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Accurate computation of surface stresses and forces with immersed boundary methods

Goza, Andres and Liska, Sebastian and Morley, Benjamin and Colonius, Tim (2016) Accurate computation of surface stresses and forces with immersed boundary methods. Journal of Computational Physics, 321 . pp. 860-873. ISSN 0021-9991. doi:10.1016/

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Many immersed boundary methods solve for surface stresses that impose the velocity boundary conditions on an immersed body. These surface stresses may contain spurious oscillations that make them ill-suited for representing the physical surface stresses on the body. Moreover, these inaccurate stresses often lead to unphysical oscillations in the history of integrated surface forces such as the coefficient of lift. While the errors in the surface stresses and forces do not necessarily affect the convergence of the velocity field, it is desirable, especially in fluid–structure interaction problems, to obtain smooth and convergent stress distributions on the surface. To this end, we show that the equation for the surface stresses is an integral equation of the first kind whose ill-posedness is the source of spurious oscillations in the stresses. We also demonstrate that for sufficiently smooth delta functions, the oscillations may be filtered out to obtain physically accurate surface stresses. The filtering is applied as a post-processing procedure, so that the convergence of the velocity field is unaffected. We demonstrate the efficacy of the method by computing stresses and forces that converge to the physical stresses and forces for several test problems.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Goza, Andres0000-0002-9372-7713
Liska, Sebastian0000-0003-4139-9364
Colonius, Tim0000-0003-0326-3909
Additional Information:© 2016 Elsevier Inc. Received 9 December 2015; Received in revised form 7 June 2016; Accepted 8 June 2016; Available online 9 June 2016. This research was partially supported by a grant from the Jet Propulsion Laboratory (Grant No.1492185). Many of the simulations were performed using the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by National Science Foundation grant number ACI-1053575. The first author gratefully acknowledges funding from the National Science Foundation Graduate Research Fellowship Program (Grant No. DGE-1144469). We thank Dr. Aaron Towne for insightful conversations about spectral decompositions of inverse operators, and Ms. Tess Saxton-Fox for her help in editing the manuscript.
Funding AgencyGrant Number
NSF Graduate Research FellowshipDGE-1144469
Subject Keywords:Immersed boundary method; Non-physical surface forces; Integral equation of the first kind; Regularization; Fluid–structure interaction
Record Number:CaltechAUTHORS:20160714-085129783
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Official Citation:Andres Goza, Sebastian Liska, Benjamin Morley, Tim Colonius, Accurate computation of surface stresses and forces with immersed boundary methods, Journal of Computational Physics, Volume 321, 15 September 2016, Pages 860-873, ISSN 0021-9991, (
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:69026
Deposited By: Tony Diaz
Deposited On:27 Jul 2016 21:29
Last Modified:11 Nov 2021 04:08

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