputs and to provide local indicators for adaptive refinement. This article reviews recent work on these techniques for Computational Fluid Dynamics (CFD) applications in aerospace engineering. The definition of the adjoint as the sensitivity of an output to residual source perturbations is used to derive both the adjoint equation, in fullydiscrete and variational formulations, and the adjointweighted residual method for error estimation. Assumptions and approximations made in the calculations are discussed. Presentation of the discrete and variational formulations enables a sidebyside comparison of recent work in output error estimation using the finite volume method and the finite element method. Recent adaptive results from a variety of applications show the power of outputbased adaptive methods for improving the robustness of CFD computations. However, challenges and areas of additional future research remain, including computable error bounds and robust mesh adaptation mechanics. I
On the evaluation of finite element sensitivities to nodal coordinates
 Special Volume with Selected Papers from the 20th Chemnitz Finite Element Symposium:134–144, 2008. http://etna.mcs.kent.edu/vol.32.2008, Published online 04/03/2009
"... Abstract. We present a derivation of the derivative of general systems of nite element equations with respect to the coordinates of the nodes in the underlying nite element mesh. The resulting expressions allow the systematic evaluation of such derivatives without the need to resort to automatic di ..."
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Abstract. We present a derivation of the derivative of general systems of nite element equations with respect to the coordinates of the nodes in the underlying nite element mesh. The resulting expressions allow the systematic evaluation of such derivatives without the need to resort to automatic differentiation or the expense associated with nite difference approximations. The principal motivation for this work comes from problems in optimal design, however, other potential applications are also described. The results obtained are validated through numerical examples.
A Robust hpAdaptation Method for Discontinuous Galerkin Discretizations Applied to Aerodynamic Flows
, 2013
"... For my amazing family ii ACKNOWLEDGEMENTS First and foremost, I express my gratitude to my advisor, Professor Krzysztof Fidkowski. His guidance during the past four years was instrumental to the success of this thesis work. He was also very skilled in keeping me on track while I tried different idea ..."
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For my amazing family ii ACKNOWLEDGEMENTS First and foremost, I express my gratitude to my advisor, Professor Krzysztof Fidkowski. His guidance during the past four years was instrumental to the success of this thesis work. He was also very skilled in keeping me on track while I tried different ideas and in motivating me during the difficult times. It was an honor being part of his research group. I would like to thank my committee members, Professor Bram van Leer, Professor David Zingg and Professor Eric Johnsen. Their questions and comments during our meetings helped shape this work. I thank Professor Bram van Leer for recruiting me for graduate school and for our discussions in the early stages of my research. I thank Professor David Zingg for the challenging questions during our meetings and for our discussions about the physicality constrained solver during my time at NASA Ames. I also thank Professor Eric Johnsen for agreeing to be a cognate committee member.
Adaptivity and A Posteriori Error Estimation For DG Methods on Anisotropic Meshes
"... In many application areas involving the mathematical modeling of convection, diusion, and reaction processes, diusion can be small (compared to the convection and the reaction coecients), degenerate, or even identically equal to zero in subregions of the computational domain. This multiscale behav ..."
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In many application areas involving the mathematical modeling of convection, diusion, and reaction processes, diusion can be small (compared to the convection and the reaction coecients), degenerate, or even identically equal to zero in subregions of the computational domain. This multiscale behavior between convection and diusion creates various challenges in the
Int. Conference on Boundary and Interior Layers
"... Derivation of an adjoint consistent discontinuous Galerkin discretization of the compressible Euler equations ..."
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Derivation of an adjoint consistent discontinuous Galerkin discretization of the compressible Euler equations
On adaptive anisotropic mesh optimisation for convectiondiffusion problems
, 2012
"... 27/09/2012 On adaptive anisotropic mesh optimisation for convectiondiffusion problems ..."
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27/09/2012 On adaptive anisotropic mesh optimisation for convectiondiffusion problems