Energy pile-up at high wavenumbers

[Bkv-1915]

Dear Neko team,
Greetings.

I recently ran turbulent channelf flow simulation using NEKO example case for:
Re_tau = 180,
Re_bulk = 2800,
Box mesh: 36,36,36 elements
Polynomial order: 5
Dealias: true
time_order: 3

Please see the attached figure of turbulent kinetic enrgy spectra obtained after interpolation to equispaced grid.
There is an energy pile-up at high wavenumbers. Is it common in SEM formulation for the above polynomial order and elements combination to observe such energy pile-up? or There is something else going on. Please let me know if this could be solved only by adding a LES model.

[timofeymukha]

Hi @Bkv-1915
I just wanted to say that I converted the issue to a "discussion", this is our preferred place for Q&A.

[timofeymukha]

Regarding the spectrum, I just want to point out that the turb_channel example was never meant to meshed for getting good results. Rather we wanted to demonstrate the case setup and make it fast enough to run even on a consumer GPU.

But based on your description, you remeshed yourself, or?

I don't recall seeing such a build-up in the high frequencies for channels in my runs. I guess the expert on such matters is @pschlatt1 !

[pschlatt1]

Indeed, the mesh for the channel example is not a DNS mesh; and the tripping is not really perfect (yet).

However, some wiggles may persist at LES resolutions. For this, perhaps this paper could be an interesting read for what to expect with SEM: https://doi.org/10.1007/s00707-025-04607-z

[Bkv-1915]

I used genmeshbox with 36 elements to generate the box.nmsh. Further, in the user_mesh_scale subroutine in the turb_channel.f90, I replaced: el_in_y = 36
el_in_visc_lay = 6
viscous_layer = 0.0888889

[Shiyu-Sandy-Du]

Which tool did you use to do the interpolation?

[Bkv-1915]

I used PySEMtools first. And then the mapto1D available in the contrib. Both gave same spectrum.

[Shiyu-Sandy-Du]

did you eliminate the duplicated DOF on the element boundaries?

[Bkv-1915]

After interpolation, I extracted the correct 180x180x180 points discarding the overlapping values at the element boundaries.

[Shiyu-Sandy-Du]

I think in general you are doing the correct thing, but you need to interpolate your field onto a finer mesh to keep your resolution close to the element boundaries. You can find an example here https://github.com/Shiyu-Sandy-Du/neko_postprocessing/blob/32eec4bcad815060af20554ae08384231cbd8a50/GJP_paper/tgv/tgv_spectra.py, especially https://github.com/Shiyu-Sandy-Du/neko_postprocessing/blob/32eec4bcad815060af20554ae08384231cbd8a50/GJP_paper/tgv/tgv_spectra.py#L47-L53 for the number of points per element you needs for spectra calculation