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Cited by 4,603Lattice Boltzmann Simulation StudiesAdvanced Numerical Methods in Computational MathematicsFluid Dynamics Simulations and Interactions

The immersed boundary method

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Peskin, Charles S.·2002·Acta Numerica
DOI 10.1017/s0962492902000077
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Abstract

This paper is concerned with the mathematical structure of the immersed boundary (IB) method, which is intended for the computer simulation of fluid–structure interaction, especially in biological fluid dynamics. The IB formulation of such problems, derived here from the principle of least action, involves both Eulerian and Lagrangian variables, linked by the Dirac delta function. Spatial discretization of the IB equations is based on a fixed Cartesian mesh for the Eulerian variables, and a moving curvilinear mesh for the Lagrangian variables. The two types of variables are linked by interaction equations that involve a smoothed approximation to the Dirac delta function. Eulerian/Lagrangian identities govern the transfer of data from one mesh to the other. Temporal discretization is by a second-order Runge–Kutta method. Current and future research directions are pointed out, and applications of the IB method are briefly discussed.

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  • Simulations using Peskin's standard immersed boundary method to resolve the shedding of vortex structures off sharp boundaries for Re > 1000 requires spatial grid sizes that are prohibitively small.

    “simulations using Peskin's standard immersed boundary method [31] to resolve the shedding of vortex structures off these sharp boundaries for Re > 1000 requires spatial grid sizes that are prohibitively small.”

    From Reynolds number limits for jet propulsion: a numerical study of simplified jellyfish (2011) · cites this paper as [31]

    Section 8 (Research directions; page not provided) says Peskin’s method uses a uniform Eulerian grid and that high-Reynolds-number flows need high resolution in thin boundary layers or regions of concentrated vorticity. It does not establish a threshold of Re > 1000 or say that resolving vortex shedding from sharp boundaries requires prohibitively small grid cells. (LLM, conf=0.84)

    Experimental — accuracy not yet measured

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Cites

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Research works printed but not linked: 3

  1. [28]28. Y. Haoyu (2000) Three dimensional computational modeling and simulation of platelet aggregation on parallel computers. PhD thesis, University of Utah.
  2. [50]50. C. S. Peskin (1981), Vortex dynamics of the aortic sinus. In Mathematical Aspects of Physiology (Hoppensteadt FC, ed.), Vol. 19 of Lectures in Applied Math- ematics, AMS, Providence, RI, pp. 93-104.
  3. [71]71. L. Zhu (2001), Simulation of a flapping filament in a flowing soap film by the immersed boundary method. PhD Thesis, New York University.

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Authors
Peskin, C. S.
Affiliations
Courant Institute of Mathematical Sciences (US)
Corresponding author
Peskin, Charles S.
ORCID
Peskin, Charles S.
Venue
Acta Numerica
Publisher
Cambridge University Press (CUP)
Published
2002-01
Volume
11
Pages
479-517
ISSN
  • 0962-4929 (ISSN-L)
  • 1474-0508
DOI
10.1017/s0962492902000077
OpenAlex
W2084131634
Semantic Scholar
4c0c0a95d7f710a7b9e698b58d3ff17824aff750
Cited by
4,603
References
72
Citations by year
2026: 247 · 2025: 270 · 2024: 284 · 2023: 271 · 2022: 319 · 2021: 295 · 2020: 252 · 2019: 287 · 2018: 267 · 2017: 256 · 2016: 217 · 2015: 227 · 2014: 248 · 2013: 192 · 2012: 173
FWCI
41.15
Type
journal article
Language
en
Open access
Licence
www.cambridge.org/core/terms (unspecified, 560 d)
Locations
Acta Numerica (publishedVersion)
Funders
  • National Science Foundation (9980069)
  • National Institutes of Health
Topics
  • Physical Sciences › Engineering › Computational Mechanics › Lattice Boltzmann Simulation Studies
  • Physical Sciences › Engineering › Computational Mechanics › Advanced Numerical Methods in Computational Mathematics
  • Physical Sciences › Engineering › Computational Mechanics › Fluid Dynamics Simulations and Interactions
Keywords
immersed boundary method, fluid-structure interaction, biological fluid dynamics, Dirac delta function, Eulerian-Lagrangian coupling, principle of least action, Runge-Kutta time integration, Cartesian mesh

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