Galilean-invariant lattice-Boltzmann models with H theorem.
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.
Boghosian
Bruce M
BM
Department of Mathematics, Bromfield-Pearson Hall, Tufts University, Medford, Massachusetts 02155, USA.
Love
Peter J
PJ
Coveney
Peter V
PV
Karlin
Iliya V
IV
Succi
Sauro
S
Yepez
Jeffrey
J