Skip to main content

Lattice-Boltzmann Method on Quadtree-Type Grids for Fluid-Structure Interaction

  • Conference paper

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 53))

Abstract

In this work a Lattice Boltzmann (LB) fluid flow solver based on unstructured quadtree/octree type Eulerian grids is coupled with a spectral Finite Element (p-FEM) structural mechanics solver based on a Lagrangian description to predict bidirectional fluid-structure interaction (FSI). The methods and algorithms are described in detail. Benchmark computations of a coupled transient problem of a 2D beam-like structure in a channel as defined by the DFG-Research Unit 493 are presented.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. P.L. Bhatnagar, E.P. Gross, M. Krook. A Model for Collision Processes in Gases, Phys. Rev. 94, 511, (1954).

    Google Scholar 

  2. M. Bouzidi, M. Firdaouss, P. Lallemand. Momentum transfer of a Boltzmann- Lattice fluid with boundaries, Physics of Fluids 13(11), 3452–3459, (2001).

    Article  Google Scholar 

  3. M. Brenk, H.-J. Bungartz, M. Mehl, and T. Neckel. Fluid-Structure Interaction on Cartesian Grids: Flow Simulation and Coupling Environment, In H.-J. Bungartz and M. Schäfer, editors, Fluid-Structure Interaction: Modelling, Simulation, Optimisation. Springer Verlag, (2006).

    Google Scholar 

  4. S. Chapman, T.G. Cowling. The mathematical theory of non-uniform gases, Cambridge University Press, (1970).

    Google Scholar 

  5. J. Chung, G. Hulbert. A Time Integration Algorithm for Structural Dynamics with Improved Numerical Dissipation: The Generalized-á-Method. J. of Applied Mechanics, vol. 60, pp. 1562–1566, (1993).

    MathSciNet  Google Scholar 

  6. B. Crouse, E. Rank, M. Krafczyk, J. Tölke. A LB-based approach for adaptive flow simulations, Int. J. of Modern Physics B 17, 109–112, (2002).

    Google Scholar 

  7. B. Crouse. Lattice-Boltzmann Strömungssimulationen auf Baumdatenstrukturen, PhD thesis (german), TU München, (2002).

    Google Scholar 

  8. A. Düster, H. Bröker, H. Heidkamp, U. Heißerer, S. Kollmannsberger, R. Krause, A. Muthler, A. Niggl, V. Nübel, M. Rücker, D. Scholz. AdhoC 4 - User’s Guide. Lehrstuhl für Bauinformatik, TU München, (2004).

    Google Scholar 

  9. O. Filippova, D. Hänel. Boundary-Fitting and Local Grid Re.nement for LBGK Models, Int. J. Mod. Phys. C(8), 1271, (1998).

    Google Scholar 

  10. U. Frisch, D. d’Humiéres, B. Hasslacher, P. Lallemand, Y. Pomeau, J.P. Rivet. Lattice gas hydrodynamics in two and three dimensions, Complex Sys. 1, 649- 707, (1987).

    MATH  Google Scholar 

  11. S. Geller, M. Krafczyk, J. Tölke, S. Turek, J. Hron. Benchmark computations based on Lattice-Boltzmann, Finite Element and Finite Volume Methods for laminar Flows, accepted for Comp.&Fluids, (2004).

    Google Scholar 

  12. I. Ginzburg, D. d’Humiéres. Multi-re.ection boundary conditions for Lattice- Boltzmann models, Phys. Rev. E 68, 66614, (2003).

    Google Scholar 

  13. X. He, L.-S. Luo. Lattice Boltzmann model for the incompressible Navier-Stokes equation, Journal of Statistical Physics 88, 927–944, (1997).

    Article  MATH  MathSciNet  Google Scholar 

  14. X. He, L.-S. Luo. Theory of the lattice Boltzmann method: from the Boltzmann equation to the lattice Boltzmann equation. Phys. Rev. E 56, 6811, (1997).

    Article  Google Scholar 

  15. D. d’Humiéres. in Rare.ed Gas Dynamics: Theory and Simulations, Prog. Astronaut. Aeronaut. Vol. 159, edited by B. D. Shizgal and D. P. Weaver AIAA, Washington, D.C., (1992).

    Google Scholar 

  16. D. d’Humiéres, I. Ginzburg, M. Krafczyk, P. Lallemand, L.-S. Luo. Multiplerelaxation- time lattice Boltzmann models in three-dimensions, Philosophical Transections of Royal Society of London A 360(1792), 437–451, (2002).

    Article  Google Scholar 

  17. M. Junk. A Finite Di.erence Interpretation of the Lattice Boltzmann Method, Num. Meth. Part. Di. Equations Vol. 17, 383–402, (2001).

    Article  MATH  MathSciNet  Google Scholar 

  18. M. Junk, A. Klar, L.-S. Luo. Theory of the Lattice Boltzmann Method: Mathematical Analysis of the Lattice Boltzmann Equation, preprint, (2004).

    Google Scholar 

  19. P. Lallemand, L.-S. Luo. Theory of the lattice Boltzmann method: Dispersion, dissipation, isotropy, Galilean invariance, and stability, Physical Review E 61 6546–6562, (2000).

    MathSciNet  Google Scholar 

  20. P. Lallemand, L.-S. Luo. Lattice Boltzmann method for moving boundaries, Journal of Computational Physics 184, 406–421, (2003).

    Article  MathSciNet  Google Scholar 

  21. R. Löhner, J.D. Baum, E.L. Mestreau, D. Sharov, Ch. Charman and D. Pelessone. Adaptive Embedded Unstructured Grid Methods, AIAA-03–1116, (2003).

    Google Scholar 

  22. W. E. Lorensen and H. E. Cline. Marching Cubes: a high resolution 3D surface construction algorithm, In Siggraph, volume 21, pages 163–169. ACM, (1987).

    Article  Google Scholar 

  23. L.-S. Luo. Consistent Initial Conditions for LBE Simulation, preprint, (2006).

    Google Scholar 

  24. J. Mackerle. Finite element linear and nonlinear, static and dynamic analysis of structural elements: a bibliography, International Journal for Computer-Aided Engineering, 14 (4):347–440 (1997).

    Article  MathSciNet  Google Scholar 

  25. R. Mei, D. Yu, W. Shyy, L.-S. Luo. Force evaluation in the lattice Boltzmann method involving vurved geometry, Phys. Rev. E 65, 041203, (2002).

    Google Scholar 

  26. N.-Q. Nguyen, A.J.C. Ladd. Sedimentation of hard-sphere suspensions at low Reynolds number submitted to J. Fluid Mech. (2004).

    Google Scholar 

  27. Y. H. Qian, D. d’Humiéres, P. Lallemand. Lattice BGK models for Navier- Stokes equation, Europhys. Lett. 17 479–484, (1992).

    Google Scholar 

  28. M. Rheinländer. A Consistent Grid Coupling Method for Lattice-Boltzmann Schemes, J. of Statistical Physics, Vol. 121, (2005).

    Google Scholar 

  29. P. le Tallec, J. Mouro. Fluid Structure Interaction with Large Structural Displacements, Computer Methods in Applied Mechanics and Engineering, 190, 24–25, pp 3039–3068, (2001).

    Article  MATH  Google Scholar 

  30. N. Thürey. A single-phase free-surface Lattice-Boltzmann Method, diploma thesis, IMMD10, University of Erlangen-Nuremberg, (2003).

    Google Scholar 

  31. J. Tölke, S. Freudiger, M. Krafczyk. An adaptive scheme using hierarchical grids for lattice Boltzmann multi-phase flow simulations, accepted for Comp.&Fluids, (2004).

    Google Scholar 

  32. S. Turek, J. Hron. Proposal for numerical benchmarking of fluid-structure interaction between an elastic object and laminar incompressible flow, In H.-J. Bungartz and M. Schäfer, editors, Fluid-Structure Interaction: Modelling, Simulation, Optimisation. Springer Verlag, (2006).

    Google Scholar 

  33. D. Yu. Viscous Flow Computations with the Lattice Boltzmann equation method, PhD thesis, Univ. of Florida, (2002).

    Google Scholar 

  34. D. Yu, R. Mei, W. Shyy. A multi-block lattice Boltzmann method for viscous fluid flows, Int. J. Numer. Methods Fluids 39(2), 99–120, (2002).

    Article  MATH  Google Scholar 

  35. http://www.featflow.de/

    Google Scholar 

  36. http://www-waterloo.ansys.com/cfx/

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer

About this paper

Cite this paper

Geller, S., Tölke, J., Krafczyk, M. (2006). Lattice-Boltzmann Method on Quadtree-Type Grids for Fluid-Structure Interaction. In: Bungartz, HJ., Schäfer, M. (eds) Fluid-Structure Interaction. Lecture Notes in Computational Science and Engineering, vol 53. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-34596-5_11

Download citation

Publish with us

Policies and ethics