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A non-oscillatory face-centred finite volume method for compressible flows

Jordi Vila-Pérez, Matteo Giacomini, Rubén Sevilla Orcid Logo, Antonio Huerta

Computers & Fluids, Volume: 235, Start page: 105272

Swansea University Author: Rubén Sevilla Orcid Logo

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Abstract

This work presents the face-centred finite volume (FCFV) paradigm for the simulation of compressible flows. The FCFV method defines the unknowns at the face barycentre and uses a hybridisation procedure to eliminate all the degrees of freedom inside the cells. In addition, Riemann solvers are define...

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Published in: Computers & Fluids
ISSN: 0045-7930
Published: Elsevier BV 2022
Online Access: Check full text

URI: https://cronfa.swan.ac.uk/Record/cronfa58994
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Abstract: This work presents the face-centred finite volume (FCFV) paradigm for the simulation of compressible flows. The FCFV method defines the unknowns at the face barycentre and uses a hybridisation procedure to eliminate all the degrees of freedom inside the cells. In addition, Riemann solvers are defined implicitly within the expressions of the numerical fluxes. The resultingmethodology provides first-order accurate approximations of the conservative quantities, i.e. density, momentum and energy, as well as of the viscous stress tensor and of the heat flux, without the need of any gradient reconstruction procedure. Hence, the FCFV solver preserves the accuracy of theapproximation in presence of distorted and highly stretched cells, providing a solver insensitive to mesh quality. In addition, FCFV is capable of constructing non-oscillatory approximations of sharp discontinuities without resorting to shock capturing or limiting techniques. For flows at low Machnumber, the method is robust and is capable of computing accurate solutions in the incompressible limit without the need of introducing specific pressure correction strategies. A set of 2D and 3D benchmarks of external flows is presented to validate the methodology in different flow regimes, from inviscid to viscous laminar flows, from transonic to subsonic incompressible flows, demonstrating its potential to handle compressible flows in realistic scenarios.
Keywords: Finite volume method, face-centred, hybridisable discontinuous Galerkin, compressible flows, Riemann solvers, incompressible limit
College: College of Engineering
Funders: This work was supported by the Spanish Ministry of Economy and Competitiveness, through the María de Maeztu programme for units of excellence in R&D that financed the PhD fellowship of J.V.P. (MDM- 2014-0445), the Spanish Ministry of Science and Innovation and the Spanish State Research Agency MCIN/AEI/10.13039/501100011033 (PID2020-113463RB-C33 to M.G., PID2020-113463RB-C32 to A.H., CEX2018-000797-S to A.H. and M.G.), the Generalitat de Catalunya, Spain (2017-SGR-1278 to A.H. and M.G.) and the Engineering and Physical Sciences Research Council, United Kingdom (EP/P033997/1 to R.S.). M.G. also acknowledges the support of the Serra Húnter Programme of the Generalitat de Catalunya.
Start Page: 105272