# Smagorinsky-Lilly model

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 Revision as of 16:24, 13 September 2005 (view source)Jasond (Talk | contribs)m← Older edit Revision as of 21:52, 13 September 2005 (view source)Zxaar (Talk | contribs) Newer edit → Line 12: Line 12:

- Where + Where the filter length is given by :[itex] :[itex] \bar \Delta  = \nabla ^{\frac{1}{3}} \bar \Delta  = \nabla ^{\frac{1}{3}}

## Revision as of 21:52, 13 September 2005

The Smagorinsky model could be summerised as:

$\tau _{ij} - \frac{1}{3}\tau _{kk} \delta _{ij} = - 2\left( {C_s \bar \Delta } \right)^2 \left| {\bar S} \right|S_{ij}$

In the Smagorinsky-Lilly model, the eddy-viscosity is modeled by

$\mu _{sgs} = \rho \left( {C_s \bar \Delta } \right)^2 \left| {\bar S} \right|$

Where the filter length is given by

$\bar \Delta = \nabla ^{\frac{1}{3}}$

and

$\bar S = \sqrt {2S_{ij} S_{ij} }$

The effective viscosity is calculated from

$\mu _{eff} = \mu _{mol} + \mu _{sgs}$

The Smagorinsky constant usually has the value:

$C_s = 0.1 - 0.2$