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Strain rate calculation for explicitly filtered constant smagorinsky model

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Old   December 1, 2013, 09:25
Default Strain rate calculation for explicitly filtered constant smagorinsky model
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MMS
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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.

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Old   December 1, 2013, 09:55
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Quote:
Originally Posted by cfdmms View Post
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
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Old   December 2, 2013, 15:09
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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.
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