[Nek5000-users] Smoothness of the derivatives

Tue Jun 26 11:25:44 CDT 2018

Here is another, on how to filter in complex domains:

  1.  J.S. Mullen and P.F. Fischer, "Filtering techniques for complex geometry fluid flows" <http://www.mcs.anl.gov/~fischer/pubhtml/filter99.pdf> Comm. in Num. Meth. in Eng. 15 pp. 9-18 (1999).

It's basically a Helmholtz solve with a prescribed filter width.

Paul

________________________________
From: Nek5000-users <nek5000-users-bounces at lists.mcs.anl.gov> on behalf of nek5000-users at lists.mcs.anl.gov <nek5000-users at lists.mcs.anl.gov>
Sent: Tuesday, June 26, 2018 11:05:34 AM
To: nek5000-users at lists.mcs.anl.gov
Subject: Re: [Nek5000-users] Smoothness of the derivatives

Might be helpful:
https://www.ffi.no/no/Forskningen/totalforsvar/applied_fluid_mechanics/Documents/Post-processing_of_marginally_resolved_spectral_element_data.pdf

-----Original message-----
> From:nek5000-users at lists.mcs.anl.gov <nek5000-users at lists.mcs.anl.gov>
> Sent: Tuesday 26th June 2018 17:55
> To: nek5000-users at lists.mcs.anl.gov
> Subject: Re: [Nek5000-users] Smoothness of the derivatives
>
> Hi,
> as Stefan says, dssum does not do a filtering, it just makes sure that a
> certain quantity becomes continuous over element boundaries. It just
> sums up the values in the points with multiplicity>1.
>
> What you want is a filter that operates in nodal space, i.e. in physical
> space rather than in spectral space (nodal vs modal filter). The reason
> for the wiggles in the dissipation (and other statistics such as e.g.
> convection) is related to the specific continuity constraints by
> Nek5000, i.e. that only the function values (via dssum) are continuous,
> but not the derivatives. As I wrote earlier, this does not necessarily
> mean that the result is inaccurate, but it is just done in weak sense.
>
> So I guess what you want is to apply a filter in nodal space. I have not
> done that (recently), but I guess one could apply some controlled
> diffusion using the Helmholtz operator, to smoothen out the highest
> wavenumbers. Alternatively, you could quite easily implement an own
> nodal filter with a given transfer function using convolution
> (implemented then with a global scalar products between the function and
> specific weight functions).
>
> Philipp
>
> On 2018-06-26 16:03, nek5000-users at lists.mcs.anl.gov wrote:
> > Vlad,
> >
> > dssum will just sum up the shared points between elements - so no filtering. Note, currently there is no easy accessable mechanism in place to make your field smooth. As pointed out already modal filtering won't help.
> >
> > Cheers,
> > Stefan
> >
> > -----Original message-----
> >> From:nek5000-users at lists.mcs.anl.gov <nek5000-users at lists.mcs.anl.gov>
> >> Sent: Tuesday 26th June 2018 15:34
> >> To: nek5000-users at lists.mcs.anl.gov
> >> Subject: Re: [Nek5000-users] Smoothness of the derivatives
> >>
> >> Hi Philipp!
> >>
> >> Thank you for your answer!
> >>
> >> In fact I have almost the DNS resolution (the grid spacing is comparable with the Kolmogorov scale from the literature data) and rather small error in the dissipation field. But I want to see a smooth dissipation, so I really want to try to filter it.
> >>
> >> As I understood filtering procedure is in dssum subroutine. But looking at it didn't help to me to realize the process of the filtering.
> >> So could you explain, please, how can I choose the filter to be used? Cause now I think that my filter doesn't go beyond one element and it is the reason why it makes my dissipation field worse.
> >>
> >> Best regards,
> >> Vlad
> >>
> >>
> >>
> >>
> >>     Понедельник, 25 июня 2018, 23:05 +07:00 от nek5000-users at lists.mcs.anl.gov:
> >>
> >> Hi,
> >> I guess your only chance is to increase the resolution, which will make
> >> the discontinuities of the derivatives decrease. This is one of the
> >> characteristics of spectral methods; you will see a lack of resolution
> >> directly in the fields. Similar resolution with other methods will not
> >> give you more accurate results, but they appear nicer (smoother).
> >>
> >> Indeed, filtering does not help much. But if you want to try, make sure
> >> you use a filter that actually goes beyond one element (e.g. using a
> >> Laplace operator).
> >> Philipp
> >>
> >> On 2018-06-25 17:54, nek5000-users at lists.mcs.anl.gov <mailto:nek5000-users at lists.mcs.anl.gov> wrote:
> >>> Because I need to analyze the dissipation field
> >>>
> >>> понедельник, 25 июня 2018г., 20:58 +07:00 от
> >>> nek5000-users at lists.mcs.anl.gov <mailto:nek5000-users at lists.mcs.anl.gov> <mailto:nek5000-users at lists.mcs.anl.gov>:
> >>>
> >>>      This is correct, derivatives in SEM are not C0. Your code forces the
> >>>      field to be C0 but it does not make it smooth across elements.
> >>>      Typically filtering doesn’t help. Why do you want a smooth
> >>>      derivative field?
> >>>
> >>>
> >>>       > On 25 Jun 2018, at 12:55, "nek5000-users at lists.mcs.anl.gov <mailto:nek5000-users at lists.mcs.anl.gov>
> >>>      <mailto:nek5000-users at lists.mcs.anl.gov>"
> >>>      <nek5000-users at lists.mcs.anl.gov <mailto:nek5000-users at lists.mcs.anl.gov>
> >>>      <mailto:nek5000-users at lists.mcs.anl.gov>> wrote:
> >>>       >
> >>>       > Hi, Neks!
> >>>       >
> >>>       > 1) I am doing a DNS study of turbulent pipe jets and looking at
> >>>      turbulent kinetic energy budgets.
> >>>       >
> >>>       > I take derivatives via gradm1 subroutine, for example:
> >>>       >
> >>>       > call gradm1(uxdx,uxdy,uxdz,ux)
> >>>       >
> >>>       > After all, if I look at my dissipation field (via outpost), I see
> >>>      some wrong values on the surface between spectral elements.
> >>>       > I want to filter them using:
> >>>       >
> >>>       > call col2(uxdx,bm1,ntot)
> >>>       > call dssum(uxdx,lx1,ly1,lz1)
> >>>       > call col2(uxdx,binvm1,ntot)
> >>>       >
> >>>       > call dsavg(dxux)
> >>>       >
> >>>       > for every array. But conversely it leads to an increase in gaps.
> >>>      What am I doing wrong?
> >>>       >
> >>>       > 2) How does a filter-function in dssum look and how much points
> >>>      does it use for filtering? 
> >>>       >
> >>>       > Best regards,
> >>>       > Vlad.
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> >> Иващенко Владислав, ИТ СО РАН
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