J. Phys. II France
Volume 4, Numéro 2, February 1994
Page(s) 191 - 214
DOI: 10.1051/jp2:1994123
J. Phys. II France 4 (1994) 191-214

Boundary flow condition analysis for the three-dimensional lattice Boltzmann model

I. Ginzbourg and P. M. Adler

LPTM, Asterama 2, Avenue du Téléport, 86360 Chasseneuil, France

(Received 10 May 1993, revised 17 September 1993, accepted 22 October 1993)

In the continuum limit, the velocity of a Newtonian fluid should vanish at a solid wall. This condition is studied for the FCHC lattice Boltzmann model with rest particles. This goal is achieved by expanding the mean populations up to the second order in terms of the ratio $\varepsilon$ between the lattice unit and a characteristic overall size of the medium. This expansion is applied to two extreme flow situations. In Poiseuille flow, the second eigenvalue of the collision matrix can be chosen so that velocity vanishes at the solid walls with errors smaller than $\varepsilon^2$ ; however the choice depends on the angle between the channel walls and the axes of the lattice. In a plane stagnation flow, the tangential and normal velocities do not vanish at the same point, except for particular choices of the parameters of the model ; this point does not coincide with the solid wall. It is concluded that the boundary conditions are as a matter of fact imposed with errors of second order.

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