A high resolution PDE approach to quadrilateral mesh generation

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Title: A high resolution PDE approach to quadrilateral mesh generation
Authors: Marcon, J
Kopriva, DA
Sherwin, SJ
Peiro, J
Item 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.
Issue Date: 15-Dec-2019
Date of Acceptance: 29-Aug-2019
URI: http://hdl.handle.net/10044/1/73081
DOI: https://doi.org/10.1016/j.jcp.2019.108918
ISSN: 0021-9991
Publisher: Elsevier BV
Journal / Book Title: Journal of Computational Physics
Volume: 399
Replaces: 10044/1/71503
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/Funder: Commission of the European Communities
Funder's Grant Number: 675585
Keywords: math.NA
65N50, 65M50
Applied Mathematics
01 Mathematical Sciences
02 Physical Sciences
09 Engineering
Publication Status: Published online
Embargo Date: 2020-09-03
Article Number: 108918
Online Publication Date: 2019-09-03
Appears in Collections:Faculty of Engineering

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