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Face‐centred finite volume methods for Stokes flows with variable viscosity

Rubén Sevilla Orcid Logo, Thibault Duretz Orcid Logo

International Journal for Numerical Methods in Engineering

Swansea University Author: Rubén Sevilla Orcid Logo

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DOI (Published version): 10.1002/nme.7450

Abstract

Six face-centred finite volume formulations are derived and compared for the simulation of Stokes flows with spatially varying viscosity. The main difference between the methods derived is the mixed variable used in the mixed formulation and the use of a weak or strong form in each element using int...

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Published in: International Journal for Numerical Methods in Engineering
ISSN: 0029-5981 1097-0207
Published: Wiley 2024
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URI: https://cronfa.swan.ac.uk/Record/cronfa65639
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first_indexed 2024-02-14T14:36:12Z
last_indexed 2024-02-14T14:36:12Z
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spelling v2 65639 2024-02-14 Face‐centred finite volume methods for Stokes flows with variable viscosity b542c87f1b891262844e95a682f045b6 0000-0002-0061-6214 Rubén Sevilla Rubén Sevilla true false 2024-02-14 CIVL Six face-centred finite volume formulations are derived and compared for the simulation of Stokes flows with spatially varying viscosity. The main difference between the methods derived is the mixed variable used in the mixed formulation and the use of a weak or strong form in each element using integration by parts. A brief discussion about the properties of the different methods is provided, including comments on the computational cost and the symmetry of the resulting global system of equations. Finally, numerical examples in two and three dimensions are used to compare the accuracy of all the formulations presented. The examples include a problem where the methods are employed to simulate a steep variation of the viscosity, showing the ability to perform these simulations without using a mesh conforming to a material interface. The performance of different element types and different choices of the stabilisation is also discussed. Journal Article International Journal for Numerical Methods in Engineering 0 Wiley 0029-5981 1097-0207 Face-centred finite volume, Stokes, variable viscosity, hybridisable discontinuous Galerkin 14 2 2024 2024-02-14 10.1002/nme.7450 Data availability:The data supporting the findings of this study are openly available and can be accessed via the following link: https://github.com/tduretz/FCFV_NME23. COLLEGE NANME Civil Engineering COLLEGE CODE CIVL Swansea University SU Library paid the OA fee (TA Institutional Deal) 2024-04-03T16:31:48.9304368 2024-02-14T14:32:21.7347613 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 65639__29743__5bd176c7c4e840669473022c6baac02a.pdf 65639_VoR.pdf 2024-03-18T18:11:30.3773189 Output 3703786 application/pdf Version of Record true © 2024 The Authors. This is an open access article under the terms of the Creative Commons Attribution License. true eng http://creativecommons.org/licenses/by/4.0/
title Face‐centred finite volume methods for Stokes flows with variable viscosity
spellingShingle Face‐centred finite volume methods for Stokes flows with variable viscosity
Rubén Sevilla
title_short Face‐centred finite volume methods for Stokes flows with variable viscosity
title_full Face‐centred finite volume methods for Stokes flows with variable viscosity
title_fullStr Face‐centred finite volume methods for Stokes flows with variable viscosity
title_full_unstemmed Face‐centred finite volume methods for Stokes flows with variable viscosity
title_sort Face‐centred finite volume methods for Stokes flows with variable viscosity
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 0
publishDate 2024
institution Swansea University
issn 0029-5981
1097-0207
doi_str_mv 10.1002/nme.7450
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 Six face-centred finite volume formulations are derived and compared for the simulation of Stokes flows with spatially varying viscosity. The main difference between the methods derived is the mixed variable used in the mixed formulation and the use of a weak or strong form in each element using integration by parts. A brief discussion about the properties of the different methods is provided, including comments on the computational cost and the symmetry of the resulting global system of equations. Finally, numerical examples in two and three dimensions are used to compare the accuracy of all the formulations presented. The examples include a problem where the methods are employed to simulate a steep variation of the viscosity, showing the ability to perform these simulations without using a mesh conforming to a material interface. The performance of different element types and different choices of the stabilisation is also discussed.
published_date 2024-02-14T16:31:45Z
_version_ 1795328107076386816
score 11.013148

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