Journal
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
Volume 338, Issue 3-4, Pages 379-394Publisher
ELSEVIER
DOI: 10.1016/j.physa.2004.02.013
Keywords
Boltzmann equation; Navier-Stokes equation; coarse-graining; hydrodynamic limit; subgrid model; turbulence
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A mean-field approach (filtering out subgrid scales) is applied to the Boltzmann equation in order to derive a subgrid turbulence model based on kinetic theory. It is demonstrated that the only Smagorinsky type model which survives in the hydrodynamic limit on the viscosity time scale is the so-called tensor-diffusivity model. Scaling of the filter-width with Reynolds number and Knudsen number is established. This sets the first rigorous step in deriving turbulence models from kinetic theory. (C) 2004 Elsevier B.V. All rights reserved.
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