[Nek5000-users] Spectral coefficients for velocity

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

Hi Nicolas,
Thanks a lot for your help.
I wanted to compute spectral coefficients in NEK5000.

Andrey

2016-05-25 17:06 GMT+02:00 <nek5000-users at lists.mcs.anl.gov>:

> Hi Andrey,
>
> I don't know if you got an answer yet but here are my suggestions.
>
> If you are asking about the theory behind spectral transforms, I suggest
> that you look at appendix B in the book "High-Order Methods for
> Incompressible Fluid Flow" by Fischer, Deville and Mund. In particular,
> Section B.3.1 gives the formula for the spectral coefficients uh_k
>
> uh_k = 1/gamma_k \int_-1^1 w(x) u(x) p_k(x) dx
>
> where gamma_k=||p_k||^2 is the discrete norm and w(x) is the weight
> function, both of them associated to polynomial p_k.
>
> If you want to compute these coefficients in Nek5000, then you can look at
> the routine "local_err_est" in the file navier5.f. There, one goes to the
> Legendre space by using
>
> call tensr3(uh,nx,u,nx,Lj,Ljt,Ljt,w)
>
> where uh is the array of spectral elements and the operators Lj and Ljt
> are computed in the routine "build_legend_transform" (also in navier5.f)
> from the GLL points.
>
> I hope that helps.
>
> Best regards,
> Nicolas Offermans
>
>
> Quoting nek5000-users at lists.mcs.anl.gov:
>
> Hi Neks,
>>
>> Priviously, the parameters p101 and p103 have been discussed:
>>
>> "In each direction, on each element, the solution is represented as a
>> polynomial of degree N in the reference element (i.e., on the interval
>> [-1,1]).
>>
>> For any Nth-order polynomial there is a modal expansion of the form:
>>
>>    u(x) = \sum_k=0^N   uh_k phi_k(x)
>>
>> where   phi_0 = 1, phi_1 = x, and phi_k(x)=L_k(x) - L_{k-1} (x) for k > 1,
>> where L_k(x)=kth Legendre polynomial."
>>
>> How can I obtain these coefficients "uh_k" on the several elements?
>>
>> Thanks in advance for any suggestion,
>>
>> Andrey
>>
>
>
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