title: An efficient immersed boundary-lattice Boltzmann method for the hydrodynamic interaction of elastic filaments.
abstract: We have introduced a modified penalty approach into the flow-structure interaction solver that combines an immersed boundary method (IBM) and a multi-block lattice Boltzmann method (LBM) to model an incompressible flow and elastic boundaries with finite mass. The effect of the solid structure is handled by the IBM in which the stress exerted by the structure on the fluid is spread onto the collocated grid points near the boundary. The fluid motion is obtained by solving the discrete lattice Boltzmann equation. The inertial force of the thin solid structure is incorporated by connecting this structure through virtual springs to a ghost structure with the equivalent mass. This treatment ameliorates the numerical instability issue encountered in this type of problems. Thanks to the superior efficiency of the IBM and LBM, the overall method is extremely fast for a class of flow-structure interaction problems where details of flow patterns need to be resolved. Numerical examples, including those involving multiple solid bodies, are presented to verify the method and illustrate its efficiency. As an application of the present method, an elastic filament flapping in the Kármán gait and the entrainment regions near a cylinder is studied to model fish swimming in these regions. Significant drag reduction is found for the filament, and the result is consistent with the metabolic cost measured experimentally for the live fish.
authors.affiliation: Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230026, China ; Department of Mechanical Engineering, Vanderbilt University, 2301 Vanderbilt Pl, Nashville, TN 37235-1592, USA.
authors.forename: Fang-Bao
authors.initials: FB
authors.lastname: Tian
authors.forename: Haoxiang
authors.initials: H
authors.lastname: Luo
authors.forename: Luoding
authors.initials: L
authors.lastname: Zhu
authors.forename: James C
authors.initials: JC
authors.lastname: Liao
authors.forename: Xi-Yun
authors.initials: XY
authors.lastname: Lu
keywords: Fish swimming; Flapping flags; Flow-structure interaction; Immersed boundary method; Lattice Boltzmann method
references.citation: Phys Rev E Stat Nonlin Soft Matter Phys. 2002 Apr;65(4 Pt 2B):046308
references.pmid: 12006014
references.citation: J Exp Biol. 2006 Oct;209(Pt 20):4077-90
references.pmid: 17023602
references.citation: Nature. 2000 Dec 14;408(6814):835-9
references.pmid: 11130717
references.citation: Phys Biol. 2007 Nov 21;4(4):285-95
references.pmid: 18185006
references.citation: J Exp Biol. 2003 Mar;206(Pt 6):1059-73
references.pmid: 12582148
references.citation: Phys Rev Lett. 2005 Mar 11;94(9):094302
references.pmid: 15783968
references.citation: Phys Rev Lett. 2008 Nov 7;101(19):194502
references.pmid: 19113271
references.citation: Philos Trans R Soc Lond B Biol Sci. 2007 Nov 29;362(1487):1973-93
references.pmid: 17472925
references.citation: Science. 2003 Nov 28;302(5650):1566-9
references.pmid: 14645849