No Cover Image

Journal article 123 views 15 downloads

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

  • nme.70037.pdf

    PDF | Version of Record

    © 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).

    Download (9.54MB)

Check full text

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...

Full description

Published in: International Journal for Numerical Methods in Engineering
ISSN: 0029-5981 1097-0207
Published: Wiley 2025
Online Access: Check full text

URI: https://cronfa.swan.ac.uk/Record/cronfa69557
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 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.
Keywords: face-centred, finite volume methods, hybrid methods, hybridizable discontinuous Galerkin, incompressible Navier-Stokes
College: Faculty of Science and Engineering
Funders: 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.
Issue: 10
Start Page: e70037

Similar Items