zbMATH — the first resource for mathematics

Accuracy of discrete-velocity BGK models for the simulation of the incompressible Navier-Stokes equations. (English) Zbl 0845.76086
Since 1988 the so-called lattice Boltzmann (LB) model is used to obtain the lattice gas automata retaining a number of characteristics of the Navier-Stokes equation. In this paper, the LB method is considered as a discretization of the discrete Boltzmann equation. It is shown numerically that the employed 9-velocity scheme converges to incompressible Navier-Stokes equation. The evolution of Taylor vortices in a periodic domain is chosen as a test problem. As mentioned by the authors, the “time step restrictions require a tremendous number of computations to produce accuracy, thus degrading the overall performance of the method”.

76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics
76M20 Finite difference methods applied to problems in fluid mechanics
76D05 Navier-Stokes equations for incompressible viscous fluids
Full Text: DOI
[1] Frisch, U.; Hasslacher, B.; Pomeau, Y., Lattice-gas automata for the Navier-Stokes equation, Phys. rev. lett., 56, 1505, (1986)
[2] ()
[3] (), reprinted from
[4] McNamara, G.; Zanetti, G., Use of the Boltzmann equation to simulate lattice-gas automata, Phys. rev. lett., 61, 2332, (1988)
[5] Bhatnagar, P.L.; Gross, E.P.; Krook, M., A model for collision processes in gases. I. small amplitude processes in charged and neutral one-component systems, Phys. rev., 94, 511, (1954) · Zbl 0055.23609
[6] Dukowicz, J., Computational efficiency of the hybrid penalty-pseudocompressibility method for incompressible flow, Computers fluids, 23, 479, (1994) · Zbl 0809.76060
[7] Succi, S.; Benzi, R.; Higuera, F., The lattice Boltzmann equation: a new tool for computational fluid-dynamics, Physica D, 47, 219, (1991)
[8] Chen, S.; Wang, Z.; Shan, X.; Doolen, G.D., J. stat. phys., 68, 379, (1992)
[9] Martinez, D.O.; Matthaeus, W.H.; Chen, S.; Montgomery, D.C., A comparison of spectral methods and lattice Boltzmann simulations of two-dimensional hydrodynamics, Phys. fluids A, (1994) · Zbl 0826.76069
[10] McNamara, G.; Alder, B., Analysis of the lattice Boltzmann treatment of hydrodynamics, Physica A, 194, 218, (1993) · Zbl 0941.82527
[11] Kadanoff, L.; McNamara, G.; Zanetti, G., Complex systems, 1, 791, (1987)
[12] Skordos, P.A., Initial and boundary conditions for the lattice Boltzmann method, Phys. rev. E, (1994)
[13] Ancona, M., Fully-Lagrangian and lattice-Boltzmann methods for solving systems of conservation equations, J. comp. phys., (1994) · Zbl 0808.65087
[14] Sterling, J.; Chen, S., Stability analysis of lattice Boltzmann methods, J. comp. phys., (1994)
[15] Klainerman, S.; Majda, A., Compressible and incompressible fluids, Commun. pure appl. math., 35, 629, (1982) · Zbl 0478.76091
[16] Alexander, F.J.; Chen, S.; Sterling, J.D., Lattice Boltzmann thermohydrodynamics, Phys. rev. E, 47, 2249, (1993)
[17] Dahlquist, G.; Bjorck, A., ()
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.