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-   -   Orszag 2/3 rule (https://www.cfd-online.com/Forums/main/104795-orszag-2-3-rule.html)

Eifoehn4 July 16, 2012 09:58
Orszag 2/3 rule
 
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 k_x, k_y, k_z?
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?


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