About the accuracy of the DNS study in the streamwise flow direction.

[X. G. Zhou]

Dear community, 

I'm X.G. Zhou, a new comer to Nek5000 and spectral element method. 

I have a question on the numerical accuracy of the DNS stduy in the streamwise direction. 

Just think about a DNS of the turbulent channel flow, and $x$ is the streamwise direction, $y$ denotes the wall normal direction, and $z$ stands for the spanwise direction. 

Current calculations have found that it seems that the spanwise spectra (kz-Euu, kz-Evv, ...) are easier to achieve the spectral accuracy than the streamwise spectra (kx-Euu, kx-Evv, ...). 

We want to know:

1. The non-uniform GLL grid points are adopted in Nek5000 to robust the stability. However, did Nek5000 use methods such as SUPG in finite element method to further enhance the numerical stability, making it difficult to achieve spectral accuracy in the streamwise direction?
2. What are the suggestions or opinions on achieving spectral accuracy in the direction in the streamwise diection with Nek5000 for DNS?
   

Any suggestion would be appreciated, thank you. 

Regards,

X.G. Zhou. 

[Fischer, Paul]

There is no supg, so no anisotropic diffusion.

Perhaps try increasing the resolution in the streamwise direction?

hth,

Paul

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From: nek...@googlegroups.com <nek...@googlegroups.com> on behalf of X. G. Zhou <starlig...@163.com>
Sent: Saturday, July 13, 2024 4:35 AM
To: Nek5000 <nek...@googlegroups.com>
Subject: [nek5000] About the accuracy of the DNS study in the streamwise flow direction.

 

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[Tony Zahtila]

Dear X.G,

We wrote a paper on the topic of grid refinement for collection of accurate statistics in spectral element method simulations,

https://www.sciencedirect.com/science/article/abs/pii/S0045793022003371

Please feel free to write to us with any questions. 

Tony 

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[Fischer, Paul]

Thanks Tony - this is very helpful!

Paul

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From: nek...@googlegroups.com <nek...@googlegroups.com> on behalf of Tony Zahtila <tonyz...@gmail.com>
Sent: Saturday, July 13, 2024 11:21 AM
To: X. G. Zhou <starlig...@163.com>
Cc: Nek5000 <nek...@googlegroups.com>
Subject: Re: [nek5000] About the accuracy of the DNS study in the streamwise flow direction.

 

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[X. G. Zhou]

Thanks for your paper prof. Tony, we will study it in detail :D

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[Mohamed El Mellouki]

attached a link to DNS study performed using NEK5000, i think it may help you a little bit

https://www.sciencedirect.com/science/article/pii/S0017931022002150

[nadeem...@cantab.net]

Thanks, Tony, for this paper.

 

In the 2^nd paragraph of the Introduction it says:

 

“However, although high-order accuracy is achieved within spectral macro-elements, at the element interfaces, only 𝐶0 continuity is enforced. This has two important consequences. The first consequence may be visualization of the fluid field with an imprint of the mesh, where element boundaries are visible. A second consequence is that fluxes of derivative quantities, such as viscous dissipation, are not guaranteed to be continuous between elements.”

 

How serious are these errors? Both consequences are undesirable, and I want to ask if there are ways to reduce/eliminate them?

 

For example, when I run the example case of the turbJet I can see the fluid field imprints in my visualizations – especially in the vorticity field (which is the curl (essentially the spatial derivatives) of the velocity field). The example case uses lx1=8; so would lx1=10 or lx1=12 reduce the mesh imprint problem and/or the discontinuity in the derivative based fluxes?

 

To use lx1=10 or 12 with the same mesh that is given, is it a simple matter of recompiling (using ./makenek) with lx1=10 (or 12) in SIZE [e.g. line 13: parameter (lx1=10)]? Or do you have to generate a new mesh entirely, or something else?

 

Thank you

Nadeem

 

 

From: nek...@googlegroups.com <nek...@googlegroups.com> on behalf of Tony Zahtila <tonyz...@gmail.com>
Date: Saturday, July 13, 2024 at 11:21 AM
To: X. G. Zhou <starlig...@163.com>
Cc: Nek5000 <nek...@googlegroups.com>
Subject: Re: [nek5000] About the accuracy of the DNS study in the streamwise flow direction.

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[Catherine Mavriplis]

Yes to all your questions except the last! 

On Jul 15, 2024, at 6:09 PM, nadeem...@cantab.net wrote:



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[nadeem...@cantab.net]

So, I interpret that as:

 

1. The example case uses lx1=8; so, would lx1=10 or lx1=12 reduce the mesh imprint problem and/or the discontinuity in the derivative based fluxes?  YES

 

2. To use lx1=10 or 12 with the same mesh that is given, is it a simple matter of recompiling (using ./makenek) with lx1=10 (or 12) in SIZE [e.g. line 13: parameter (lx1=10)]?  YES

 

3. Or do you have to generate a new mesh entirely, or something else?  NO

 

?

Thanks

Nadeem

 

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[Catherine Mavriplis]

Correct! 
Assuming your grid is good enough to start with. Of course it’s cheaper to increase the number of elements vs the polynomial order but for a quick check on your part (less work) it’s easier to just increase lx1 

On Jul 15, 2024, at 8:02 PM, nadeem...@cantab.net wrote:



[X. G. Zhou]

Thanks for your paper, Mohamedel :)

Zhou.