Galilean-Invariant Lattice-Boltzmann Models with H-Theorem

TL;DR

This paper identifies the specific entropy functions needed for galilean-invariant lattice Boltzmann models and constructs a stable, explicit model for incompressible Navier-Stokes equations with high Reynolds number capability.

Contribution

It determines the form of the H function for galilean invariance and develops a fully explicit, stable lattice Boltzmann model based on this insight.

Findings

The H function is Burg entropy in 2D and Tsallis entropy in higher dimensions.

Constructed a fully explicit, unconditionally stable lattice Boltzmann model.

Model's Reynolds number limited only by grid resolution.

Abstract

We demonstrate that the requirement of galilean invariance determines the choice of H function for a wide class of entropic lattice Boltzmann models for the incompressible Navier-Stokes equations. The required H function has the form of the Burg entropy for D=2, and of a Tsallis entropy with q=1-2/D for D>2, where D is the number of spatial dimensions. We use this observation to construct a fully explicit, unconditionally stable, galilean invariant, lattice-Boltzmann model for the incompressible Navier-Stokes equations, for which attainable Reynolds number is limited only by grid resolution.