Commun. Comput. Phys., 15 (2014), pp. 265-284.

Simulation of Power-Law Fluid Flows in Two-Dimensional Square Cavity Using Multi-Relaxation-Time Lattice Boltzmann Method

Qiuxiang Li 1, Ning Hong 2, Baochang Shi 3*, Zhenhua Chai 3

1 State Key Laboratory of Coal Combustion, Huazhong University of Science and Technology, Wuhan, 430074, P.R. China.
2 Department of Foundational Courses, Jiangcheng College, China University of Geosciences, Wuhan, 430200, P.R. China.
3 School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, 430074, P.R. China.

Received 16 February 2012; Accepted (in revised version) 21 May 2013
Available online 16 August 2013


In this paper, the power-law fluid flows in a two-dimensional square cavity are investigated in detail with multi-relaxation-time lattice Boltzmann method (MRT-LBM). The influence of the Reynolds number (Re) and the power-law index (n) on the vortex strength, vortex position and velocity distribution are extensively studied. In our numerical simulations, Re is varied from 100 to 10000, and n is ranged from 0.25 to 1.75, covering both cases of shear-thinning and shear-thickening. Compared with the Newtonian fluid, numerical results show that the flow structure and number of vortex of power-law fluid are not only dependent on the Reynolds number, but also related to power-law index.

AMS subject classifications: 76A05, 76M28, 76D05, 81T80

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Key words: Multi-relaxation-time lattice Boltzmann method, power-law fluid, shear-thinning, shear-thickening.

*Corresponding author.
Email: (B. Shi), (Q. Li), (N. Hong), (Z. Chai)

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