# Smagorinsky-Lilly model

(Difference between revisions)
 Revision as of 21:52, 13 September 2005 (view source)Zxaar (Talk | contribs)← Older edit Latest revision as of 19:42, 19 June 2009 (view source)Baldy (Talk | contribs) m (Grammatical correction) (6 intermediate revisions not shown) Line 1: Line 1: - The Smagorinsky model could be summerised as: + The Smagorinsky model could be summarised as: :$:[itex] - \tau _{ij} - \frac{1}{3}\tau _{kk} \delta _{ij} = - 2\left( {C_s \bar \Delta } \right)^2 \left| {\bar S} \right|S_{ij} + \tau _{ij} - \frac{1}{3}\tau _{kk} \delta _{ij} = - 2\left( {C_s \Delta } \right)^2 \left| {\bar S} \right|S_{ij}$
[/itex]
- In the Smagorinsky-Lilly model, the eddy-viscosity is modeled by
+ In the Smagorinsky-Lilly model, the eddy viscosity is modeled by
:$:[itex] - \mu _{sgs} = \rho \left( {C_s \bar \Delta } \right)^2 \left| {\bar S} \right| + \mu _{sgs} = \rho \left( {C_s \Delta } \right)^2 \left| {\bar S} \right|$ [/itex]

- Where the filter length is given by + Where the filter width is usually taken to be :$:[itex] - \bar \Delta = \nabla ^{\frac{1}{3}} + \Delta = \left( \mbox{Volume} \right)^{\frac{1}{3}}$ [/itex]

## 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:

$C_s = 0.1 - 0.2$