Nonexistence of H theorems for the athermal lattice Boltzmann models with polynomial equilibria

Wen-An Yong and Li-Shi Luo
Phys. Rev. E 67, 051105 – Published 19 May 2003
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Abstract

We prove that no H theorem exists for the athermal lattice Boltzmann equation with polynomial equilibria satisfying the conservation laws exactly and explicitly. The proof is demonstrated by using the seven-velocity model in a triangular lattice in two dimensions, and can be readily extended to other lattice Boltzmann models in two and three dimensions. Some issues pertinent to the numerical instabilities of the lattice Boltzmann method are disscussed.

  • Received 22 November 2002

DOI:https://doi.org/10.1103/PhysRevE.67.051105

©2003 American Physical Society

Authors & Affiliations

Wen-An Yong1,* and Li-Shi Luo2,†

  • 1IWR, Universität Heidelberg, Im Neuenheimer Feld 294, 69120 Heidelberg, Germany
  • 2ICASE, MS 132C, NASA Langley Research Center, 3 West Reid Street, Building 1152, Hampton, Virginia 23681-2199

  • *Electronic address: yong.wen-an@iwr.uni-heidelberg.de
  • †Present address: National Institute of Aerospace, 144 Research Dr., Hampton, VA 23666; electronic address: luo@nianet.org; URL: http://research.nianet.org/∼luo

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Vol. 67, Iss. 5 — May 2003

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