Commun. Comput. Phys., 11 (2012), pp. 1569-1590.

Lattice BGK Model for Incompressible Axisymmetric Flows

Ting Zhang 1, Baochang Shi 2*, Zhenhua Chai 2, Fumei Rong 1

1 State Key Laboratory of Coal Combustion, Huazhong University of Science and Technology, Wuhan 430074, China.
2 School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China.

Received 29 August 2010; Accepted (in revised version) 5 August 2011
Available online 3 January 2012


In this paper, a lattice Boltzmann BGK (LBGK) model is proposed for simulating incompressible axisymmetric flows. Unlike other existing axisymmetric lattice Boltzmann models, the present LBGK model can eliminate the compressible effects only with the small Mach number limit. Furthermore the source terms of the model are simple and contain no velocity gradients. Through the Chapman-Enskog expansion, the macroscopic equations for incompressible axisymmetric flows can be exactly recovered from the present LBGK model. Numerical simulations of the Hagen-Poiseuille flow, the pulsatile Womersley flow, the flow over a sphere, and the swirling flow in a closed cylindrical cavity are performed. The results agree well with the analytic solutions and the existing numerical or experimental data reported in some previous studies.

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PACS: 47.11-j, 02.60.Cb
Key words: Lattice BGK model, incompressible axisymmetric.

*Corresponding author.
Email: (T. Zhang), (B. Shi), (Z. Chai), (F. Rong)

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