Europhys. Lett.
Volume 73, Number 3, February 2006
Page(s) 370 - 376
Section Electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics
Published online 23 December 2005
Europhys. Lett., 73 (3), pp. 370-376 (2006)
DOI: 10.1209/epl/i2005-10404-8

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

M. Sbragaglia1 and S. Succi2

1  Dipartimento di Fisica, Università "Tor Vergata", and INFN Via della Ricerca Scientifica 1, I-00133 Roma, Italy
2  CNR, IAC - Viale del Policlinico 137, I-00161 Roma, Italy

received 8 September 2005; accepted in final form 2 December 2005
published online 23 December 2005

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 challenges the pessimistic stance, according to which the lattice Boltzmann method should only be used for strictly hydrodynamic purposes. It may also help the interpretation of recent simulations of microflows, which show satisfactory agreement with continuum kinetic theory in the moderate-Knudsen regime.

47.11+j - Computational methods in fluid dynamics.
47.45-n - Rarefied gas dynamics.

© EDP Sciences 2006