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

magicsquirrel · December 8, 2011, 13:40

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, 13:38

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

nimav · December 13, 2011, 02:53

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

magicsquirrel · December 13, 2011, 12:35

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, 17:45

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, 13:40	DNS: how to compute nonlinear term in the spectral kinetic energy equation	#1
magicsquirrel New Member Join Date: Jul 2011 Posts: 8 Rep Power: 13	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, 12:35		#4
magicsquirrel New Member Join Date: Jul 2011 Posts: 8 Rep Power: 13	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))

Thread Tools	Search this Thread
Show Printable Version Email this Page	Search this Thread: Advanced Search
Display Modes
Linear Mode Switch to Hybrid Mode Switch to Threaded Mode

Similar Threads
Thread	Thread Starter	Forum	Replies	Last Post
question about turbulent kinetic energy	junker4236	Main CFD Forum	19	April 19, 2017 04:46
Is it possible to use divergence in the source term of an scalar transport equation?	jannnesss	CFX	0	January 8, 2010 19:53
SIMPLE and energy equation convergence	Fabio	Main CFD Forum	0	June 1, 2007 06:06
bouyancy term in epsilon equation	Michael	Main CFD Forum	1	June 25, 1999 10:20
Why FVM for high-Re flows?	Zhong Lei	Main CFD Forum	23	May 14, 1999 13:22

December 12, 2011, 13:38		#2
cfdnewbie Senior Member cfdnewbie Join Date: Mar 2010 Posts: 557 Rep Power: 19	pseudospectrally in physical space is out of the question, I guess?

December 13, 2011, 02:53		#3
nimav New Member nima vaziri Join Date: Aug 2011 Posts: 5 Rep Power: 13	I think you must use a transformation method first and compute parameters on that.

December 13, 2011, 17:45		#5
cfdnewbie Senior Member cfdnewbie Join Date: Mar 2010 Posts: 557 Rep Power: 19	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....