An H-theorem for the lattice Boltzmann approach to hydrodynamics

Theoretical Physics, University of Oxford - 1 Keble Rd., Oxford OX1 3BN, Great Britain

Received: 18 May 1998
Accepted: 17 August 1998

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.