DNS: how to compute nonlinear term in the spectral kinetic energy equation
Dear CFD Onliner,
What is the best way to compute the nonlinear term in the spectral kinetic energy equation in triperiodic 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 
:) pseudospectrally in physical space is out of the question, I guess?

I think you must use a transformation method first and compute parameters on that.

Yes probably doing this pseudospectrally is the best way.
Something like that: Code:
1) (u.grad).u 
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 nonlinear 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.... 
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