×

zbMATH — the first resource for mathematics

Derivation of the lattice Boltzmann method by means of the discrete ordinate method for the Boltzmann equation. (English) Zbl 0877.76062
The lattice Boltzmann method is derived by means of the discrete ordinate method, in the frame of the BGK approximation. Appropriate references are quoted.
Reviewer: V.C.Boffi (Roma)

MSC:
76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics
82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Monaco, R., Discrete kinetic theory, lattice gas dynamics and foundations of hydrodynamics, (1989), World Scientific · Zbl 0734.76002
[2] Boon, J.P., J. statist. phys., 68, (1992)
[3] Rothman, D.; Zaleski, S., Rev. modern phys., 66, 1417, (1994)
[4] Hou, S.; Zou, Q.; Chen, S.; Doolen, G.; Cogley, A.C., Simulation of cavity flow by the lattice Boltzmann method, J. comput. phys., 118, 329, (1995) · Zbl 0821.76060
[5] Inamuro, T.; Yoshino, Y.; Ogino, F., A non-slip boundary condition for lattice Boltzmann simulations, Phys. fluids, 6, 2928, (1995) · Zbl 1027.76631
[6] Chen, S.; Chen, H.; Martinez, D.; Matthaeus, W.H., Lattice Boltzmann model for simulation of magnetohydrodynamics, Phys. rev. lett., 67, 3776, (1991)
[7] Chen, H.; Matthaeus, W.H., Phys. rev. A, 45, 5339, (1992)
[8] Qian, Y.; d’Humieres, D.; Lallemand, P., Lattice BGK models for Navier-Stokes equation, Europhys. lett., 17, 479, (1992) · Zbl 1116.76419
[9] Bhatnagar, P.L.; Gross, E.P.; Krook, M., Phys. rev., 94, 511, (1954)
[10] Frisch, U.; Hasslacher, B.; Pomeau, Y., Phys. lett., 56, 1505, (1986)
[11] Frisch, U.; d’Humieres, D.; Hasslacher, B.; Lallemand, P.; Pomeau, Y.; Rivet, J.-P., Complex systems, 1, 649, (1987)
[12] Wolfram, S., J. statist. phys., 45, 471, (1986)
[13] Doolen, G.D., Lattice gas methods for partial differential equations, (1989), Addison-Wesley Reading
[14] Doolen, G.D., Lattice gas methods; applications and hardware, Phys. D, 47, (1991)
[15] Bird, G.A., Molecular gas dynamics, (1976), Clarendon Press Oxford
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.