Griffith, B. E. and Luo, X. (2017) Hybrid finite difference/finite element immersed boundary method. International Journal for Numerical Methods in Biomedical Engineering, 33(12), e2888. (doi: 10.1002/cnm.2888) (PMID:28425587)
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Abstract
The immersed boundary method is an approach to fluid-structure interaction that uses a Lagrangian description of the structural deformations, stresses, and forces along with an Eulerian description of the momentum, viscosity, and incompressibility of the fluid-structure system. The original immersed boundary methods described immersed elastic structures using systems of flexible fibers, and even now, most immersed boundary methods still require Lagrangian meshes that are finer than the Eulerian grid. This work introduces a coupling scheme for the immersed boundary method to link the Lagrangian and Eulerian variables that facilitates independent spatial discretizations for the structure and background grid. This approach employs a finite element discretization of the structure while retaining a finite difference scheme for the Eulerian variables. We apply this method to benchmark problems involving elastic, rigid, and actively contracting structures, including an idealized model of the left ventricle of the heart. Our tests include cases in which, for a fixed Eulerian grid spacing, coarser Lagrangian structural meshes yield discretization errors that are as much as several orders of magnitude smaller than errors obtained using finer structural meshes. The Lagrangian-Eulerian coupling approach developed in this work enables the effective use of these coarse structural meshes with the immersed boundary method. This work also contrasts two different weak forms of the equations, one of which is demonstrated to be more effective for the coarse structural discretizations facilitated by our coupling approach.
Item Type: | Articles |
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Status: | Published |
Refereed: | Yes |
Glasgow Author(s) Enlighten ID: | Luo, Professor Xiaoyu |
Authors: | Griffith, B. E., and Luo, X. |
College/School: | College of Science and Engineering > School of Mathematics and Statistics > Mathematics |
Journal Name: | International Journal for Numerical Methods in Biomedical Engineering |
Publisher: | Wiley |
ISSN: | 2040-7939 |
ISSN (Online): | 2040-7947 |
Published Online: | 20 April 2017 |
Copyright Holders: | Copyright © 2017 The Authors |
First Published: | First published in International Journal for Numerical Methods in Biomedical Engineering 33(12):e2888 |
Publisher Policy: | Reproduced under a Creative Commons License |
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