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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.

MSC:
82C40 Kinetic theory of gases in time-dependent statistical mechanics
76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics
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[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)
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