Comparison of 2D boundary curving methods with modal shape functions and a piecewise linear target mesh
Comparison of 2D boundary curving methods with modal shape functions and a piecewise linear target mesh
t is well known that high-order simulation techniques demand an accurate geometric representation and a coarse mesh. To fulfill both requirements, curved meshes are generated. In most cases, curving methods assume that the exact geometry is known. But it can be useful to develop curving methods with only a limited knowledge of the target geometry. In this paper, three curving methods are described that take a piecewise fine linear mesh as input: a least squares approach, a direct optimisation in the H1-seminorm, and a H1-seminorm optimisation in a reference space. Hierarchic, modal shape functions are used as basis for the geometric approximation. The methods are compared on two test geometries, a unit circle and a distorted ellipse. Considering both test cases, the direct optimisation approach shows the most promising results. Finally, the main steps for the extension to 3D are outlined.
Mesh Curving, High-Order Methods, Integrated Legendre Polynomials, Lobatto Polynomials, Linear Target Mesh
91-101
Ziel, Verena, Stephanie
105c1e47-78c5-49ca-81c3-a834117c98d0
Bériot, H.
d73aea9a-8247-493f-9603-e76dc60e99ba
Atak, O
3a68e4ba-8e41-4e51-8146-651bcda11ded
Gabard, Gwenael
bfd82aee-20f2-4e2c-ad92-087dc8ff6ce7
18 October 2017
Ziel, Verena, Stephanie
105c1e47-78c5-49ca-81c3-a834117c98d0
Bériot, H.
d73aea9a-8247-493f-9603-e76dc60e99ba
Atak, O
3a68e4ba-8e41-4e51-8146-651bcda11ded
Gabard, Gwenael
bfd82aee-20f2-4e2c-ad92-087dc8ff6ce7
Ziel, Verena, Stephanie, Bériot, H., Atak, O and Gabard, Gwenael
(2017)
Comparison of 2D boundary curving methods with modal shape functions and a piecewise linear target mesh.
Procedia Engineering, 203, .
(doi:10.1016/j.proeng.2017.09.791).
Abstract
t is well known that high-order simulation techniques demand an accurate geometric representation and a coarse mesh. To fulfill both requirements, curved meshes are generated. In most cases, curving methods assume that the exact geometry is known. But it can be useful to develop curving methods with only a limited knowledge of the target geometry. In this paper, three curving methods are described that take a piecewise fine linear mesh as input: a least squares approach, a direct optimisation in the H1-seminorm, and a H1-seminorm optimisation in a reference space. Hierarchic, modal shape functions are used as basis for the geometric approximation. The methods are compared on two test geometries, a unit circle and a distorted ellipse. Considering both test cases, the direct optimisation approach shows the most promising results. Finally, the main steps for the extension to 3D are outlined.
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proeng_imr_ziel
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More information
Accepted/In Press date: 1 April 2016
e-pub ahead of print date: 18 October 2017
Published date: 18 October 2017
Keywords:
Mesh Curving, High-Order Methods, Integrated Legendre Polynomials, Lobatto Polynomials, Linear Target Mesh
Identifiers
Local EPrints ID: 417737
URI: http://eprints.soton.ac.uk/id/eprint/417737
ISSN: 1877-7058
PURE UUID: f4a2b963-a50f-4563-91e8-a107924d2858
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Date deposited: 12 Feb 2018 17:30
Last modified: 15 Mar 2024 18:11
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Contributors
Author:
Verena, Stephanie Ziel
Author:
H. Bériot
Author:
O Atak
Author:
Gwenael Gabard
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