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Application of the multi distribution function lattice Boltzmann approach to thermal flows

  • A. ParmigianiEmail author
  • C. Huber
  • B. Chopard
  • J. Latt
  • O. Bachmann
Article

Abstract

Numerical methods able to model high Rayleigh (Ra) and high Prandtl (Pr) number thermal convection are important to study large-scale geophysical phenomena occuring in very viscous fluids such as magma chamber dynamics (104 < Pr < 107 and 107 < Ra < 1011). The important variable to quantify the thermal state of a convective fluid is a generalized dimensionless heat transfer coefficient (the Nusselt number) whose measure indicates the relative efficiency of the thermal convection. In this paper we test the ability of Multi-distribution Function approach (MDF) Thermal Lattice Boltzmann method to study the well-established scaling result for the Nusselt number (NuRa 1/3) in Rayleigh Bénard convection for 104Ra ≤ 109 and 101Pr ≤ 104. We explore its main drawbacks in the range of Pr and Ra number under investigation: (1) high computational time N c required for the algorithm to converge and (2) high spatial accuracy needed to resolve the thickness of thermal plumes and both thermal and velocity boundary layer. We try to decrease the computational demands of the method using a multiscale approach based on the implicit dependence of the Pr number on the relaxation time, the spatial and temporal resolution characteristic of the MDF thermal model.

Keywords

Nusselt Number Rayleigh Number European Physical Journal Special Topic Lattice Boltzmann Method Lattice Node 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. F. Massaioli, R. Benzi, S. Succi, Europhys. Lett. 21, 305 (1993)Google Scholar
  2. U.R. Christensen, Geophys. Res. Lett. 14, 220 (1987)Google Scholar
  3. U. Hansen, D.A. Yuen, S.E. Kroening, Phys. Fluids A 2, 2157 (1990)Google Scholar
  4. M. Manga, D. Weeraratne, Phys. Fluids 11, 2969 (1999)Google Scholar
  5. F.M. Richter, H. Nataf, S.F. Daly, J. Fluid Mech. 129, 173 (1983)Google Scholar
  6. C. Huber, A. Parmigiani, B. Chopard, M. Manga, O. Bachmann, Int. J. Heat Fluid Flow (in press)Google Scholar
  7. X. Shan, S. Chen, Phys. Rev. E 47, 1815 (1993)Google Scholar
  8. X. Shan, Phys. Rev. E 55, 2780 (1997)Google Scholar
  9. Z. Guo, B. Shi, C. Zheng, Int. J. Num. Meth. Fluids 39, 325 (2002)Google Scholar
  10. S. Suga, Int. J. Mod. Phys. C 17, 1563 (2006)Google Scholar
  11. D. Shepard, Proceeding of the 23rd ACM National Conference (1968), p. 517Google Scholar
  12. B. Chopard, M. Droz, Cellular Automata and Modeling of Physical Systems (Cambridge University Press, 1998), p. 353Google Scholar
  13. D.A. Wolf-Gladrow, Lattice-Gas Cellular Automata and Lattice Boltzmann Models: An introduction (Springer, 2000), p. 308Google Scholar
  14. D.L. Turcotte, G. Schubert Geodynamics (Cambridge University Press, 2002), p. 450Google Scholar
  15. A. Bejan Convection heat transfer (Wiley, 2004), p. 450Google Scholar

Copyright information

© EDP Sciences and Springer 2009

Authors and Affiliations

  • A. Parmigiani
    • 1
    Email author
  • C. Huber
    • 2
  • B. Chopard
    • 1
  • J. Latt
    • 3
  • O. Bachmann
    • 4
  1. 1.Computer Science DepartmentUniversity of GenevaGeneva 4Switzerland
  2. 2.Department of Earth and Planetary ScienceUniversity of California – BerkeleyBerkeleyUSA
  3. 3.Department of MathematicsTufts UniversityMedfordUSA
  4. 4.Department of Earth and Space ScienceUniversity of WashingtonSeattleUSA

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