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Analytical solution of axi-symmetrical lattice Boltzmann model for cylindrical Couette flows

An, Hongyan and Zhang, Chuhua and Meng, Jian-Ping and Zhang, Yonghao (2012) Analytical solution of axi-symmetrical lattice Boltzmann model for cylindrical Couette flows. Physica A: Statistical Mechanics and its Applications, 391 (1-2). pp. 8-14. ISSN 0378-4371

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Abstract

Analytical solution for the axi-symmetrical lattice Boltzmann model is obtained for the low-Mach number cylindrical Couette flows. In the hydrodynamic limit, the present solution is in excellent agreement with the result of the Navier-Stokes equation. Since the kinetic boundary condition is used, the present analytical solution using nine discrete velocities can describe flows with the Knudsen number up to 0.1. Meanwhile, the comparison with the simulation data obtained by the direct simulation Monte Carlo method shows that higher-order lattice Boltzmann models with more discrete velocities are needed for highly rarefied flows.