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

✍ Scribed by Santosh Ansumali; Iliya V. Karlin; Sauro Succi

Publisher
Elsevier Science
Year
2004
Tongue
English
Weight
259 KB
Volume
338
Category
Article
ISSN
0378-4371

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✦ Synopsis

A mean-ΓΏeld approach (ΓΏltering 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-di usivity model. Scaling of the ΓΏlter-width with Reynolds number and Knudsen number is established. This sets the ΓΏrst rigorous step in deriving turbulence models from kinetic theory.

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