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A Hybrid Pressure Formulation of the Face‐Centred Finite Volume Method for Viscous Laminar Incompressible Flows

Matteo Giacomini Orcid Logo, Davide Cortellessa, LUAN VIEIRA, Rubén Sevilla Orcid Logo, Antonio Huerta

International Journal for Numerical Methods in Engineering, Volume: 126, Issue: 10, Start page: e70037

Swansea University Authors: LUAN VIEIRA, Rubén Sevilla Orcid Logo

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DOI (Published version): 10.1002/nme.70037

Abstract

This work presents a hybrid pressure face‐centred finite volume (FCFV) solver to simulate steady‐state incompressible Navier‐Stokes flows. The method leverages the robustness, in the incompressible limit, of the hybridisable discontinuous Galerkin paradigm for compressible and weakly compressible fl...

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Published in: International Journal for Numerical Methods in Engineering
ISSN: 0029-5981 1097-0207
Published: Wiley 2025
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URI: https://cronfa.swan.ac.uk/Record/cronfa69557
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spelling 2025-06-11T11:24:42.1464176 v2 69557 2025-05-22 A Hybrid Pressure Formulation of the Face‐Centred Finite Volume Method for Viscous Laminar Incompressible Flows 53118ba8e77e55452a5228efae6f2fc1 LUAN VIEIRA LUAN VIEIRA true false b542c87f1b891262844e95a682f045b6 0000-0002-0061-6214 Rubén Sevilla Rubén Sevilla true false 2025-05-22 This work presents a hybrid pressure face‐centred finite volume (FCFV) solver to simulate steady‐state incompressible Navier‐Stokes flows. The method leverages the robustness, in the incompressible limit, of the hybridisable discontinuous Galerkin paradigm for compressible and weakly compressible flows to derive the formulation of a novel, low‐order face‐based discretization. The incompressibility constraint is enforced in a weak sense by introducing an inter‐cell mass flux, defined in terms of a new, hybrid variable that represents the pressure at the cell faces. This results in a new hybridization strategy where cell variables (velocity, pressure, and deviatoric strain rate tensor) are expressed as a function of velocity and pressure at the barycentre of the cell faces. The hybrid pressure formulation provides first‐order convergence of all variables, including the stress, without the need for gradient reconstruction, thus being less sensitive to cell type, stretching, distortion, and skewness than traditional low‐order finite volume solvers. Numerical benchmarks of Navier‐Stokes flows at low and moderate Reynolds numbers, in two and three dimensions, are presented to evaluate the accuracy and robustness of the method. In particular, the hybrid pressure formulation outperforms the FCFV method when convective effects are relevant, achieving accurate predictions on significantly coarser meshes. Journal Article International Journal for Numerical Methods in Engineering 126 10 e70037 Wiley 0029-5981 1097-0207 face-centred, finite volume methods, hybrid methods, hybridizable discontinuous Galerkin, incompressible Navier-Stokes 30 5 2025 2025-05-30 10.1002/nme.70037 COLLEGE NANME COLLEGE CODE Swansea University Another institution paid the OA fee The authors acknowledge the support of: Generalitat de Catalunya that partially funded the PhD scholarship of DC; H2020 MSCA ITN-EJD ProTechTion (Grant No. 764636) that partially funded the PhD scholarship of L.M.V.; Spanish Ministry of Science, Innovation and Universities and Spanish State Research Agency MICIU/AEI/10.13039/501100011033 (Grants No. PID2020-113463RB-C33 to M.G., PID2020-113463RB-C32 to A.H. and CEX2018-000797-S to M.G. and A.H.); Generalitat de Catalunya (Grant No. 2021-SGR-01049 to M.G. and A.H.); M.G. is Fellow of the Serra Húnter Programme of the Generalitat de Catalunya. 2025-06-11T11:24:42.1464176 2025-05-22T14:18:24.9788829 Faculty of Science and Engineering School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Civil Engineering Matteo Giacomini 0000-0001-6094-5944 1 Davide Cortellessa 2 LUAN VIEIRA 3 Rubén Sevilla 0000-0002-0061-6214 4 Antonio Huerta 5 69557__34331__a22a7a979797420f86a27b086388a9f8.pdf nme.70037.pdf 2025-05-22T14:18:24.9731064 Output 10003091 application/pdf Version of Record true © 2025 The Author(s). This is an open access article under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs License (CC BY-NC-ND). true eng http://creativecommons.org/licenses/by-nc-nd/4.0/
title A Hybrid Pressure Formulation of the Face‐Centred Finite Volume Method for Viscous Laminar Incompressible Flows
spellingShingle A Hybrid Pressure Formulation of the Face‐Centred Finite Volume Method for Viscous Laminar Incompressible Flows
LUAN VIEIRA
Rubén Sevilla
title_short A Hybrid Pressure Formulation of the Face‐Centred Finite Volume Method for Viscous Laminar Incompressible Flows
title_full A Hybrid Pressure Formulation of the Face‐Centred Finite Volume Method for Viscous Laminar Incompressible Flows
title_fullStr A Hybrid Pressure Formulation of the Face‐Centred Finite Volume Method for Viscous Laminar Incompressible Flows
title_full_unstemmed A Hybrid Pressure Formulation of the Face‐Centred Finite Volume Method for Viscous Laminar Incompressible Flows
title_sort A Hybrid Pressure Formulation of the Face‐Centred Finite Volume Method for Viscous Laminar Incompressible Flows
author_id_str_mv 53118ba8e77e55452a5228efae6f2fc1
b542c87f1b891262844e95a682f045b6
author_id_fullname_str_mv 53118ba8e77e55452a5228efae6f2fc1_***_LUAN VIEIRA
b542c87f1b891262844e95a682f045b6_***_Rubén Sevilla
author LUAN VIEIRA
Rubén Sevilla
author2 Matteo Giacomini
Davide Cortellessa
LUAN VIEIRA
Rubén Sevilla
Antonio Huerta
format Journal article
container_title International Journal for Numerical Methods in Engineering
container_volume 126
container_issue 10
container_start_page e70037
publishDate 2025
institution Swansea University
issn 0029-5981
1097-0207
doi_str_mv 10.1002/nme.70037
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 presents a hybrid pressure face‐centred finite volume (FCFV) solver to simulate steady‐state incompressible Navier‐Stokes flows. The method leverages the robustness, in the incompressible limit, of the hybridisable discontinuous Galerkin paradigm for compressible and weakly compressible flows to derive the formulation of a novel, low‐order face‐based discretization. The incompressibility constraint is enforced in a weak sense by introducing an inter‐cell mass flux, defined in terms of a new, hybrid variable that represents the pressure at the cell faces. This results in a new hybridization strategy where cell variables (velocity, pressure, and deviatoric strain rate tensor) are expressed as a function of velocity and pressure at the barycentre of the cell faces. The hybrid pressure formulation provides first‐order convergence of all variables, including the stress, without the need for gradient reconstruction, thus being less sensitive to cell type, stretching, distortion, and skewness than traditional low‐order finite volume solvers. Numerical benchmarks of Navier‐Stokes flows at low and moderate Reynolds numbers, in two and three dimensions, are presented to evaluate the accuracy and robustness of the method. In particular, the hybrid pressure formulation outperforms the FCFV method when convective effects are relevant, achieving accurate predictions on significantly coarser meshes.
published_date 2025-05-30T05:24:59Z
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score 11.090091

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