# Smagorinsky-Lilly model

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- | The Smagorinsky model could be | + | The Smagorinsky model could be summarised 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> | ||

- | In the Smagorinsky-Lilly model, the eddy | + | In the Smagorinsky-Lilly model, the eddy viscosity is modeled by <br> |

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

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

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

<br> | <br> | ||

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

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

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

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

<br> | <br> |

## Latest revision as of 19:42, 19 June 2009

The Smagorinsky model could be summarised 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: