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

Rowlatt, C. F. and Phillips, T. N. 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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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)
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: 19 Nov 2020 11:00

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