TY - JOUR

T1 - Accurate computation of surface stresses and forces with immersed boundary methods

AU - Goza, Andres

AU - Liska, Sebastian

AU - Morley, Benjamin

AU - Colonius, Tim

N1 - Funding Information:
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.
Publisher Copyright:
© 2016 Elsevier Inc.

PY - 2016/9/15

Y1 - 2016/9/15

N2 - 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.

AB - 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.

KW - Fluid-structure interaction

KW - Immersed boundary method

KW - Integral equation of the first kind

KW - Non-physical surface forces

KW - Regularization

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U2 - 10.1016/j.jcp.2016.06.014

DO - 10.1016/j.jcp.2016.06.014

M3 - Article

AN - SCOPUS:84974559629

SN - 0021-9991

VL - 321

SP - 860

EP - 873

JO - Journal of Computational Physics

JF - Journal of Computational Physics

ER -