A note on the lattice Boltzmann method beyond the Chapman Enskog limits

Details A note on the lattice Boltzmann method beyond the Chapman Enskog limits A note on the lattice Boltzmann method beyond the Chapman Enskog limits

2005-09-12

arxiv.org/abs/cond-mat/0509283v1

Europhys. Lett. 73, 370 (2006)

Physics

Condensed Matter

Statistical Mechanics

7 PAGES, 1 FIGURE

Scientific paper

10.1209/epl/i2005-10404-8

A non-perturbative analysis of the Bhatnagar-Gross-Krook (BGK) model kinetic equation for finite values of the Knudsen number is presented. This analysis indicates why discrete kinetic versions of the BGK equation, and notably the Lattice Boltzmann method, can provide semi-quantitative results also in the non-hydrodynamic, finite-Knudsen regime, up to $Kn\sim {\cal O}(1)$. This may help the interpretation of recent Lattice Boltzmann simulations of microflows, which show satisfactory agreement with continuum kinetic theory in the moderate-Knudsen regime.

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