The University of Southampton
University of Southampton Institutional Repository

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
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
1877-7058
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
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, 91-101. (doi:10.1016/j.proeng.2017.09.791).

Record type: Article

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.

Text
proeng_imr_ziel - Version of Record
Download (939kB)

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

Catalogue record

Date deposited: 12 Feb 2018 17:30
Last modified: 16 Dec 2019 18:29

Export record

Altmetrics

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of http://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×