A spectral element formulation of the immersed boundary method for Newtonian fluids

Rowlatt, C. F. and Phillips, T. N. ORCID: https://orcid.org/0000-0001-6455-1205 2016. A spectral element formulation of the immersed boundary method for Newtonian fluids. Computer Methods in Applied Mechanics and Engineering 298 , pp. 29-57. 10.1016/j.cma.2015.08.010

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Abstract

A spectral element formulation of the immersed boundary method (IBM) is presented. The spectral element formulation (SE-IBM) is a generalisation of the finite element immersed boundary method (FE-IBM) based on high-order approximations of the fluid variables. Several schemes for tracking the movement of the immersed boundary are considered and a semi-implicit Euler scheme is shown to offer advantages in terms of accuracy and efficiency. High-order spectral element approximations provide improved area conservation properties of the IBM due to the incompressibility constraint being more accurately satisfied. Superior orders of convergence are obtained for SE-IBM compared with FE-IBM in both L2 and H1 norms. The area conservation and convergence properties of the scheme are demonstrated on a series of benchmark problems.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Advanced Research Computing @ Cardiff (ARCCA) Mathematics
Subjects:	Q Science > QA Mathematics
Uncontrolled Keywords:	Immersed boundary method; Spectral element; Newtonian; Fluid-structure interaction
Additional Information:	This is an open access article under the CC BY license (http://creativecommons. org/licenses/by/4.0/).
Publisher:	Elsevier
ISSN:	0045-7825
Funders:	EPSRC
Date of First Compliant Deposit:	30 March 2016
Date of Acceptance:	20 August 2015
Last Modified:	04 May 2023 20:22
URI:	https://orca.cardiff.ac.uk/id/eprint/77399

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