Commun. Comput. Phys., 8 (2010), pp. 1208-1223.


Application of Lattice Boltzmann Method to Simulation of Compressible Turbulent Flow

Congshan Zhuo 1, Chengwen Zhong 2, Kai Li 1, Shengwei Xiong 1, Xiaopeng Chen 3, Jun Cao 4*

1 National Key Laboratory of Science and Technology on Aerodynamic Design and Research, Northwestern Polytechnical University, Xi'an, Shaanxi 710072, China.
2 National Key Laboratory of Science and Technology on Aerodynamic Design and Research, Northwestern Polytechnical University, Xi'an, Shaanxi 710072, China; and Center for High Performance Computing, Northwestern Polytechnical University, Xi'an, Shaanxi 710072, China.
3 School of Mechanics, Civil Engineering and Architecture, Northwestern Polytechnical University, Xi'an, Shaanxi 710072, China.
4 Department of Mechanical and Industrial Engineering, Ryerson University, Toronto, Ontario, M5B 2K3, Canada.

Received 30 January 2010; Accepted (in revised version) 7 May 2010
Available online 23 June 2010
doi:10.4208/cicp.300110.070510a

Abstract

The main goal of this paper is to develop the coupled double-distribution-function (DDF) lattice Boltzmann method (LBM) for simulation of subsonic and transonic turbulent flows. In the present study, we adopt the second-order implicit-explicit (IMEX) Runge-Kutta schemes for time discretization and the Non-Oscillatory and Non-Free-Parameters Dissipative (NND) finite difference scheme for space discretization. The Sutherland's law is used for expressing the viscosity of the fluid due to considerable temperature change. Also, the Spalart-Allmaras (SA) turbulence model is incorporated in order for the turbulent flow effect to be pronounced. Numerical experiments are performed on different turbulent compressible flows around a NACA0012 airfoil with body-fitted grid. Our numerical results are found to be in good agreement with experiment data and/or other numerical solutions, demonstrating the applicability of the method presented in this study to simulations of both subsonic and transonic turbulent flows.

AMS subject classifications: 76M28, 82B40, 76N15, 76F55

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Key words: Lattice Boltzmann method, compressible turbulent flow, airfoil, body-fitted grid.

*Corresponding author.
Email: zhuocs@mail.nwpu.edu.cn (C. Zhuo), zhongcw@nwpu.edu.cn (C. Zhong), li040384@mail.nwpu.edu.cn (K. Li), xiongshengwei@mail.nwpu.edu.cn (S. Xiong), xchen76@nwpu.edu.cn (X. Chen), jcao@ryerson.ca (J. Cao)
 

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