A Three-Dimensional Adaptive Wavelet Method for Fluid-Structure Interaction

  • N. K.-R. Kevlahan
  • O. V. Vasilyev
  • D. Goldstein
  • A. Jay
Conference paper
Part of the ERCOFTAC Series book series (ERCO, volume 9)

Abstract

An adaptive wavelet collocation method for three-dimensional fluid-structure interaction at large Reynolds numbers is presented. This approach is shown to give accurate results with a reduced number of computational elements. The method is applied to two-dimensional flow past moving and fixed cylinders at Re = 102 and Re = 104, and to three-dimensional flow past a sphere at Re = 500. This is the first three-dimensional calculation of a flow past an obstacle using a dynamically adapted wavelet based approach.

Keywords

Turbulence fluid-structure interaction wavelets penalization 

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References

  1. [1]
    Angot, P. (1999). Analysis of singular perturbations on the brinkman problem for fictitious domain models of viscous flows.Mathematical Methods in the Applied Science, 22: 1395–1412.MathSciNetMATHGoogle Scholar
  2. [2]
    Angot, P., Bruneau, C.-H., and Fabrie, P. (1999). A penalization method to take into account obstacles in viscous flows.Numerische Mathematik, 81: 497–520.MathSciNetMATHGoogle Scholar
  3. [3]
    Brandt, A. (1982). Guide to multigrid development. In Hackbusch, W. and Trottenberg, U.,editors, Multigrid methods, volume 960 of Lecture Notes in Mathematics, pages 220–312.Springer-Verlag.Google Scholar
  4. [4]
    Farge, M., Schneider, K., and Kevlahan, N. K.-R. (1999). Non-gaussianity and coherent vortex simulation for two-dimensional turbulence using an adaptive orthogonal wavelet basis.Phys.Fluids, 11: 2187–2201.MathSciNetMATHGoogle Scholar
  5. [5]
    Griebel, M. and Koster, K. (2002). Multiscale methods for the simulation of turbulent flows. In Hirschel, E.H., editor,DFG/CNRS Workshop, Nice, 2001, Notes on Numerical Fluid Mechanics. Vieweg-Verlag.Google Scholar
  6. [6]
    Kevlahan, N. and Ghidaglia, J.-M. (2001). Computation of turbulent flow past an array of cylinders using a spectral method with brinkman penalization. Eur. J. Mech./B, 20:333– 350.Google Scholar
  7. [7]
    Kevlahan, N. and Vasilyev, O. (2003). An adaptive wavelet collocation method for fluid– structure interaction at high reynolds numbers. SIAM J. Sci. Comput. Submitted.Google Scholar
  8. [8]
    Schneider, K., Kevlahan, N. K.-R., and Farge, M. (1997). Comparison of an adaptive wavelet method and nonlinearly filtered pseudo-spectral methods for two-dimensional turbulence.Theoret. Comput. Fluid Dynamics, 9: 191–206.Google Scholar
  9. [9]
    Shiels, D., Leonard, A., and Roshko, A. (2001). Flow-induced vibration of a circular cylinder at limiting structural parameters. J. Fluids Structures, 15: 3–21.ADSCrossRefGoogle Scholar
  10. [10]
    Sweldens, W. (1998). The lifting scheme: A construction of second generation wavelets.SIAMJ. Math. Anal., 29 (2): 511–546.MathSciNetMATHGoogle Scholar
  11. [11]
    Vasilyev, O. V. (2003). Solving multi-dimensional evolution problems with localized structures using second generation wavelets. Int. J. Comp. Fluid Dyn., Special issue on high-resolution methods in Computational Fluid Dynamics, 17 (2): 151–168.MathSciNetMATHGoogle Scholar
  12. [12]
    Vasilyev, O. V. and Bowman, C. (2000). Second generation wavelet collocation method for the solution of partial differential equations.J. Comput. Phys., 165: 660–693.Google Scholar
  13. [13]
    Vasilyev, O. V. and Kevlahan, N. K.-R. (2002). Hybrid wavelet collocation-brinkman penalization method for complex geometry flows.Int. J. Num. Meth. Fluids., 30: 531–538.Google Scholar
  14. [14]
    Vasilyev, O. V. and Kevlahan, N. K.-R. (2003). An adaptive multilevel wavelet collocation method for elliptic problems. In preparation.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2004

Authors and Affiliations

  • N. K.-R. Kevlahan
    • 1
  • O. V. Vasilyev
    • 2
  • D. Goldstein
    • 2
  • A. Jay
    • 1
    • 3
  1. 1.Department of Mathematics & StatisticsMcMaster UniversityHamiltonCanada
  2. 2.Mechanical & Aerospace EngineeringUniversity of Colorado at BoulderBoulderUSA
  3. 3.École MatMécaUniversité de Bordeaux 1TalenceFrance

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