[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]

PS: Additionally, to answer your question "

*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*?"

-- Within each element, every variable is expanded as a function of
Legendre polynomials. Note, that higher the order (mode) of the polynomial
the more frequent oscillations it has. So in this sense, the highly
frequent oscillations are somewhat very similar to the frequency/wavenumber
in a classical Fourier series. A relation between mode and frequency would
be worth a derivation, but the idea is just as a function can be thought of
as a series of different frequency/wave number content sine/cosine
oscillations, similarly an aperiodic function can be thought of as a series
of Legendre polynomials of different modes. In this sense, removing/
filtering a highest modes of the transfer function, is equivalent to
removing the high frequency content of the flow variables. It would have a
similar effect in removing the high frequency content of a turbulent flow
field.

HTH,

Tanmoy


On Thu, Mar 15, 2018 at 10:58 AM, <nek5000-users at lists.mcs.anl.gov> wrote:

> 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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>>
>>
>
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