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Smagorinsky-Lilly model

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Where the filter length is given by
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Where the filter width is usually taken to be
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\bar \Delta  = Vol ^{\frac{1}{3}}  
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\bar \Delta  = \left( \mbox{Volume} \right)^{\frac{1}{3}}  
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Revision as of 13:51, 21 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 width is usually taken to be


\bar \Delta  = \left( \mbox{Volume} \right)^{\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
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