A GENERAL MULTIPLE-RELAXATION-TIME BOLTZMANN COLLISION MODEL

Xiaowen Shan () and Hudong Chen ()
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Xiaowen Shan: Exa Corporation, 3 Burlington Woods Drive, Burlington, MA 01803, USA
Hudong Chen: Exa Corporation, 3 Burlington Woods Drive, Burlington, MA 01803, USA

International Journal of Modern Physics C (IJMPC), 2007, vol. 18, issue 04, 635-643

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.

Keywords: Multiple-relaxation-time; lattice Boltzmann; kinetic theory; computational fluid dynamics; 47.11.-j; 47.11.Qr; 47.45.Ab; 05.20.Dd (search for similar items in EconPapers)
Date: 2007
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DOI: 10.1142/S0129183107010887

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