Penalty immersed boundary method for an elastic boundary with mass

Yongsam Kim, Charles Peskin

Research output: Contribution to journalArticle

Abstract

The immersed boundary (IB) method has been widely applied to problems involving a moving elastic boundary that is immersed in fluid and interacting with it. Most of the previous applications of the IB method have involved a massless elastic boundary and used efficient Fourier transform methods for the numerical solutions. Extending the method to cover the case of a massive boundary has required spreading the boundary mass out onto the fluid grid and then solving the Navier-Stokes equations with a variable mass density. The variable mass density of this previous approach makes Fourier transform methods inapplicable, and requires a multigrid solver. Here we propose a new and simple way to give mass to the elastic boundary and show that the method can be applied to many problems for which the boundary mass is important. The method does not spread mass to the fluid grid, retains the use of Fourier transform methodology, and is easy to implement in the context of an existing IB method code for the massless case. Two verifications of the method are given. One is a numerical convergence study that shows that our numerical scheme is second-order accurate for a particular test problem. The other is direct comparison with experimental data of vortex-induced vibrations of a massive cylinder, which shows that the results obtained by the present method are quite comparable to the experimental data.

Original languageEnglish (US)
Article number053103
JournalPhysics of Fluids
Volume19
Issue number5
DOIs
StatePublished - May 2007

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penalties
Fourier transforms
Fluids
Navier Stokes equations
Vortex flow
fluids
grids
Navier-Stokes equation
methodology
vortices
vibration

ASJC Scopus subject areas

  • Fluid Flow and Transfer Processes
  • Computational Mechanics
  • Mechanics of Materials
  • Physics and Astronomy(all)
  • Condensed Matter Physics

Cite this

Penalty immersed boundary method for an elastic boundary with mass. / Kim, Yongsam; Peskin, Charles.

In: Physics of Fluids, Vol. 19, No. 5, 053103, 05.2007.

Research output: Contribution to journalArticle

Kim, Yongsam ; Peskin, Charles. / Penalty immersed boundary method for an elastic boundary with mass. In: Physics of Fluids. 2007 ; Vol. 19, No. 5.
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