LES Test Filtering

Nabi

Hi All; I am working on Dynamics model. I need to filter the variables to have L_ij and M_ij. In M_ij we need to filter S_ij (test filtering). There exist two ways to filter S_ij. One is to calculate S_ij from the calculated velocities, and then use Simpson or trapezoidal rule to filter it. The second way is to filter the velocities and calculate the filtered S_ij from the filtered velocities.

S_ij = (uf_i/x_j+uf_j/x_i)/2 -- ---- uf is the double filtered velocity.

And also same for |S|. It is possible to calculate |S| and then filter, or filter S_ij and calculate the filtered |S| from the filtered S_ij. Can you please guide me, which one is correct? Thank you in advance.