CFD Online Logo CFD Online URL
www.cfd-online.com
[Sponsors]
Home > Wiki > Smagorinsky-Lilly model

Smagorinsky-Lilly model

From CFD-Wiki

(Difference between revisions)
Jump to: navigation, search
m (Reverted edits by OucapAspas (Talk) to last version by Salva)
m (Grammatical correction)
 
Line 1: Line 1:
-
The Smagorinsky model could be summerised as:
+
The Smagorinsky model could be summarised as:
:<math>
:<math>
\tau _{ij}  - \frac{1}{3}\tau _{kk} \delta _{ij}  =  - 2\left( {C_s \Delta } \right)^2 \left| {\bar S} \right|S_{ij}  
\tau _{ij}  - \frac{1}{3}\tau _{kk} \delta _{ij}  =  - 2\left( {C_s \Delta } \right)^2 \left| {\bar S} \right|S_{ij}  

Latest revision as of 19:42, 19 June 2009

The Smagorinsky model could be summarised as:


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


Where the filter width is usually taken to be


 \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
My wiki