Analytical solution of axi-symmetrical lattice Boltzmann model for cylindrical Couette flows |
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| Authors: | Hongyan An Chuhua Zhang Jianping Meng Yonghao Zhang |
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| Institution: | 1. Department of Fluid Machinery and Engineering, School of Energy and Power Engineering, Xi’an Jiaotong University, 28 West Xianning Road, Xi’an 710049, Shanxi, China;2. Department of Mechanical Engineering, University of Strathclyde, Glasgow, G1 1XJ, United Kingdom |
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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. |
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