The European Physical Journal Special Topics

, Volume 171, Issue 1, pp 181–187 | Cite as

A lattice Boltzmann method for thermal nonideal fluids

  • G. Gonnella
  • A. Lamura
  • V. Sofonea


A Lattice Boltzmann Method for van der Waals fluids with variable temperature is described. Thermo-hydrodynamic equations are correctly reproduced at second order of a Chapman-Enskog expansion. The method is applied to study initial stages of phase separation of a fluid quenched by contact with colder walls. Thermal equilibration is favoured by pressure waves which propagate with the sound velocity.


European Physical Journal Special Topic Pressure Wave Lattice Boltzmann Method Lattice Node Cold Wall 
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  1. A. Onuki, Phase Transition Dynamics (Cambridge University Press, Cambridge, 2002)Google Scholar
  2. J.M. Yeomans, Ann. Rev. Comput. Phys. VII, 61 (2000)Google Scholar
  3. S. Succi, The Lattice Boltzmann Equation for Fluid Dynamics and Beyond (Clarendon Press, Oxford, 2001)Google Scholar
  4. A. Onuki, Phys. Rev. Lett. 94, 054501 (2005); Phys. Rev. E 75, 036304 (2007)Google Scholar
  5. F.J. Alexander, S. Chen, J.D. Sterling, Phys. Rev. E 47, R2249 (1993); C. Teixeira, H. Chen, D.M. Freed, Comp. Phys. Comm. 129, 207 (2000)Google Scholar
  6. B.J. Palmer, D.R. Rector, Phys. Rev. E 61, 5295 (2000); T. Ihle, D.M. Kroll, Comp. Phys. Comm. 129, 1 (2000); R. Zhang, H. Chen, Phys. Rev. E 67, 066711 (2003)Google Scholar
  7. T. Seta, K. Kono, S. Chen, Int. J. Mod. Phys. B 17, 169 (2003)Google Scholar
  8. See, e.g., A.J. Bray, Adv. Phys. 43, 357 (1994)Google Scholar
  9. M. Watari, M. Tsutahara, Phys. Rev. E 67, 036306 (2003)Google Scholar
  10. D.A. Wolf–Gladrow, Lattice Gas Cellular Automata and Lattice Boltzmann Models (Springer, Berlin, 2000)Google Scholar
  11. V. Sofonea, R.F. Sekerka, Phys. Rev. E 71, 066709 (2005)Google Scholar
  12. R.J. LeVeque, Numerical Methods for Conservation Laws (Birkhäuser, Basel, 1992)Google Scholar
  13. E.F. Toro, Riemann Solvers and Numerical Methods for Fluid Dynamics, Second Edition (Springer, Berlin, 1999)Google Scholar
  14. V. Sofonea, A. Lamura, G. Gonnella, A. Cristea, Phys. Rev. E 70, 046702 (2004); A. Cristea, V. Sofonea, Cent. Eur. J. Phys 2, 382 (2004)Google Scholar
  15. S. Ansumali, I.V. Karlin, Phys. Rev. E 66, 026311 (2002); V. Sofonea, Europhys. Lett. 76, 829 (2006); V. Sofonea, Phys. Rev. E 74, 056705 (2006)Google Scholar
  16. Y.L. Klimontovich, Kinetic Theory of Nonideal Gases and Nonideal Plasmas (Pergamon Press, Oxford, 1982)Google Scholar
  17. L.D. Landau, E.M. Lifshitz, Fluid Mechanics (Butterworth-Heinenann, Oxford, 1987)Google Scholar
  18. G. Gonnella, A. Lamura, V. Sofonea, Phys. Rev. E 76, 036703 (2007)Google Scholar
  19. B. Zappoli, D. Bailly, Y. Garrabos, B. Le Neindre, P. Guenon, D. Beysens, Phys. Rev. A 41, 2264 (1990)Google Scholar

Copyright information

© EDP Sciences and Springer 2009

Authors and Affiliations

  • G. Gonnella
    • 1
  • A. Lamura
    • 2
  • V. Sofonea
    • 3
  1. 1.Dipartimento di FisicaUniversità di Bari and Istituto Nazionale di Fisica NucleareBariItaly
  2. 2.Istituto Applicazioni Calcolo, CNR, via Amendola 122/DBariItaly
  3. 3.Center for Fundamental and Advanced Technical Research, Romanian AcademyTimişoaraRomania

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