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

Luan M. Vieira, Matteo Giacomini, Rubén Sevilla Orcid Logo, Antonio Huerta

Computer Methods in Applied Mechanics and Engineering, Volume: 358, Start page: 112655

Swansea University Author: Rubén Sevilla Orcid Logo

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DOI (Published version): 10.1016/j.cma.2019.112655

Abstract

A second-order face-centred finite volume method (FCFV) is proposed. Contrary to the more popular cell-centred and vertex-centred finite volume (FV) techniques, the proposed method defines the solution on the faces of the mesh (edges in two dimensions). The method is based on a mixed formulation and...

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Published in: Computer Methods in Applied Mechanics and Engineering
ISSN: 0045-7825
Published: 2020
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URI: https://cronfa.swan.ac.uk/Record/cronfa52110
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first_indexed 2019-09-26T14:20:14Z
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spelling 2019-10-10T09:01:29.7557860 v2 52110 2019-09-26 A second-order face-centred finite volume method for elliptic problems b542c87f1b891262844e95a682f045b6 0000-0002-0061-6214 Rubén Sevilla Rubén Sevilla true false 2019-09-26 CIVL A second-order face-centred finite volume method (FCFV) is proposed. Contrary to the more popular cell-centred and vertex-centred finite volume (FV) techniques, the proposed method defines the solution on the faces of the mesh (edges in two dimensions). The method is based on a mixed formulation and therefore considers the solution and its gradient as independent unknowns. They are computed solving a cell-by-cell problem after the solution at the faces is determined. The proposed approach avoids the need of reconstructing the solution gradient, as required by cell-centred and vertex-centred FV methods. This strategy leads to a method that is insensitive to mesh distortion and stretching. The current method is second-order and requires the solution of a global system of equations of identical size and identical number of non-zero elements when compared to the recently proposed first-order FCFV. The formulation is presented for Poisson and Stokes problems. Numerical examples are used to illustrate the approximation properties of the method as well as to demonstrate its potential in three dimensional problems with complex geometries. The integration of a mesh adaptive procedure in the FCFV solution algorithm is also presented. Journal Article Computer Methods in Applied Mechanics and Engineering 358 112655 0045-7825 Finite volume method, Face-centred, Second-order convergence, Hybridisable discontinuous Galerkin 1 1 2020 2020-01-01 10.1016/j.cma.2019.112655 COLLEGE NANME Civil Engineering COLLEGE CODE CIVL Swansea University 2019-10-10T09:01:29.7557860 2019-09-26T10:41:39.5815830 Faculty of Science and Engineering School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Civil Engineering Luan M. Vieira 1 Matteo Giacomini 2 Rubén Sevilla 0000-0002-0061-6214 3 Antonio Huerta 4 0052110-26092019104347.pdf vieira2019.pdf 2019-09-26T10:43:47.4430000 Output 25463506 application/pdf Accepted Manuscript true 2020-10-03T00:00:00.0000000 false eng
title A second-order face-centred finite volume method for elliptic problems
spellingShingle A second-order face-centred finite volume method for elliptic problems
Rubén Sevilla
title_short A second-order face-centred finite volume method for elliptic problems
title_full A second-order face-centred finite volume method for elliptic problems
title_fullStr A second-order face-centred finite volume method for elliptic problems
title_full_unstemmed A second-order face-centred finite volume method for elliptic problems
title_sort A second-order face-centred finite volume method for elliptic problems
author_id_str_mv b542c87f1b891262844e95a682f045b6
author_id_fullname_str_mv b542c87f1b891262844e95a682f045b6_***_Rubén Sevilla
author Rubén Sevilla
author2 Luan M. Vieira
Matteo Giacomini
Rubén Sevilla
Antonio Huerta
format Journal article
container_title Computer Methods in Applied Mechanics and Engineering
container_volume 358
container_start_page 112655
publishDate 2020
institution Swansea University
issn 0045-7825
doi_str_mv 10.1016/j.cma.2019.112655
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 A second-order face-centred finite volume method (FCFV) is proposed. Contrary to the more popular cell-centred and vertex-centred finite volume (FV) techniques, the proposed method defines the solution on the faces of the mesh (edges in two dimensions). The method is based on a mixed formulation and therefore considers the solution and its gradient as independent unknowns. They are computed solving a cell-by-cell problem after the solution at the faces is determined. The proposed approach avoids the need of reconstructing the solution gradient, as required by cell-centred and vertex-centred FV methods. This strategy leads to a method that is insensitive to mesh distortion and stretching. The current method is second-order and requires the solution of a global system of equations of identical size and identical number of non-zero elements when compared to the recently proposed first-order FCFV. The formulation is presented for Poisson and Stokes problems. Numerical examples are used to illustrate the approximation properties of the method as well as to demonstrate its potential in three dimensional problems with complex geometries. The integration of a mesh adaptive procedure in the FCFV solution algorithm is also presented.
published_date 2020-01-01T04:04:18Z
_version_ 1763753337408192512
score 11.016235

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