Ranner, T orcid.org/0000-0001-7682-3175 (2020) A stable finite element method for low inertia undulatory locomotion in three dimensions. Applied Numerical Mathematics, 156. pp. 422-445. ISSN 0168-9274
Abstract
We present and analyse a numerical method for understanding the low-inertia dynamics of an open, inextensible viscoelastic rod - a long and thin three dimensional object - representing the body of a long, thin microswimmer. Our model allows for both elastic and viscous, bending and twisting deformations and describes the evolution of the midline curve of the rod as well as an orthonormal frame which fully determines the rod's three dimensional geometry. The numerical method is based on using a combination of piecewise linear and piecewise constant finite element functions based on a novel rewriting of the model equations. We derive a stability estimate for the semi-discrete scheme and show that at the fully discrete level that we have good control over the length element and preserve the frame orthonormality conditions up to machine precision. Numerical experiments demonstrate both the good properties of the method as well as the applicability of the method for simulating undulatory locomotion in the low-inertia regime.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2020 IMACS. Published by Elsevier B.V. This is an author produced version of a paper published in Applied Numerical Mathematics. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Kirchoff rod; Viscoelastic materials; Finite element methods; Biomechanics; undulatory locomotion |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Computing (Leeds) |
Funding Information: | Funder Grant number Leverhulme Trust ECF-2017-591 |
Depositing User: | Symplectic Publications |
Date Deposited: | 10 Jun 2020 11:02 |
Last Modified: | 22 Nov 2023 14:40 |
Status: | Published |
Publisher: | Elsevier |
Identification Number: | 10.1016/j.apnum.2020.05.009 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:144404 |