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

magicsquirrel · December 8, 2011, 14:40

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....

December 8, 2011, 14:40	DNS: how to compute nonlinear term in the spectral kinetic energy equation	#1
magicsquirrel New Member Join Date: Jul 2011 Posts: 8 Rep Power: 15	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 13, 2011, 13:35		#4
magicsquirrel New Member Join Date: Jul 2011 Posts: 8 Rep Power: 15	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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December 12, 2011, 14:38		#2
cfdnewbie Senior Member cfdnewbie Join Date: Mar 2010 Posts: 557 Rep Power: 20	pseudospectrally in physical space is out of the question, I guess?

December 13, 2011, 03:53		#3
nimav New Member nima vaziri Join Date: Aug 2011 Posts: 5 Rep Power: 15	I think you must use a transformation method first and compute parameters on that.

December 13, 2011, 18:45		#5
cfdnewbie Senior Member cfdnewbie Join Date: Mar 2010 Posts: 557 Rep Power: 20	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....