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A second‐order face‐centred finite volume method on general meshes with automatic mesh adaptation

Matteo Giacomini, Rubén Sevilla Orcid Logo

International Journal for Numerical Methods in Engineering, Volume: 121, Issue: 23

Swansea University Author: Rubén Sevilla Orcid Logo

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DOI (Published version): 10.1002/nme.6428

Abstract

A second‐order face‐centred finite volume strategy on general meshes is proposed. The method uses a mixed formulation in which a constant approximation of the unknown is computed on the faces of the mesh. Such information is then used to solve a set of problems, independent cell‐by‐cell, to retrieve...

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Published in: International Journal for Numerical Methods in Engineering
ISSN: 0029-5981 1097-0207
Published: Wiley 2020
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URI: https://cronfa.swan.ac.uk/Record/cronfa54125
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spelling 2021-07-22T14:30:20.7171856 v2 54125 2020-05-04 A second‐order face‐centred finite volume method on general meshes with automatic mesh adaptation b542c87f1b891262844e95a682f045b6 0000-0002-0061-6214 Rubén Sevilla Rubén Sevilla true false 2020-05-04 CIVL A second‐order face‐centred finite volume strategy on general meshes is proposed. The method uses a mixed formulation in which a constant approximation of the unknown is computed on the faces of the mesh. Such information is then used to solve a set of problems, independent cell‐by‐cell, to retrieve the local values of the solution and its gradient. The main novelty of this approach is the introduction of a new basis function, utilised for the linear approximation of the primal variable in each cell. Contrary to the commonly used nodal basis, the proposed basis is suitable for computations on general meshes, including meshes with different cell types. The resulting approach provides second‐order accuracy for the solution and first‐order for its gradient, without the need of reconstruction procedures, is robust in the incompressible limit and insensitive to cell distortion and stretching. The second‐order accuracy of the solution is exploited to devise an automatic mesh adaptivity strategy. An efficient error indicator is obtained from the computation of one extra local problem, independent cell‐by‐cell, and is used to drive mesh adaptivity. Numerical examples illustrating the approximation properties of the method and of the mesh adaptivity procedure are presented. The potential of the proposed method with automatic mesh adaptation is demonstrated in the context of microfluidics. Journal Article International Journal for Numerical Methods in Engineering 121 23 Wiley 0029-5981 1097-0207 finite volume methods, face-centred, second-order, general meshes, automatic adaptivity, hybridisable discontinuous Galerkin 21 7 2020 2020-07-21 10.1002/nme.6428 COLLEGE NANME Civil Engineering COLLEGE CODE CIVL Swansea University SU Library paid the OA fee (TA Institutional Deal) Agència de Gestió d'Ajuts Universitaris i de Recerca (GrantNumber(s): 2017‐SGR‐1278) Engineering and Physical Sciences Research Council (GrantNumber(s): EP/P033997/1) H2020 Marie Skłodowska-Curie Actions (GrantNumber(s): 764636) Secretaría de Estado de Investigación, Desarrollo e Innovación (GrantNumber(s): DPI2017‐85139‐C2‐2‐R) 2017‐SGR‐1278), EP/P033997/1), 2021-07-22T14:30:20.7171856 2020-05-04T16:25:43.1087606 Faculty of Science and Engineering School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Civil Engineering Matteo Giacomini 1 Rubén Sevilla 0000-0002-0061-6214 2 54125__17849__07e6a9320d0f470098d1bf1b19625e2d.pdf 54125.pdf 2020-08-04T13:37:48.8266200 Output 5693263 application/pdf Version of Record true Copyright: The Authors. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. true eng https://creativecommons.org/licenses/by/4.0/
title A second‐order face‐centred finite volume method on general meshes with automatic mesh adaptation
spellingShingle A second‐order face‐centred finite volume method on general meshes with automatic mesh adaptation
Rubén Sevilla
title_short A second‐order face‐centred finite volume method on general meshes with automatic mesh adaptation
title_full A second‐order face‐centred finite volume method on general meshes with automatic mesh adaptation
title_fullStr A second‐order face‐centred finite volume method on general meshes with automatic mesh adaptation
title_full_unstemmed A second‐order face‐centred finite volume method on general meshes with automatic mesh adaptation
title_sort A second‐order face‐centred finite volume method on general meshes with automatic mesh adaptation
author_id_str_mv b542c87f1b891262844e95a682f045b6
author_id_fullname_str_mv b542c87f1b891262844e95a682f045b6_***_Rubén Sevilla
author Rubén Sevilla
author2 Matteo Giacomini
Rubén Sevilla
format Journal article
container_title International Journal for Numerical Methods in Engineering
container_volume 121
container_issue 23
publishDate 2020
institution Swansea University
issn 0029-5981
1097-0207
doi_str_mv 10.1002/nme.6428
publisher Wiley
college_str Faculty of Science and Engineering
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hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Civil Engineering{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Civil Engineering
document_store_str 1
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description A second‐order face‐centred finite volume strategy on general meshes is proposed. The method uses a mixed formulation in which a constant approximation of the unknown is computed on the faces of the mesh. Such information is then used to solve a set of problems, independent cell‐by‐cell, to retrieve the local values of the solution and its gradient. The main novelty of this approach is the introduction of a new basis function, utilised for the linear approximation of the primal variable in each cell. Contrary to the commonly used nodal basis, the proposed basis is suitable for computations on general meshes, including meshes with different cell types. The resulting approach provides second‐order accuracy for the solution and first‐order for its gradient, without the need of reconstruction procedures, is robust in the incompressible limit and insensitive to cell distortion and stretching. The second‐order accuracy of the solution is exploited to devise an automatic mesh adaptivity strategy. An efficient error indicator is obtained from the computation of one extra local problem, independent cell‐by‐cell, and is used to drive mesh adaptivity. Numerical examples illustrating the approximation properties of the method and of the mesh adaptivity procedure are presented. The potential of the proposed method with automatic mesh adaptation is demonstrated in the context of microfluidics.
published_date 2020-07-21T04:07:28Z
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score 11.016235

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