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On algorithms with good mesh properties for problems with moving boundaries based on the harmonic map heat flow and the DeTurck trick
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Elliott, Charles M. and Fritz, Hans (2016) On algorithms with good mesh properties for problems with moving boundaries based on the harmonic map heat flow and the DeTurck trick. Journal of Computational Mathematics, 2 . pp. 141-176. doi:10.5802/smai-jcm.12 ISSN 2426-8399.
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Official URL: https://doi.org/10.5802/smai-jcm.12
Abstract
In this paper, we present a general approach to obtain numerical schemes with good mesh properties for problems with moving boundaries, that is for evolving submanifolds with boundaries. This includes moving domains and surfaces with boundaries. Our approach is based on a variant of the so-called the DeTurck trick. By reparametrizing the evolution of the submanifold via solutions to the harmonic map heat flow of manifolds with boundary, we obtain a new velocity field for the motion of the submanifold. Moving the vertices of the computational mesh according to this velocity field automatically leads to computational meshes of high quality both for the submanifold and its boundary. Using the ALE-method in [16], this idea can be easily built into algorithms for the computation of physical problems with moving boundaries.
Item Type: | Journal Article | ||||||
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Subjects: | Q Science > QA Mathematics | ||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||
Library of Congress Subject Headings (LCSH): | Algorithms, Harmonic maps, Submanifolds | ||||||
Journal or Publication Title: | Journal of Computational Mathematics | ||||||
Publisher: | Global Science Press | ||||||
ISSN: | 2426-8399 | ||||||
Official Date: | 2016 | ||||||
Dates: |
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Volume: | 2 | ||||||
Page Range: | pp. 141-176 | ||||||
DOI: | 10.5802/smai-jcm.12 | ||||||
Status: | Peer Reviewed | ||||||
Publication Status: | Published | ||||||
Access rights to Published version: | Open Access (Creative Commons) | ||||||
Date of first compliant deposit: | 13 September 2016 | ||||||
Date of first compliant Open Access: | 13 September 2016 | ||||||
Funder: | Alexander von Humboldt-Stiftung (AvHS), University of Warwick | ||||||
Open Access Version: |
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