Orszag 2/3 rule

Eifoehn4 · July 16, 2012, 09:58

Hi,

I have a question about dealaising a Fourier-Pseudospectral-Code for the 3D incompressible Navier-Stokes-Equation by using the Orszag 2/3-Rule.

Does the rule refer to every single wavenumber direction

?
Or does it refer to the spherical wavenumber $|k|=\sqrt{k_x^2+k_y^2+k_z^2}$ ?

Thanks,...

cfdnewbie · July 17, 2012, 08:51

From the theoretical derivation of the 2/3 rule, it should refer to kx, ky, kz.

Eifoehn4 · July 17, 2012, 13:30

That would mean i have to use such a filter:

- 2D example
- high modes are concentrated in the middle after using FFT (FFTW)

(like a cross)

$D_{Filter}=\begin{pmatrix} 1 & 1 & 1 & 0 & 0 & 0 & 1 & 1 & 1\\ 1 & 1 & 1 & 0 & 0 & 0 & 1 & 1 & 1\\ 1 & 1 & 1 & 0 & 0 & 0 & 1 & 1 & 1\\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\ 1 & 1 & 1 & 0 & 0 & 0 & 1 & 1 & 1\\ 1 & 1 & 1 & 0 & 0 & 0 & 1 & 1 & 1\\ 1 & 1 & 1 & 0 & 0 & 0 & 1 & 1 & 1\\ \end{pmatrix}$

Instead of:

(like a circle)

$D_{Filter}=\begin{pmatrix} 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1\\ 1 & 1 & 1 & 0 & 0 & 0 & 1 & 1 & 1\\ 1 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 1\\ 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1\\ 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1\\ 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1\\ 1 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 1\\ 1 & 1 & 1 & 0 & 0 & 0 & 1 & 1 & 1\\ 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1\\ \end{pmatrix}$

Right?

July 16, 2012, 09:58	Orszag 2/3 rule	#1
Eifoehn4 Senior Member - Join Date: Jul 2012 Location: Germany Posts: 184 Rep Power: 13	Hi, I have a question about dealaising a Fourier-Pseudospectral-Code for the 3D incompressible Navier-Stokes-Equation by using the Orszag 2/3-Rule. Does the rule refer to every single wavenumber direction ? Or does it refer to the spherical wavenumber $\|k\|=\sqrt{k_x^2+k_y^2+k_z^2}$ ? Thanks,... Last edited by Eifoehn4; July 17, 2012 at 05:07.

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July 17, 2012, 08:51		#2
cfdnewbie Senior Member cfdnewbie Join Date: Mar 2010 Posts: 557 Rep Power: 20	From the theoretical derivation of the 2/3 rule, it should refer to kx, ky, kz.

July 17, 2012, 13:30		#3
Eifoehn4 Senior Member - Join Date: Jul 2012 Location: Germany Posts: 184 Rep Power: 13	That would mean i have to use such a filter: - 2D example - high modes are concentrated in the middle after using FFT (FFTW) (like a cross) $D_{Filter}=\begin{pmatrix} 1 & 1 & 1 & 0 & 0 & 0 & 1 & 1 & 1\\ 1 & 1 & 1 & 0 & 0 & 0 & 1 & 1 & 1\\ 1 & 1 & 1 & 0 & 0 & 0 & 1 & 1 & 1\\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\ 1 & 1 & 1 & 0 & 0 & 0 & 1 & 1 & 1\\ 1 & 1 & 1 & 0 & 0 & 0 & 1 & 1 & 1\\ 1 & 1 & 1 & 0 & 0 & 0 & 1 & 1 & 1\\ \end{pmatrix}$ Instead of: (like a circle) $D_{Filter}=\begin{pmatrix} 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1\\ 1 & 1 & 1 & 0 & 0 & 0 & 1 & 1 & 1\\ 1 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 1\\ 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1\\ 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1\\ 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1\\ 1 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 1\\ 1 & 1 & 1 & 0 & 0 & 0 & 1 & 1 & 1\\ 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1\\ \end{pmatrix}$ Right?