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 $q=1\mathrm{}-\mathrm{}(2/D)\mathrm{}$ for $D>\mathrm{}2,$ 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.

• Received 5 November 2002

DOI:https://doi.org/10.1103/PhysRevE.68.025103