zbMATH — the first resource for mathematics

Analysis of the lattice Boltzmann treatment of hydrodynamics. (English) Zbl 0941.82527
Summary: It is shown that the lattice Boltzmann model can be made to obey the three-dimensional thermal Navier-Stokes equations by fixing 26 moments of the equilibrium distribution function. This can be achieved on a cubic lattice with particle velocities connecting each lattice site to its first, second and third nearest neighbors; however, this minimal model is not linearly stable in the limit of low transport coefficients. Additional particle velocities must be selected to achieve linear stability.

82C40 Kinetic theory of gases in time-dependent statistical mechanics
76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics
Full Text: DOI
[1] Frisch, U.; Hasslacher, B.; Pomeau, Y., Phys. rev. lett., 56, 1505, (1986)
[2] d’Humieres, D.; Lallemand, P.; Frisch, U., Europhys. lett., 2, 297, (1986)
[3] Frisch, U.; d’Humieres, D.; Hasslacher, B.; Lallemand, P.; Pomeau, Y.; Rivet, J.-P., Complex syst., 1, 649, (1987)
[4] McNamara, G.R.; Zanetti, G., Phys. rev. lett., 61, 2332, (1988)
[5] Higuera, F.J.; Jimenez, J., Europhys. lett., 9, 663, (1989)
[6] Higuera, F.J.; Succi, S., Europhys. lett., 8, 517, (1989)
[7] Higuera, F.J.; Succi, S.; Benzi, R., Europhys. lett., 9, 345, (1989)
[8] McNamara, G.R.; Alder, B., Microscopic simulation of complex hydrodynamic phenomena, ()
[9] Irving, J.H.; Kirkwood, J.G., J. chem. phys., 18, 817, (1950)
[10] Chapman, S.; Cowling, T.G., The mathematical theory of non-uniform gases, (1939), Cambridge Univ. Press Cambridge · Zbl 0063.00782
[11] Koelman, J.M.V.A., Europhys. lett., 15, 603, (1991)
[12] Grad, H., Commun. pure appl. math., 2, 331, (1949)
[13] Chen, S.; Wang, Z.; Shan, X.; Doolen, G., J. stat. phys., 68, 379, (1992)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.