Kinetic theory of turbulence modeling: smallness parameter, scaling and microscopic derivation of Smagorinsky model

Santosh Ansumali, Iliya V. Karlin and Sauro Succi

Physica A: Statistical Mechanics and its Applications, 2004, vol. 338, issue 3, 379-394

Abstract: 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.

Keywords: Boltzmann equation; Navier–Stokes equation; Coarse-graining; Hydrodynamic limit; Subgrid model; Turbulence (search for similar items in EconPapers)
Date: 2004
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Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:338:y:2004:i:3:p:379-394

DOI: 10.1016/j.physa.2004.02.013

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