# Smagorinsky-Lilly model

### From CFD-Wiki

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The Smagorinsky model could be summerised as: | The Smagorinsky model could be summerised as: | ||

:<math> | :<math> | ||

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

</math> <br> | </math> <br> | ||

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:<math> | :<math> | ||

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

</math> | </math> | ||

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Where the filter width is usually taken to be | Where the filter width is usually taken to be | ||

:<math> | :<math> | ||

- | + | \Delta = \left( \mbox{Volume} \right)^{\frac{1}{3}} | |

</math> | </math> | ||

<br> | <br> |

## Revision as of 12:20, 8 May 2006

The Smagorinsky model could be summerised as:

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

Where the filter width is usually taken to be

and

The effective viscosity is calculated from

The Smagorinsky constant usually has the value: