Anisotropic adaptation: metrics and meshes
We present a method for anisotropic mesh refinement to high-order numerical solutions. We accomplish this by assigning metrics to vertices that approximate the error in that region. To choose values for each metric, we first reconstruct an error equation from the leading order terms of the Taylor ex...
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ndltd-LACETR-oai-collectionscanada.gc.ca-BVAU.2429-4152014-03-26T03:34:52Z Anisotropic adaptation: metrics and meshes Pagnutti, Douglas Anisotropic Adaptation High Order CFD Anisotropic Meshing We present a method for anisotropic mesh refinement to high-order numerical solutions. We accomplish this by assigning metrics to vertices that approximate the error in that region. To choose values for each metric, we first reconstruct an error equation from the leading order terms of the Taylor expansion. Then, we use a Fourier approximation to choose the metric associated with that vertex. After assigning a metric to each vertex, we refine the mesh anisotropically using three mesh operations. The three mesh operations we use are swapping to maximize quality, inserting at approximate circumcenters to decrease cell size, and vertex removal to eliminate small edges. Because there are no guarantees on the results of these modification tools, we use them iteratively to produce a quasi-optimal mesh. We present examples demonstrating that our anisotropic refinement algorithm improves solution accuracy for both second and third order solutions compared with uniform refinement and isotropic refinement. We also analyze the effect of using second derivatives for refining third order solutions. 2008-02-21T17:14:31Z 2008-02-21T17:14:31Z 2008 2008-02-21T17:14:31Z 2008-05 Electronic Thesis or Dissertation http://hdl.handle.net/2429/415 en University of British Columbia |
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en |
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topic |
Anisotropic Adaptation High Order CFD Anisotropic Meshing |
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Anisotropic Adaptation High Order CFD Anisotropic Meshing Pagnutti, Douglas Anisotropic adaptation: metrics and meshes |
description |
We present a method for anisotropic mesh refinement to high-order numerical solutions. We accomplish this by assigning metrics to vertices that approximate the error in that region. To choose values for each metric, we first reconstruct an error equation from the leading order terms of the Taylor expansion. Then, we use a Fourier approximation to choose the metric associated with that vertex. After assigning a metric to each vertex, we refine the mesh anisotropically using three mesh operations. The three mesh operations we use are swapping to maximize quality, inserting at approximate circumcenters to decrease cell size, and vertex removal to eliminate small edges. Because there are no guarantees on the results of these modification tools, we use them iteratively to produce a quasi-optimal mesh. We present examples demonstrating that our anisotropic refinement algorithm improves solution accuracy for both second and third order solutions compared with uniform refinement and isotropic refinement. We also analyze the effect of using second derivatives for refining third order solutions. |
author |
Pagnutti, Douglas |
author_facet |
Pagnutti, Douglas |
author_sort |
Pagnutti, Douglas |
title |
Anisotropic adaptation: metrics and meshes |
title_short |
Anisotropic adaptation: metrics and meshes |
title_full |
Anisotropic adaptation: metrics and meshes |
title_fullStr |
Anisotropic adaptation: metrics and meshes |
title_full_unstemmed |
Anisotropic adaptation: metrics and meshes |
title_sort |
anisotropic adaptation: metrics and meshes |
publisher |
University of British Columbia |
publishDate |
2008 |
url |
http://hdl.handle.net/2429/415 |
work_keys_str_mv |
AT pagnuttidouglas anisotropicadaptationmetricsandmeshes |
_version_ |
1716654945069957120 |