Journal of Statistical Physics, Vol. 107, Nos. 1/2, April 2002. p. 291-308.
In this paper, we present the construction of the Lattice Boltzmann method equipped with the H-theorem. Based on entropy functions whose local equilibria are suitable to recover the Navier-Stokes equations in the framework of the Lattice Boltzmann method, we derive a collision integral which enables simple identification of transport coefficients, and which circumvents construction of the equilibrium. We discuss performance of this approach as compared to the standard realizations.