# DNS: how to compute nonlinear term in the spectral kinetic energy equation

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 December 8, 2011, 14:40 DNS: how to compute nonlinear term in the spectral kinetic energy equation #1 New Member   Join Date: Jul 2011 Posts: 8 Rep Power: 8 Sponsored Links Dear CFD Onliner, What is the best way to compute the nonlinear term in the spectral kinetic energy equation in tri-periodic Fourier DNS code ? I mean the T(k)=-i sum_{k+p+q=0} P_ijm(k) u_j(p) u_m(q) u_i(k) with k,p,q waves numbers in R^3. Cheers

 December 12, 2011, 14:38 #2 Senior Member   cfdnewbie Join Date: Mar 2010 Posts: 557 Rep Power: 13 pseudospectrally in physical space is out of the question, I guess?

 December 13, 2011, 03:53 #3 New Member   nima vaziri Join Date: Aug 2011 Posts: 5 Rep Power: 8 I think you must use a transformation method first and compute parameters on that.

 December 13, 2011, 13:35 #4 New Member   Join Date: Jul 2011 Posts: 8 Rep Power: 8 Yes probably doing this pseudo-spectrally is the best way. Something like that: Code: ```1) (u.grad).u 2) FFT((u.grad).u) 3) P(FFT((u.grad).u)) 4) FFT(u).P(FFT((u.grad).u))```

 December 13, 2011, 18:45 #5 Senior Member   cfdnewbie Join Date: Mar 2010 Posts: 557 Rep Power: 13 I'm no expert in this, but I'd guess it would have to look sth like this: 1) start with u(k) (velocity field in spectral space) 2) iFFT(u) (gives you u(x) in physical space) 3) evaluate non-linear products of u by collocation, i.e. u(x_i)*u(x_i) 4) FFT the product back to spectral space not sure if this is what you had in mind, it is just the approach i took to evaluate (double) products a while ago....

 Tags dns, energy, fourier, nonlinear, transfer

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