An H-Theorem for the Lattice Boltzmann Approach to Hydrodynamics

Preprint

5 August 1998

preprint
Published by arXiv in arXiv

https://doi.org/10.48550/arXiv.cond-mat/9808052

Abstract

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.

Keywords

BOLTZMANN EQUATION
BOLTZMANN APPROACH
LATTICE BOLTZMANN
ALGORITHMS
CONTINUOUS
THEOREM
MODELS
OBEY

All Related Versions

Version 1, 1998-08-05, ArXiv
Published version: Europhysics Letters, 44 (2), 144.

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