Skip to main content
Log in

Heat transfer in lattice BGK modeled fluid

  • Articles
  • Published:
Journal of Statistical Physics Aims and scope Submit manuscript

Abstract

The thermal lattice BGK model is a recently suggested numerical tool aiming at solving problems of thermohydrodynamics. The quality of the lattice BGK simulation is checked in this paper by calculating temperature profiles in the Couette flow under different Eckert and Mach numbers. A revised lower order model is proposed to improve the accuracy and the higher order model is proved to be advantageous in this respect, especially in the flow regime with a higher Mach number.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. U. Frisch, B. Hassalacher, and Y. Pomeau, Lattice-gas automata for the Navier-Stokes equation,Phys. Rev. Lett. 56(14):1505–1508 (1986).

    Google Scholar 

  2. G. McNamara and G. Zanetti, Use of the Boltzmann equation to simulate lattice-gas automata,Phys. Rev. Lett. 61(20):2332–2335 (1988).

    Google Scholar 

  3. S. Chen, H. Chen, D. Martinez, and W. Matthaeus, Lattice Boltzmann model for simulation of Magnetohydrodynamics.Phys. Rev. Lett. 67(27):3776–3779 (1991).

    Google Scholar 

  4. Y. H. Qian, D. d'Humières, and P. Lallemand, Lattice BGK models for Navier-Stokes equation,Europhys. Lett. 17(6):479–484 (1992).

    Google Scholar 

  5. H. Chen, S. Chen and W. H. Matthaeus, Recovery of Navier-Stokes equations using a lattice-gas Boltzmann method.Phys. Rev. A 45(8):R5339–42 (1992).

    Google Scholar 

  6. P. Bhatnagar, E. P. Gross, and M. K. Krook, A model for collision process in gases. I. Small amplitude processes in charged and neutral one-component system.Phys. Rev. 94:511 (1954).

    Google Scholar 

  7. S. Chen, Z. Wang, X. Shan, and G. D. Doolen, Lattice Boltzmann computational fluid dynamics,J. Stat. Phys. 68:379 (1992).

    Google Scholar 

  8. D. Martinez, W. H. Matthaeus, and S. Chen, Comparison of spectral method and lattice Boltzmann simulations of two-dimensional hydrodynamics,Phys. Fluids 6(3):1285–1298 (1993).

    Google Scholar 

  9. S. Hou, Z. Qisu, S. Chen, G. Doolen, and A. C. Cogley, Simulation of cavity flow by the lattice Boltzmann method, preprint.

  10. F. J. Alexander, S. Chen, and J. D. Sterling, Lattice Boltzmann thermohydrodynamics,Phys. Rev. E 47:2249–2252 (1991).

    Google Scholar 

  11. Y. H. Qian and S. A. Orszag, Simulating thermohydrodynamics with lattice BGK models.J. Sci. Comp. 8(3):231–242 (1993).

    Google Scholar 

  12. Y. Chen, Lattice Bhatnagar-Gross-Krook method for fluid dynamics: Compressible, thermal and multi-phase models,Doctoral Thesis (1994).

  13. Y. Chen, H. Ohashi, and M. Akiyama, Thermal lattice Bhatnagar-Gross-Krook model without nonlinear deviations in macro-dynamic equations,Phys. Rev. E 50:2776–2783 (1994).

    Google Scholar 

  14. S. Wolfram, Cellular automaton fluids 1: Basic theory,J. Stat. Phys. 45:471–526 (1986).

    Google Scholar 

  15. G. McNamara and B. Alder, Analysis of the lattice Boltzmann treatment of hydrodynamics,Physica A 194:218–228 (1993).

    Google Scholar 

  16. R. Benzi, S. Succi, and M. Vergassola, The lattice Boltzmann equation: Theory and applications,Phys. Rep. 222(3):145–197 (1992).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chen, Y., Ohashi, H. & Akiyama, M. Heat transfer in lattice BGK modeled fluid. J Stat Phys 81, 71–85 (1995). https://doi.org/10.1007/BF02179969

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02179969

Key Words

Navigation