An H-Theorem for the Lattice Boltzmann Approach to Hydrodynamics

Details An H-Theorem for the Lattice Boltzmann Approach to Hydrodynamics An H-Theorem for the Lattice Boltzmann Approach to Hydrodynamics

1998-08-05

arxiv.org/abs/cond-mat/9808052v1

Physics

Condensed Matter

Statistical Mechanics

6 pages, latex, no figures, accepted for publication in Europhys. Lett

Scientific paper

10.1209/epl/i1998-00448-8

The lattice Boltzmann equation can be viewed as a discretization of the continuous Boltzmann equation. Because of this connection it has long been speculated that lattice Boltzmann algorithms might obey an H-theorem. In this letter we prove that usual nine-velocity models do not obey an H-theorem but models that do obey an H-theorem can be constructed. We consider the general conditions a lattice Boltzmann scheme must satisfy in order to obey an H-theorem and show why on a lattice, unlike the continuous case, dynamics that decrease an H-functional do not necessarily lead to a unique ground state.

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