Europhys. Lett.
Volume 47, Number 2, July 1999
Page(s) 182 - 188
Section Electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics
Published online 01 September 2002
DOI: 10.1209/epl/i1999-00370-1

Europhys. Lett, 47 (2), pp. 182-188 (1999)

Perfect entropy functions of the Lattice Boltzmann method

I. V. Karlin, A. Ferrante and H. C. Öttinger

ETH Zürich, Department of Materials, Institute of Polymers
CH-8092 Zürich, Switzerland

(received 4 January 1999; accepted in final form 19 May 1999)

PACS. 47.11${\rm +j}$ - Computational methods in fluid dynamics.


In this letter, we derive entropy functions whose local equilibria are suitable to recover the Navier-Stokes equations in the framework of the Lattice Boltzmann method. For the two-dimensional nine-velocity lattice we demonstrate that such an entropy function is unique, and that the expansion of the corresponding local equilibrium is the well-known local equilibrium of Y. H. Qian et al. (Europhys. Lett., 17 (1992) 479). Based on the knowledge of entropy functions, we introduce a new version of the Lattice Boltzmann method with an H-theorem built in.


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