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A face-centred finite volume method for second-order elliptic problems / Ruben, Sevilla

International Journal for Numerical Methods in Engineering

Swansea University Author: Ruben, Sevilla

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DOI (Published version): 10.1002/nme.5833

Abstract

The paper proposes a novel face-centred finite volume method. Contrary to existing cell-centred and vertex-centred finite volume methods, the proposed approach defines the global unknowns on the element faces. The solution and its gradient on the elements can then be recovered by solving an inexpens...

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Published in: International Journal for Numerical Methods in Engineering
ISSN: 00295981
Published: 2018
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URI: https://cronfa.swan.ac.uk/Record/cronfa39642
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Abstract: The paper proposes a novel face-centred finite volume method. Contrary to existing cell-centred and vertex-centred finite volume methods, the proposed approach defines the global unknowns on the element faces. The solution and its gradient on the elements can then be recovered by solving an inexpensive element by element problem. The method, inspired by the hybridisable discontinuous Galerkin, inherits all the mathematical properties of such methods, including the ability to satisfy the LBB condition using the same functional approximation for the velocity and the pressure fields. The paper presents a complete list of numerical examples to demonstrate the optimal approximation properties and its robustness with respect to the stabilisation parameter. In addition, three dimensional examples involving realistic geometries are included to show the efficiency of the method, capable of simulating the irrotational flow around a full aircraft configuration in less than ten minutes.
Keywords: finite volume method, face‐centred, hybridisable discontinuous Galerkin, lowest‐order approximation
College: College of Engineering