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Orszag 2/3 rule

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Old   July 16, 2012, 09:58
Default Orszag 2/3 rule
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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,...

Last edited by Eifoehn4; July 17, 2012 at 05:07.
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Old   July 17, 2012, 08:51
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From the theoretical derivation of the 2/3 rule, it should refer to kx, ky, kz.
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Old   July 17, 2012, 13:30
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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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