[Nek5000-users] Filtering in the turbChannel, it that possible to use another filter, such as top-hat filter or Gaussian filter?

[nek5000-users at lists.mcs.anl.gov]

Hello Zhenrong,

fh is the 1D filter transformation matrix i.e. applied by kronecker product
transformation for 3D. So, for 3D case, is u_ijk is the velocity data at
each element, fh X fh X fh . u_ijk is the filtered variable, where X
denotes the kronecker multiplication and . denotes the matrix
multiplication. fht is the transpose of fh. You can look into the tens3d1()
routine in postpro.f for more details.

If you denote fh as *F* in matrix notation, then

*F* =* V D V^*-1, where *V *is the transformation matrix from nodal to
modal (Legendre) space, and V ^-1, the inverse transformation. Now, D is
the diagonal transfer function, which is referred to as diag in the
routine. You can design your diag() in any way you want. diag is a nx X nx
matrix, with non-zero diagonal. The first two entries of the diagonal needs
to be 1, probably to maintain C0 continuity of u (I need to check that),
and you can design the shape of the diagonal entries, in any way you want,
(.i.e. as a function of cut-off modes.) You can look into the appendix of
the paper https://aip.scitation.org/doi/pdf/10.1063/1.4994603 for details
regarding the filtering operation.

On Thu, Mar 15, 2018 at 6:20 AM, <nek5000-users at lists.mcs.anl.gov> wrote:

> Hello everyone,
>
> I have been working on the turbulent channel case for some time. But I am
> quite confused with the filtering technique in the turbChannel.usr.
> I understand well the filtering technique for improving stability (p101
> and p103), thanks to the discussion on the forum. However, is the same
> technique used in the build_1d_filt ? basically, partly removing the high
> wavenumber spectral in the expansion ?
>
> I have a question about transfer function also:
>
>       diag(nx-0) = 0.05
>       diag(nx-1) = 0.50
>       diag(nx-2) = 0.95
>
> It seems to me that the diag(:) would determine how much energy will be
> removed for the high wave number spectral? but what are the variables fh,
> fht in the subroutine
> build_1d_filt (fh,fht,diag,nx,nid) ?
>
> it seems quite difficult to apply the more traditional filters like
> top-hat filter or Gaussian filter in the Nek5000.
>
> Lastly, removing high wave number parts of Legendre expansion seems makes
> no sense physically. After all, the energy spectral of turbulence is
> represented in Fourier  series.
>
> Does anyone has any idea on these puzzles? Any discussion is greatly
> appreciated.
>
> Best regards
>
> Bien cordialement
>
> Zhenrong JING
>
> Doctorant (Doctor Candidate)
>
> LHEEA
>
> Ecole Centrale de Nantes
>
> 1 Rue de la Noë, 44321 Nantes, France
>
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