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Multi-relaxation-time lattice Boltzmann simulations of lid driven flows using graphics processing unit

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Abstract

Large eddy simulation (LES) using the Smagorinsky eddy viscosity model is added to the two-dimensional nine velocity components (D2Q9) lattice Boltzmann equation (LBE) with multi-relaxation-time (MRT) to simulate incompressible turbulent cavity flows with the Reynolds numbers up to 1 × 107. To improve the computation efficiency of LBM on the numerical simulations of turbulent flows, the massively parallel computing power from a graphic processing unit (GPU) with a computing unified device architecture (CUDA) is introduced into the MRT-LBE-LES model. The model performs well, compared with the results from others, with an increase of 76 times in computation efficiency. It appears that the higher the Reynolds numbers is, the smaller the Smagorinsky constant should be, if the lattice number is fixed. Also, for a selected high Reynolds number and a selected proper Smagorinsky constant, there is a minimum requirement for the lattice number so that the Smagorinsky eddy viscosity will not be excessively large.

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Acknowledgements

The authors would like to thank Prof. Lishi LUO for providing the initial MRT-LBE CPU code. This work is supported by College of William and Mary, Virginia Institute of Marine Science for the study environment.

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Authors and Affiliations

  1. National Engineering Laboratory for Methanol to Olefins, Dalian National Laboratory for Clean Energy, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, 116023, Dalian, Liaoning Province, China

    Chenggong Li

  2. College of William and Mary, Virginia Institute of Marine Science, Gloucester Point, Virginia, 23062, USA

    J. P. Y. Maa

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  1. Chenggong Li
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  2. J. P. Y. Maa
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Correspondence to Chenggong Li.

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Li, C., Maa, J.P.Y. Multi-relaxation-time lattice Boltzmann simulations of lid driven flows using graphics processing unit. Appl. Math. Mech.-Engl. Ed. 38, 707–722 (2017). https://doi.org/10.1007/s10483-017-2194-9

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  • DOI: https://doi.org/10.1007/s10483-017-2194-9

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