WALE model definition !?

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 September 2, 2013, 11:49 WALE model definition !? #1 New Member   Join Date: Jan 2010 Location: Netherlands Posts: 28 Rep Power: 15 Hello, I'm trying to implement WALE model in LES code using Fortran for channel flow. Now the model definition for sgs viscosity is: = where, = I'm having problems understanding the last term in the above equation . Can anyone please explain how to expand the above term? Cheers

 September 2, 2013, 14:26 #2 Senior Member     Paolo Lampitella Join Date: Mar 2009 Location: Italy Posts: 1,987 Blog Entries: 29 Rep Power: 36 It seems that there is some algebra which can be exploited: http://www.math.univ-montp2.fr/~nico...S_BayaToda.pdf However, if you define S2=S^2 and W2=W^2 (S_ik S_kj & W_ik W_kj rispectively), you will notice that the term is just S2_mn W2_nm... i guess

 October 3, 2013, 06:18 #3 Senior Member   Rami Ben-Zvi Join Date: Mar 2009 Posts: 155 Rep Power: 15 It seems that tensor notation is used here, implying summation of repeated indices. If this is the case, the last equation is merely a sum over the all the indices i,j,k,l (each in the proper range, e.g. from 1 to 3 in 3D).

 Tags large eddy simulation, les, model functions, sgs, wale