Possibility and Impossibility of the Entropy Balance in Lattice Boltzmann Collisions

TL;DR

This paper explores the conditions under which entropy-balanced collisions are possible or impossible in lattice Boltzmann methods, highlighting the need for strategies to handle highly nonequilibrium states.

Contribution

It identifies regions in the distribution space where entropy balance collisions can or cannot occur, emphasizing the incompleteness of current entropic LBM definitions.

Findings

Existence of a vicinity of equilibrium with possible entropy balance collisions.

Presence of a nonequilibrium area where such collisions are impossible.

Need for explicit strategies to manage highly nonequilibrium states.

Abstract

We demonstrate that in the space of distributions operated on by lattice Boltzmann methods that there exists a vicinity of the equilibrium where collisions with entropy balance are possible and, at the same time, there exist an area of nonequilibrium distributions where such collisions are impossible. We calculate and graphically represent these areas for some simple entropic equilibria using single relaxation time models. Therefore it is shown that the definition of an entropic LBM is incomplete without a strategy to deal with certain highly nonequilibrium states. Such strategies should be explicitly stated as they may result in the production of additional entropy.