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

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Old   December 8, 2011, 14:40
Question DNS: how to compute nonlinear term in the spectral kinetic energy equation
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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.
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Old   December 12, 2011, 14:38
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pseudospectrally in physical space is out of the question, I guess?
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Old   December 13, 2011, 03:53
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I think you must use a transformation method first and compute parameters on that.
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Old   December 13, 2011, 13:35
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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))
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Old   December 13, 2011, 18:45
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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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