A triangular cut-cell adaptive method for high-order discretizations of the compressible Navier–Stokes equations

Fidkowski, Krzysztof J.; Darmofal, David L.

doi:10.1016/j.jcp.2007.02.007

Cited by 145 publications

(149 citation statements)

References 33 publications

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“…35,36 This cut cell method has also been applied to simplex meshes. 13,14,37,38 When the constraint of providing a body-fitted grid is removed, the grid generation and adaptation task becomes much simpler. Local incremental modification of an existing grid is then able to produce grids with high anisotropy without curved boundary related robustness issues.…”

Section: -14mentioning

confidence: 99%

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Parallel Anisotropic Tetrahedral Adaptation

Park¹,

Darmofal

2008

46th AIAA Aerospace Sciences Meeting and Exhibit

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An adaptive method that robustly produces high aspect ratio tetrahedra to a general 3D metric specification without introducing hybrid semi-structured regions is presented. The elemental operators and higher-level logic is described with their respective domaindecomposed parallelizations. An anisotropic tetrahedral grid adaptation scheme is demonstrated for 1000-1 stretching for a simple cube geometry. This form of adaptation is applicable to more complex domain boundaries via a cut-cell approach as demonstrated by a parallel 3D supersonic simulation of a complex fighter aircraft. To avoid the assumptions and approximations required to form a metric to specify adaptation, an approach is introduced that directly evaluates interpolation error. The grid is adapted to reduce and equidistribute this interpolation error calculation without the use of an intervening anisotropic metric. Direct interpolation error adaptation is illustrated for 1D and 3D domains.

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Section: -14mentioning

confidence: 99%

“…For higher order functions, a search for this direction can be employed. 13 An alternative methodology is to evaluate the (possibly weighted) interpolation error directly to define the adaptation objective function.…”

Section: Adaptation To Directly Control Interpolation Errormentioning

confidence: 99%

Parallel Anisotropic Tetrahedral Adaptation

Park¹,

Darmofal

2008

46th AIAA Aerospace Sciences Meeting and Exhibit

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“…Although the feature-based adaptation has had some successes, it is liable to overrefine the regions that have little effect on the output functionals [2][3] . In order to derive reliable and efficient adaptive algorithms to produce the desired increase in the accuracy of the output functionals, adjoint-based adaptive methods have been widely developed and studied [4][5][6][7][8][9][10][11][12][13] . Becker and Rannacher [4][5] proposed the dual weighted residual method based on the property of Galerkin orthogonality of the finite element method.…”

Section: Introductionmentioning

confidence: 99%

“…Wang and Mavriplis [11] developed the h-p adaptation approach for compressible Euler equations. Fidkowski [12] developed anisotropic and adjoint-based mesh adaptation for the DG discretization and cut-cell meshing. However, all these studies need output-based adjoint solutions as the weight in order to represent the sensitivity of the output functionals to the local primal residuals.…”

Section: Introductionmentioning

confidence: 99%