# Strain rate calculation for explicitly filtered constant smagorinsky model

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 December 1, 2013, 08:25 Strain rate calculation for explicitly filtered constant smagorinsky model #1 New Member   MMS Join Date: Nov 2013 Posts: 29 Rep Power: 10 I have very vague idea about this, if some one help me to understand it will be great help. In the constant Smagorinsky model, during the calculation of turbulent viscosity (Nu_t) we need the magnitude of the strain rate. For the implicitly filtered LES, Nu_t will be Nu_t = (Cs*DELTA)**2*STRAIN_RATE Where, Cs=0.2, DELTA= (dx*dy*dz)^(1/3)= almost equal to the cell size (h). and the magnitude of the strain rate measured for each cell in cell centre (if I am not wrong). But for explicit filtering, the filter width DELTA will be arbitrary value or multiples of cell size (h), let say DELTA=2*h. In that case how the strain rate will be linked with the filter size? Thanks.

December 1, 2013, 08:55
#2
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Filippo Maria Denaro
Join Date: Jul 2010
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Quote:
 Originally Posted by cfdmms I have very vague idea about this, if some one help me to understand it will be great help. In the constant Smagorinsky model, during the calculation of turbulent viscosity (Nu_t) we need the magnitude of the strain rate. For the implicitly filtered LES, Nu_t will be Nu_t = (Cs*DELTA)**2*STRAIN_RATE Where, Cs=0.2, DELTA= (dx*dy*dz)^(1/3)= almost equal to the cell size (h). and the magnitude of the strain rate measured for each cell in cell centre (if I am not wrong). But for explicit filtering, the filter width DELTA will be arbitrary value or multiples of cell size (h), let say DELTA=2*h. In that case how the strain rate will be linked with the filter size? Thanks.

The real measure of the filter widht is somehow uncertain both in implicit and explicit filtering... it is not true that is always delta=2h for explicit filtering, it depends on the effective way you adopt for performing filtering....you can find in literature some papers discussing about that

 December 2, 2013, 14:09 #3 Senior Member     Paolo Lampitella Join Date: Mar 2009 Location: Italy Posts: 1,779 Blog Entries: 29 Rep Power: 35 And the strain rate would be the one based on the filtered velocity. Which doesn't mean it is the best option, it is just how the Smagorinsky model is defined.