Viscoelastic flows of a lid-driven cavity using spectral element methods

Fenton, D., Bowen, P. J. ORCID: https://orcid.org/0000-0002-3644-6878 and De Angelis, E. 2024. Viscoelastic flows of a lid-driven cavity using spectral element methods. Journal of Non-Newtonian Fluid Mechanics 330 , 105263. 10.1016/j.jnnfm.2024.105263

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Abstract

The performance of a spectral element method in the DEVSS-G formulation for the solution of non-Newtonian flows is assessed by means of a systematic analysis of the benchmark lid-driven cavity problem. It is first validated by comparison with the creeping Newtonian and Oldroyd-B flows, where in the latter case a lid velocity regularisation scheme must be employed to remove the singularity at the lid-wall interfaces. In both instances, excellent agreement is found with the literature for stable, time-independent flows, and in fact it is shown that higher Weissenberg numbers can be obtained using the present methodology for these types of flow. Some physical aspects of the solutions are also presented and discussed, however at increasing Weissenberg numbers, the methodology breaks down due to a lack of convergence in the BDF/FPI time advancement scheme. By systematically assessing the effects of the levels of h p -refinement and temporal refinement on the flow fields, as well as the introduction of the extension-limiting Giesekus mobility parameter in the constitutive equations, it is demonstrated that in each instance the inability to accurately resolve the stress gradients leads to a compounding of errors in the BDF/FPI regime, ultimately causing it to diverge.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Engineering
Additional Information:	License information from Publisher: LICENSE 1: URL: http://creativecommons.org/licenses/by-nc-nd/4.0/, Start Date: 2024-05-29
Publisher:	Elsevier
ISSN:	0377-0257
Funders:	EPSRC
Date of First Compliant Deposit:	3 June 2024
Date of Acceptance:	28 May 2024
Last Modified:	12 Nov 2024 10:19
URI:	https://orca.cardiff.ac.uk/id/eprint/169394

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