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Immersed Boundary Projection Methods

Dorschner, Benedikt and Colonius, Tim (2020) Immersed Boundary Projection Methods. In: Immersed Boundary Method: Development and Applications. Computational Methods in Engineering & the Sciences. Springer , Singapore, pp. 3-43. ISBN 978-981-15-3939-8.

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Immersed boundary methods are an attractive alternative to body-fitted grids for complex geometries and fluid–structure interaction problems. The simplicity of the underlying Cartesian mesh allows for a number of useful conservation and stability properties to be embedded in the numerics, and for the resulting discrete equations to be solved efficiently and scalably. We review the immersed boundary projection method for incompressible flows, which implicitly satisfies the no-slip condition at immersed surfaces by solving a system of algebraic equations for surface traction. We discuss issues related to the smoothness of the surface stresses and solution strategies for strongly coupled fluid–structure interaction. For three-dimensional flows on unbounded domains, we discuss a fast lattice Green’s function method that provides for an adaptive domain comprising the vortical flow region and at the same time can be solved efficiently using extensions of the fast multipole method. To illustrate the methods, we present a series of benchmark simulations in two and three dimensions, ranging from inverted flag flutter, flow past spinning and inclined disks, and turbulent flow past a sphere.

Item Type:Book Section
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URLURL TypeDescription
Dorschner, Benedikt0000-0001-8926-7542
Colonius, Tim0000-0003-0326-3909
Additional Information:© 2020 Springer Nature Singapore Pte Ltd. First Online: 16 May 2020. BD gratefully acknowledges support from the Swiss National Science Foundation (SNF Grant No. P2EZP2_178436), TC was supported by ONR grant N00014-16-1-2734. We are likewise grateful to numerous students and collaborators, particularly Sam Taira, Sebastian Liska, and Andres Goza, who contributed to the development of IB projection techniques described herein. We thank Marcus Lee and Ke Yu for recent contributions to the AMR code development; Marcus Lee also contributed his results for flow past a spinning disk to this article.
Funding AgencyGrant Number
Swiss National Science Foundation (SNSF)P2EZP2_178436
Office of Naval Research (ONR)N00014-16-1-2734
Series Name:Computational Methods in Engineering & the Sciences
Record Number:CaltechAUTHORS:20200518-095000249
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:103271
Deposited By: Tony Diaz
Deposited On:18 May 2020 17:00
Last Modified:16 Nov 2021 18:19

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