Galilean Invariant Viscosity Term for an Athermal Integer Lattice Boltzmann Automaton in three Dimensions

M.C. Geier, A. Greiner and J.G. Korvink
IMTEK, Albert Ludwigs University Freiburg im Breisgau, DE

Keywords: lattice Boltzmann, cellular automaton, central moments, Galilean invariance, viscosity

Abstract:
The athermal lattice Boltzmann automata (LBA) are promising replacements for Navier Stokes solvers in computational fluid dynamics (CFD). They are inherently parallel, scale exactly linear with the number of computational elements and can be applied to arbitrary geometries. The integer LBA presented here adds unconditional stability, roundoff-error freeness, and exact fulfillment of conservation laws to the list of benefits. The original LBA had artifacts not acceptable for industrial application. With ongoing research most of them could be removed. One of the artifacts was that the viscosity of the simulated fluid depended on the flow speed in an anisotropic manner. Previous work concentrated on removing this artifact by adding degrees of freedom to the unit cell. Here we present a method reducing the errors in the viscosity term without the need for new degrees of freedom. No computational overhead is introduced by this method.

Nanotech 2004 Conference Technical Program Abstract