# Smagorinsky-Lilly model

### From CFD-Wiki

(Difference between revisions)

m (Grammatical correction) |
|||

(10 intermediate revisions not shown) | |||

Line 1: | Line 1: | ||

- | In the Smagorinsky-Lilly model, the eddy | + | The Smagorinsky model could be summarised as: |

+ | :<math> | ||

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

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

+ | |||

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

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

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

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

<br> | <br> | ||

Line 21: | Line 26: | ||

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

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

- | The | + | The Smagorinsky constant usually has the value: |

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

C_s = 0.1 - 0.2 | C_s = 0.1 - 0.2 | ||

</math> | </math> |

## 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: