Encyclopedia of Computer Graphics and Games

Living Edition
| Editors: Newton Lee

Lattice Boltzmann Method for Fluid Simulation

  • Sicilia Ferreira Judice
Living reference work entry
DOI: https://doi.org/10.1007/978-3-319-08234-9_107-1



  • Cellular Automata

    A mathematical model based on simple and local rules capable of generating complex behaviors.

  • LBM

    Lattice Boltzmann method, a numerical method based in kinetic equations formulated on a mesoscopic scale.

  • LGCA

    Lattice gas cellular automata, a specific cellular automaton, whose proposal is to simulate fluids using simple and local rules that imitate a particle dynamics.


The lattice Boltzmann method is a numerical method based in kinetic equations formulated on a mesoscopic scale, which simulates fluid dynamics on a macroscopic scale (Chen and Doolen 1998). In the last years, LBM has drawn the attention of the scientific community due to its ease of implementation and computational efficiency. Specifically in fluid dynamics, LBM has been used due to its ease of boundary conditions implementations (Chopard et al. 2002).

The method originated from the lattice gas cellular...

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


  1. Adilson Vicente Xavier.: Animac¸a˜o de fluidos via autoˆmatos celulares e sistemas de part́ıculas. Master’s thesis, LNCC – Laboratório Nacional de Computac¸a˜o Cient́ıfica, Agosto (2006)Google Scholar
  2. Bhatnagar, P.L., Gross, E.P., Krook, M.: A model for collision processes in gases: small amplitude processes in charged and neutral one-component system. Phys. Rev. 94, 511–525 (1954)CrossRefGoogle Scholar
  3. Chen, S., Doolen, G.D.: Lattice Boltzmann method for fluid flows. Annu. Rev. Fluid Mech. 30, 329–364 (1998)MathSciNetCrossRefGoogle Scholar
  4. Chopard, B., Droz, M.: Cellular Automata Modeling of Physical Systems. Cambridge University Press, Cambridge (1998)CrossRefGoogle Scholar
  5. Chopard, B., Dupuis, A., Masselot, A., Luthi, P.: Cellular automata and lattice Boltzmann techniques: an approach to model and simulate complex systems. Adv. Complex Syst. 05, 103–246 (2002)MathSciNetCrossRefGoogle Scholar
  6. Daniel Reis Golbert.: Modelos de lattice-Boltzmann aplicados a simulac¸a˜o computacional do escoamento de fluidos incompresśıveis. Master’s thesis, LNCC – Laboratório Nacional de Computac¸a˜o Cient́ıfica (2009)Google Scholar
  7. Guo, Z., Shu, C.: Lattice Boltzmann Method and its Applications in Engineering Advances in Computational Fluid Dynamics, vol. 3. World Scientific Publishing, Singapore (2013)zbMATHGoogle Scholar
  8. He, X., Luo, L.-S.: A priori derivation of the lattice Boltzmann equation. Phys. Rev. E. 55(6), R6333–R6336 (1997a)CrossRefGoogle Scholar
  9. He, X., Luo, L.-S.: Lattice Boltzmann model for the incompressible Navier-stokes equation. J. Stat. Phys. 88, 927–944 (1997b)MathSciNetCrossRefGoogle Scholar
  10. McNamara, G.R., Zanetti, G.: Use of the Boltzmann equation to simulate lattice-gas automata. Phys. Rev. Lett. 61(20), 2332–2335 (1988)CrossRefGoogle Scholar
  11. Philippi, P.C., Hegele, L.A., dos Santos, L.O.E., Surmas, R.: From the continuous to the lattice Boltzmann equation: the discretization problem and thermal models. Phys. Rev. E. 73, 56702 (2006)MathSciNetCrossRefGoogle Scholar
  12. Quian, Y.H., d’Humires, D., Lallemand, P.: Lattice bgk models for Navier-stokes equation. Europhys. Lett. 17, 479–484 (1992)CrossRefGoogle Scholar
  13. Rothman, D., Zaleski, S.: Lattice-Gas Cellular Automata: Simple Models of Complex Hydrodynamics. Cambridge University Press, Cambridge (1997)CrossRefGoogle Scholar
  14. Wolfram, S.: Cellular Automata and Complexity: Collected Papers, 1st edn. AddisonWesley. http://www.stephenwolfram.com/publications/books/ca-reprint/. (1994)
  15. Zou, Q., He, X.: On pressure and velocity boundary conditions for the lattice Boltzmann bgk model. Phys. Fluids. 9(6), 1591–1598 (1997)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Faculty of Technical Education State of Rio de JaneiroPetropolisBrazil