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A lattice Boltzmann based implicit immersed boundary method for fluid–structure interaction

Authors
Journal
Computers & Mathematics with Applications
0898-1221
Publisher
Elsevier
Volume
59
Issue
1
Identifiers
DOI: 10.1016/j.camwa.2009.06.055
Keywords
  • Immersed Boundary Method
  • Implicit Scheme
  • Lattice Boltzmann Method
  • Fluid–Structure Interaction
Disciplines
  • Computer Science
  • Mathematics

Abstract

Abstract The immersed boundary method is a practical and effective method for fluid–structure interaction problems. It has been applied to a variety of problems. Most of the time-stepping schemes used in the method are explicit, which suffer a drawback in terms of stability and restriction on the time step. We propose a lattice Boltzmann based implicit immersed boundary method where the immersed boundary force is computed at the unknown configuration of the structure at each time step. The fully nonlinear algebraic system resulting from discretizations is solved by an Inexact Newton–Krylov method in a Jacobian-free manner. The test problem of a flexible filament in a flowing viscous fluid is considered. Numerical results show that the proposed implicit immersed boundary method is much more stable with larger time steps and significantly outperforms the explicit version in terms of computational cost.

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