Adaptive finite element computational fluid dynamics using an anisotropic error estimator

Almeida, Regina C.; Feijóo, Raúl A.; Galeão, Augusto C. N. R.; Padra, Claudio; Silva, Renato S.

doi:10.1016/s0045-7825(99)00200-5

Cited by 61 publications

(47 citation statements)

References 23 publications

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“…, whereG K denotes the matrix G K (e) with the error ∇e approximated by the Zienkiewicz-Zhu error estimator as in (5). Note that [44, Theorem 4.1] requires some more regularity on the solution, i.e.…”

Section: Asymptotic Analysis and Minimal Mesh Sizementioning

confidence: 99%

“…Anisotropic mesh adaptation has proved to be a powerful strategy to improve the quality and efficiency of compressible flow simulations, at first mostly for 2D flows [5,12,21,28]. These anisotropic mesh adaptation techniques were initially based on a metric derived from a numerical approximation of the Hessian of the solutions with, in the background, the use of an a priori error estimator [25,27].…”

Section: Introductionmentioning

confidence: 99%

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On the use of anisotropic a posteriori error estimators for the adaptative solution of 3D inviscid compressible flows

Bourgault

Picasso

Alauzet

et al. 2008

Numerical Methods in Fluids

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SUMMARYThis paper describes the use of an a posteriori error estimator to control anisotropic mesh adaptation for computing inviscid compressible flows. The a posteriori error estimator and the coupling strategy with an anisotropic remesher are first introduced. The mesh adaptation is controlled by a single parameter T OL in regions where the solution is regular, while a condition on the minimal element size hmin is enforced across solution discontinuities. This hmin condition is justified on the basis of an asymptotic analysis. The efficiency of the approach is tested with a supersonic flow over an aircraft. The evolution of a mesh adaptation/flow solution loop is shown, together with the influence of the parameters T OL and hmin. We verify numerically that the effect of varying hmin is concordant with the conclusions of the asymptotic analysis, giving hints on the selection of hmin with respect to T OL. Finally we check that the results obtained with the a posteriori error estimator are at least as accurate as those obtained with anisotropic a priori error estimators. All the results presented can be obtained using a standard desktop computer, showing the efficiency of these adaptative methods. Copyright

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Section: Asymptotic Analysis and Minimal Mesh Sizementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On the use of anisotropic a posteriori error estimators for the adaptative solution of 3D inviscid compressible flows

Bourgault

Picasso

Alauzet

et al. 2008

Numerical Methods in Fluids

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show abstract

“…The most obvious concern is the ability to calculate values to the second derivatives of a discontinuous field. One approach used with ¼ finite element basis is the construction of a "recovered" Hessian [3] using patchwise projection procedures in a manner similar to that used to define the popular Zienkiewicz-Zhu error estimators [48]. Although it may be possible to use a similar approach here, the discontinuous nature of the DG basis makes it questionable.…”

Section: Approach Takenmentioning

confidence: 99%

Anisotropic adaptive simulation of transient flows using discontinuous Galerkin methods

Remacle

Shephard

et al. 2005

Int. J. Numer. Meth. Engng

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SUMMARYAn anisotropic adaptive analysis procedure based on a discontinuous Galerkin finite element discretization and local mesh modification of simplex elements is presented. The procedure is applied to transient 2-and 3-dimensional problems governed by Euler's equation. A smoothness indicator is used to isolate jump features where an aligned mesh metric field in specified. The mesh metric field in smooth portions of the domain is controlled by a Hessian matrix constructed using a variational procedure to calculate the second derivatives. The transient examples included demonstrate the ability of the mesh modification procedures to effectively track evolving interacting features of general shape as they move through a domain.

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“…Os vários métodos para computar o indicador 2 ߟ são basicamente divididos em duas classes [ALMEIDA et al, 2000]:…”

Section: Classificação Dos Estimadores De Errounclassified

Um estimador de erro a posteriori para a equação do transporte de contaminantes em regime de pequena advecção

Jesus¹

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Adaptive finite element computational fluid dynamics using an anisotropic error estimator

Cited by 61 publications

References 23 publications

On the use of anisotropic a posteriori error estimators for the adaptative solution of 3D inviscid compressible flows

On the use of anisotropic a posteriori error estimators for the adaptative solution of 3D inviscid compressible flows

Anisotropic adaptive simulation of transient flows using discontinuous Galerkin methods

Um estimador de erro a posteriori para a equação do transporte de contaminantes em regime de pequena advecção

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