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-   -   DNS: how to compute nonlinear term in the spectral kinetic energy equation (https://www.cfd-online.com/Forums/main/95189-dns-how-compute-nonlinear-term-spectral-kinetic-energy-equation.html)

 magicsquirrel December 8, 2011 14:40

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 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

 cfdnewbie December 12, 2011 14:38

:) pseudospectrally in physical space is out of the question, I guess?

 nimav December 13, 2011 03:53

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

 magicsquirrel December 13, 2011 13:35

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))```

 cfdnewbie December 13, 2011 18:45

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....

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