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A face‐centered finite volume method for high‐contrast Stokes interface problems

Rubén Sevilla Orcid Logo, Thibault Duretz Orcid Logo

International Journal for Numerical Methods in Engineering, Volume: 124, Issue: 17

Swansea University Author: Rubén Sevilla Orcid Logo

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DOI (Published version): 10.1002/nme.7294

Abstract

A new face-centred finite volume method (FCFV) for Stokes problems involving sharp interfaces is proposed. Two formulations, based on two strong forms of the Stokes problems and using different mixed variables, are presented. Particular attention is paid to the symmetry of the resulting system of gl...

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Published in: International Journal for Numerical Methods in Engineering
ISSN: 0029-5981 1097-0207
Published: Wiley
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URI: https://cronfa.swan.ac.uk/Record/cronfa63337
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spelling v2 63337 2023-05-03 A face‐centered finite volume method for high‐contrast Stokes interface problems b542c87f1b891262844e95a682f045b6 0000-0002-0061-6214 Rubén Sevilla Rubén Sevilla true false 2023-05-03 CIVL A new face-centred finite volume method (FCFV) for Stokes problems involving sharp interfaces is proposed. Two formulations, based on two strong forms of the Stokes problems and using different mixed variables, are presented. Particular attention is paid to the symmetry of the resulting system of global equations, and a simple rewriting of the interface boundary condition is proposed to ensure that one of the formulations preserves the symmetry of the linear system that is usually lost when considering material interfaces. Four numerical examples are considered to test the implementation numerically by performing mesh convergence studies, in two and three dimensions. The examples account for discontinuous viscosity as well as the effect of surface tension. The results show that one of the formulations is less sensitive to the numerical stabilisation used in FCFV methods but does not preserve the symmetry of the global system, whereas the other formulation is more sensitive tothe stabilisation, but preserves the symmetry of the resulting system of equations. The FCFV method appears as a promising alternative for the simulation of viscous flow involving internal boundaries on conformal meshes. The potential application of the FCFV method for the purpose of geodynamic modelling is discussed. Journal Article International Journal for Numerical Methods in Engineering 124 17 Wiley 0029-5981 1097-0207 Face-centred finite volume, high contrast, interface, Stokes 0 0 0 0001-01-01 10.1002/nme.7294 http://dx.doi.org/10.1002/nme.7294 COLLEGE NANME Civil Engineering COLLEGE CODE CIVL Swansea University SU Library paid the OA fee (TA Institutional Deal) Swansea University. The first author acknowledges the support of the Engineering and Physical Sciences Research Council (Grant Number: EP/T009071/1). 2023-09-05T11:52:33.3916580 2023-05-03T08:49:28.0684250 Faculty of Science and Engineering School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Civil Engineering Rubén Sevilla 0000-0002-0061-6214 1 Thibault Duretz 0000-0001-8472-7490 2 63337__27699__c87af94b59374eda917a1abb8e2d1247.pdf 63337.pdf 2023-06-05T09:19:00.9599830 Output 4411215 application/pdf Version of Record true © 2023 The Authors. International Journal for Numerical Methods in Engineering published by John Wiley & Sons Ltd. Distributed under the terms of a Creative Commons Attribution 4.0 License (CC BY 4.0). true eng http://creativecommons.org/licenses/by/4.0/
title A face‐centered finite volume method for high‐contrast Stokes interface problems
spellingShingle A face‐centered finite volume method for high‐contrast Stokes interface problems
Rubén Sevilla
title_short A face‐centered finite volume method for high‐contrast Stokes interface problems
title_full A face‐centered finite volume method for high‐contrast Stokes interface problems
title_fullStr A face‐centered finite volume method for high‐contrast Stokes interface problems
title_full_unstemmed A face‐centered finite volume method for high‐contrast Stokes interface problems
title_sort A face‐centered finite volume method for high‐contrast Stokes interface problems
author_id_str_mv b542c87f1b891262844e95a682f045b6
author_id_fullname_str_mv b542c87f1b891262844e95a682f045b6_***_Rubén Sevilla
author Rubén Sevilla
author2 Rubén Sevilla
Thibault Duretz
format Journal article
container_title International Journal for Numerical Methods in Engineering
container_volume 124
container_issue 17
institution Swansea University
issn 0029-5981
1097-0207
doi_str_mv 10.1002/nme.7294
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
url http://dx.doi.org/10.1002/nme.7294
document_store_str 1
active_str 0
description A new face-centred finite volume method (FCFV) for Stokes problems involving sharp interfaces is proposed. Two formulations, based on two strong forms of the Stokes problems and using different mixed variables, are presented. Particular attention is paid to the symmetry of the resulting system of global equations, and a simple rewriting of the interface boundary condition is proposed to ensure that one of the formulations preserves the symmetry of the linear system that is usually lost when considering material interfaces. Four numerical examples are considered to test the implementation numerically by performing mesh convergence studies, in two and three dimensions. The examples account for discontinuous viscosity as well as the effect of surface tension. The results show that one of the formulations is less sensitive to the numerical stabilisation used in FCFV methods but does not preserve the symmetry of the global system, whereas the other formulation is more sensitive tothe stabilisation, but preserves the symmetry of the resulting system of equations. The FCFV method appears as a promising alternative for the simulation of viscous flow involving internal boundaries on conformal meshes. The potential application of the FCFV method for the purpose of geodynamic modelling is discussed.
published_date 0001-01-01T11:52:34Z
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score 11.035655

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