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January 10, 2013, 07:53 |
Mean Strain rate
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#1 |
New Member
Michael Rembe
Join Date: Oct 2009
Location: Germany
Posts: 4
Rep Power: 16 |
Hi,
I'm not an expert in fluid mechanics. In the SMAGORINSKY-model I need the square root of Sij*Sij. I'm a little confused about the different notations. What is the defference between the mean strain rate defined as: and the mean strain rate defined as: Sij=0.5*(dUi/dxj+dUj/dxi) Some times I can read: S=sqrt((dUi/dxj)^2+(dUj/dxi)^2) I would be very grateful for a short explanation. Thank you very much! Michael |
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January 14, 2013, 03:11 |
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#2 |
Senior Member
Rami Ben-Zvi
Join Date: Mar 2009
Posts: 155
Rep Power: 17 |
Hi Michael,
That's simply tensor algebra (using the sum convention). If you use the definition Sij=0.5*(dUi/dxj+dUj/dxi) , substitute it in s^2 =Sij*Sij and sum over i and j, you'l get the result from the other expression, S=sqrt((dUi/dxj)^2+(dUj/dxi)^2) you get S^2=Ui,jUi,j+ Uj,iUj,i = 4SijSij - 2Ui,jUj,i so it is different due to the last term. |
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