Dynamics of a closed rod with twist and bend in fluid

Sookkyung Lim, Anca Ferent, X. Sheldon Wang, Charles Peskin

Research output: Contribution to journalArticle

Abstract

We investigate the instability and subsequent dynamics of a closed rod with twist and bend in a viscous, incompressible fluid. A new version of the immersed boundary (IB) method is used in which the immersed boundary applies torque as well as force to the surrounding fluid and in which the equations of motion of the immersed boundary involve the local angular velocity as well as the local linear velocity of the fluid. An important feature of the IB method in this context is that self-crossing of the rod is automatically avoided because the rod moves in a continuous (interpolated) velocity field. A rod with a uniformly distributed twist that has been slightly perturbed away from its circular equilibrium configuration is used as an initial condition, with the fluid initially at rest. If the twist in the rod is sufficiently small, the rod simply returns to its circular equilibrium configuration, but for larger twists that equilibrium configuration becomes unstable, and the rod undergoes large excursions before relaxing to a stable coiled configuration.

Original languageEnglish (US)
Pages (from-to)273-302
Number of pages30
JournalSIAM Journal on Scientific Computing
Volume31
Issue number1
DOIs
StatePublished - 2008

Fingerprint

Twist
Immersed Boundary
Immersed Boundary Method
Fluid
Closed
Configuration
Fluids
Excursion
Angular velocity
Incompressible Fluid
Velocity Field
Equations of motion
Torque
Equations of Motion
Initial conditions
Unstable

Keywords

  • Equilibria
  • Immersed boundary method
  • Kirchhoff theory
  • Supercoiling

ASJC Scopus subject areas

  • Applied Mathematics
  • Computational Mathematics

Cite this

Dynamics of a closed rod with twist and bend in fluid. / Lim, Sookkyung; Ferent, Anca; Wang, X. Sheldon; Peskin, Charles.

In: SIAM Journal on Scientific Computing, Vol. 31, No. 1, 2008, p. 273-302.

Research output: Contribution to journalArticle

Lim, Sookkyung ; Ferent, Anca ; Wang, X. Sheldon ; Peskin, Charles. / Dynamics of a closed rod with twist and bend in fluid. In: SIAM Journal on Scientific Computing. 2008 ; Vol. 31, No. 1. pp. 273-302.
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