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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, Volume: 125, Issue: 10

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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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 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.
Item Description: 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.
Keywords: Face-centred finite volume, Stokes, variable viscosity, hybridisable discontinuous Galerkin
College: Faculty of Science and Engineering
Issue: 10

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