Fluid Structure Interaction of Multiple Flapping Filaments Using Lattice Boltzmann and Immersed Boundary Methods

  • Julien FavierEmail author
  • Alistair Revell
  • Alfredo Pinelli
Conference paper
Part of the Notes on Numerical Fluid Mechanics and Multidisciplinary Design book series (NNFM, volume 133)


The problem of flapping filaments in an uniform incoming flow is tackled using a Lattice Boltzmann—Immersed Boundary method. The fluid momentum equations are solved on a Cartesian uniform lattice while the beating filaments are tracked through a series of markers, whose dynamics are functions of the forces exerted by the fluid, the filament flexural rigidity and the tension. The instantaneous wall conditions on the filament are imposed via a system of singular body forces, consistently discretised on the lattice of the Boltzmann equation. We first consider the case of a single beating filament, and then the case of multiple beating filaments in a side-by-side configuration, focussing on the modal behaviour of the whole dynamical systems.


Beating filaments Immersed boundary Lattice Boltzma Flapping modes 



The authors acknowledge the financial help of the PELskin European project (FP7 AAT.2012.6.3-1). This work was partially supported by the Spanish Ministry of Economics through the grant DPI2010-20746-C03-02.


  1. 1.
    Païdoussis, M.P.: Fluid-Structure Interactions: Slender Structures and Axial Flow, vol. 2. Elsevier Academic Press, Cambridge (2004)Google Scholar
  2. 2.
    Shelley, M.J., Zhang, J.: Flapping and bending bodies interacting with fluid flows. Ann. Rev. Fluid Mech. 43(1), 449–465 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Zhang, J., Childress, S., Libchaber, A., Shelley, M.: Flexible filaments in a flowing soap film as a model for one-dimensional flags in a two-dimensional wind. Nature 408, 835–839 (2000)CrossRefGoogle Scholar
  4. 4.
    Zhu, L., Peskin, C.S.: Interaction of two flapping filaments in a flowing soap film. Phys. Fluids 15, 1954–1960 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Pinelli, A., Naqavi, I.Z., Piomelli, U., Favier, J.: Immersed-boundary methods for general finite-difference and finite-volume navier-stokes solvers. J. Comput. Phys. 229(24), 9073–9091 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Domenichini, F.: On the consistency of the direct forcing method in the fractional step solution of the navier-stokes equations. J. Comput. Phys. 227(12), 6372–6384 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Schouweiler, L., Eloy, C.: Coupled flutter of parallel plates. Phys. Fluids 21, 081703 (2009)CrossRefzbMATHGoogle Scholar
  8. 8.
    Michelin, S., Llewellyn Smith, S.G.: Linear stability analysis of coupled parallel flexible plates in an axial flow. J. Fluids Struct. 25(7), 1136–1157 (2009)CrossRefGoogle Scholar
  9. 9.
    Favier, J., Dauptain, A., Basso, D., Bottaro, A.: Passive separation control using a self-adaptive hairy coating. J. Fluid Mech. 627, 451 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Favier, J., Revell, A., Pinelli, A.: A lattice boltzmann—immersed boundary method to simulate the fluid interaction with moving and slender flexible objects. HAL, hal(00822044) (2013)Google Scholar
  11. 11.
    Succi, S.: The Lattice Boltzmann Equation. Oxford University Press, New York (2001)zbMATHGoogle Scholar
  12. 12.
    Bhatnagar, P., Gross, E., Krook, M.: A model for collision processes in gases. i: small amplitude processes in charged and neutral one-component system. Phys. Rev. 94, 511–525 (1954)CrossRefzbMATHGoogle Scholar
  13. 13.
    Qian, Y., D’Humieres, D., Lallemand, P.: Lattice bgk models for navier-stokes equation. Europhys. Lett. 17(6), 479–484 (1992)CrossRefzbMATHGoogle Scholar
  14. 14.
    Guo, Z., Zheng, C., Shi, B.: Discrete lattice effects on the forcing term in the lattice boltzmann method. Phys. Rev. E 65, 046308 (2002)CrossRefzbMATHGoogle Scholar
  15. 15.
    Zhu, L., Peskin, C.S.: Simulation of a flapping flexible filament in a flowing soap film by the immersed boundary method. Phys. Fluids 179, 452–468 (2002)MathSciNetzbMATHGoogle Scholar
  16. 16.
    Huang, W.-X., Shin, S.J., Sung, H.J.: Simulation of flexible filaments in a uniform flow by the immersed boundary method. J. Comput. Phys. 226(2), 2206–2228 (2007)Google Scholar
  17. 17.
    Bagheri, Shervin, Mazzino, Andrea, Bottaro, Alessandro: Spontaneous symmetry breaking of a hinged flapping filament generates lift. Phys. Rev. Lett. 109, 154502 (2012)CrossRefGoogle Scholar
  18. 18.
    Bailey, H.: Motion of a hanging chain after the free end is given an initial velocity. Am. J. Phys. 68, 764–767 (2000)CrossRefGoogle Scholar
  19. 19.
    Tian, F.-B., Luo, H., Zhu, L., Lu, X.-Y.: Coupling modes of three filaments in side-by-side arrangement. Phys. Fluids 23(11), 111903 (2011)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Julien Favier
    • 1
    Email author
  • Alistair Revell
    • 2
  • Alfredo Pinelli
    • 3
  1. 1.Laboratoire de Mécanique, Modélisation et Procédés Propres (M2P2) Aix Marseille Université, CNRS UMR 7340Centrale MarseilleFrance
  2. 2.School of Mechanical, Aerospace and Civil Engineering (MACE) University of ManchesterManchesterUK
  3. 3.School of Engineering and Mathematical SciencesCity UniversityLondonUK

Personalised recommendations