A high resolution PDE approach to quadrilateral mesh generation
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Accepted version
Author(s)
Marcon, Julian
Kopriva, David A
Sherwin, Spencer J
Peiro, Joaquim
Type
Journal Article
Abstract
We describe a high order technique to generate quadrilateral decompositions and meshes for complex two dimensional domains using spectral elements in a field guided procedure. Inspired by cross field methods, we never actually compute crosses. Instead, we compute a high order accurate guiding field using a continuous Galerkin (CG) or discontinuous Galerkin (DG) spectral element method to solve a Laplace equation for each of the field variables using the open source code Nektar++. The spectral method provides spectral convergence and sub-element resolution of the fields. The DG approximation allows meshing of corners that are not multiples of pi/2 in a discretization consistent manner, when needed. The high order field can then be exploited to accurately find irregular nodes, and can be accurately integrated using a high order separatrix integration method to avoid features like limit cycles. The result is a mesh with naturally curved quadrilateral elements that do not need to be curved a posteriori to eliminate invalid elements. The mesh generation procedure is implemented in the open source mesh generation program NekMesh.
Date Issued
2019-12-15
Date Acceptance
2019-08-29
Citation
Journal of Computational Physics, 2019, 399, pp.1-17
ISSN
0021-9991
Publisher
Elsevier BV
Start Page
1
End Page
17
Journal / Book Title
Journal of Computational Physics
Volume
399
Copyright Statement
© 2019 Elsevier Ltd. All rights reserved. This manuscript is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International Licence http://creativecommons.org/licenses/by-nc-nd/4.0/
Sponsor
Commission of the European Communities
Identifier
http://arxiv.org/abs/1901.02405v1
Grant Number
675008
Subjects
math.NA
math.NA
65N50, 65M50
Publication Status
Published online
Article Number
108918
Date Publish Online
2019-09-03