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A face-centred finite volume method for second-order elliptic problems

Rubén Sevilla Orcid Logo, Matteo Giacomini, Antonio Huerta

International Journal for Numerical Methods in Engineering, Volume: 115, Issue: 8, Pages: 986 - 1014

Swansea University Author: Rubén Sevilla Orcid Logo

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DOI (Published version): 10.1002/nme.5833

Abstract

This work proposes a novel finite volume paradigm, ie, the face‐centred finite volume (FCFV) method. Contrary to the popular vertex and cell‐centred finite volume methods, the novel FCFV defines the solution on the mesh faces (edges in two dimensions) to construct locally conservative numerical sche...

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Published in: International Journal for Numerical Methods in Engineering
ISSN: 0029-5981
Published: Wiley 2018
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URI: https://cronfa.swan.ac.uk/Record/cronfa39642
first_indexed 2018-04-30T13:54:36Z
last_indexed 2023-02-15T03:48:48Z
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spelling 2023-02-14T15:32:04.1771263 v2 39642 2018-04-30 A face-centred finite volume method for second-order elliptic problems b542c87f1b891262844e95a682f045b6 0000-0002-0061-6214 Rubén Sevilla Rubén Sevilla true false 2018-04-30 ACEM This work proposes a novel finite volume paradigm, ie, the face‐centred finite volume (FCFV) method. Contrary to the popular vertex and cell‐centred finite volume methods, the novel FCFV defines the solution on the mesh faces (edges in two dimensions) to construct locally conservative numerical schemes. The idea of the FCFV method stems from a hybridisable discontinuous Galerkin formulation with constant degree of approximation, and thus inheriting the convergence properties of the classical hybridisable discontinuous Galerkin. The resulting FCFV features a global problem in terms of a piecewise constant function defined on the faces of the mesh. The solution and its gradient in each element are then recovered by solving a set of independent element‐by‐element problems. The mathematical formulation of FCFV for Poisson and Stokes equation is derived, and numerical evidence of optimal convergence in two dimensions and three dimensions is provided. Numerical examples are presented to illustrate the accuracy, efficiency, and robustness of the proposed methodology. The results show that, contrary to other finite volume methods, the accuracy of the FCFV method is not sensitive to mesh distortion and stretching. In addition, the FCFV method shows its better performance, accuracy, and robustness using simplicial elements, facilitating its application to problems involving complex geometries in three dimensions. Journal Article International Journal for Numerical Methods in Engineering 115 8 986 1014 Wiley 0029-5981 finite volume method, face‐centred, hybridisable discontinuous Galerkin, lowest‐order approximation 24 8 2018 2018-08-24 10.1002/nme.5833 COLLEGE NANME Aerospace, Civil, Electrical, and Mechanical Engineering COLLEGE CODE ACEM Swansea University 2023-02-14T15:32:04.1771263 2018-04-30T11:59:58.7256002 Faculty of Science and Engineering School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Civil Engineering Rubén Sevilla 0000-0002-0061-6214 1 Matteo Giacomini 2 Antonio Huerta 3 0039642-30042018134752.pdf sevilla2018(4).pdf 2018-04-30T13:47:52.2870000 Output 17382688 application/pdf Accepted Manuscript true 2019-05-07T00:00:00.0000000 true eng
title A face-centred finite volume method for second-order elliptic problems
spellingShingle A face-centred finite volume method for second-order elliptic problems
Rubén Sevilla
title_short A face-centred finite volume method for second-order elliptic problems
title_full A face-centred finite volume method for second-order elliptic problems
title_fullStr A face-centred finite volume method for second-order elliptic problems
title_full_unstemmed A face-centred finite volume method for second-order elliptic problems
title_sort A face-centred finite volume method for second-order elliptic problems
author_id_str_mv b542c87f1b891262844e95a682f045b6
author_id_fullname_str_mv b542c87f1b891262844e95a682f045b6_***_Rubén Sevilla
author Rubén Sevilla
author2 Rubén Sevilla
Matteo Giacomini
Antonio Huerta
format Journal article
container_title International Journal for Numerical Methods in Engineering
container_volume 115
container_issue 8
container_start_page 986
publishDate 2018
institution Swansea University
issn 0029-5981
doi_str_mv 10.1002/nme.5833
publisher Wiley
college_str Faculty of Science and Engineering
hierarchytype
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
active_str 0
description This work proposes a novel finite volume paradigm, ie, the face‐centred finite volume (FCFV) method. Contrary to the popular vertex and cell‐centred finite volume methods, the novel FCFV defines the solution on the mesh faces (edges in two dimensions) to construct locally conservative numerical schemes. The idea of the FCFV method stems from a hybridisable discontinuous Galerkin formulation with constant degree of approximation, and thus inheriting the convergence properties of the classical hybridisable discontinuous Galerkin. The resulting FCFV features a global problem in terms of a piecewise constant function defined on the faces of the mesh. The solution and its gradient in each element are then recovered by solving a set of independent element‐by‐element problems. The mathematical formulation of FCFV for Poisson and Stokes equation is derived, and numerical evidence of optimal convergence in two dimensions and three dimensions is provided. Numerical examples are presented to illustrate the accuracy, efficiency, and robustness of the proposed methodology. The results show that, contrary to other finite volume methods, the accuracy of the FCFV method is not sensitive to mesh distortion and stretching. In addition, the FCFV method shows its better performance, accuracy, and robustness using simplicial elements, facilitating its application to problems involving complex geometries in three dimensions.
published_date 2018-08-24T07:25:44Z
_version_ 1821389456110780416
score 11.047523

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