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A General Multiple-Relaxation-Time Boltzmann Collision Model

Author

Listed:
  • XIAOWEN SHAN

    (Exa Corporation, 3 Burlington Woods Drive, Burlington, MA 01803, USA)

  • HUDONG CHEN

    (Exa Corporation, 3 Burlington Woods Drive, Burlington, MA 01803, USA)

Abstract

We formulate a simple extension to the Bhatnagar-Gross-Krook collision model by expanding the distribution function in Hermite polynomials and assigning a relaxation time to each hydrodynamic moment. By discretizing the velocity space, multiple-relaxation-time lattice Boltzmann models can be constructed. The transport coefficients are analytically calculated and numerically verified. At the lowest order, allowing different relaxation rates for the second and third Hermite components results in a variable Prandtl number. Comparing with the previously proposed multiple-relaxation-time lattice Boltzmann models, the present formulation is general in the sense that it is independent of the underlying lattice structure and does not require a procedure for transformation of base vectors.

Suggested Citation

  • Xiaowen Shan & Hudong Chen, 2007. "A General Multiple-Relaxation-Time Boltzmann Collision Model," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 18(04), pages 635-643.
    • Handle: RePEc:wsi:ijmpcx:v:18:y:2007:i:04:n:s0129183107010887
    DOI: 10.1142/S0129183107010887
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    References listed on IDEAS

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    1. Metzger, T. & Irawan, A. & Tsotsas, E., 2006. "Remarks on the paper “Extension of Hoshen–Kopelman algorithm to non-lattice environments” by A. Al-Futaisi and T.W. Patzek, Physica A 321 (2003) 665–678," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 363(2), pages 558-560.
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