Cavity flow for Re>1000

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cwinant
Posts: 17
Joined: Wed Apr 08, 2020 9:54 pm

Cavity flow for Re>1000

Post by cwinant » Mon Jun 22, 2020 10:14 pm

Hi all

I have reproduced the results described in:
https://www.code-saturne.org/cms/sites/ ... y-flow.pdf
As in that document I find that the results of the simulation agree quite well with results published by Ghia et al 1982 for Re=1000. I found the same when I reduced the Reynolds number to 100 (by increasing mu to 0.01) (Ghia's paer includes tabulated balues for Re= 100, 1000, 5000 and 10000). When I tried Reynolds numbers of 5000 and 10000, I see significant differences between the code-saturne simulations and Ghia's results, as well as between code_saturne and a 2d finite element code (that agrees well with Ghia). I have tried increasing the resolution to 129x129 (the resolution used in the Ghia study), and I have tried running the simulation for longer than the 400 cycles indicated in the tutorial notes. Neither change has any effect on the results.

I am clearly doing something wrong, and would be grateful for suggestions.

The attached tarball includes the Grid129x129 file and the .xml files for each case, I have also included a plot of my results, in the same format as in the tutorial.
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cmp_CS_Ghia.tar.gz
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Yvan Fournier
Posts: 2990
Joined: Mon Feb 20, 2012 3:25 pm

Re: Cavity flow for Re>1000

Post by Yvan Fournier » Mon Jun 22, 2020 11:08 pm

Hello,

Did you adapt the time step (or even better, check the time step sensitivity) ?

Also, did you try refining the mesh ?

I will move this post back into the "usage" section,where it should be.

Best regards,

Yvan

cwinant
Posts: 17
Joined: Wed Apr 08, 2020 9:54 pm

Re: Cavity flow for Re>1000

Post by cwinant » Fri Jun 26, 2020 10:58 pm

Hi All

I have considered eight new cases: four with a grid of 129 on side and four based on a grid of 200 on side. For each resolution I have run the cavity calculation for mu=0.0002, with four values of the time increment: 0.01,0.02,0.05 and 0.1. The last value is the one used in the Cavity tutorial for a Reynolds number of 1000 and a grid of 50 on side.

The results are presented in two pairs of plots, one for each grid resolution: cmpCSGhiaRe5000129.png and cmpCSGhiaRe5000200.png. Each pair is shown following the pattern chosen in the code-saturne tutorial titled Shear Driven Cavity Flow on page 46, but with the symbols now representing the Ghia results for Re=5000.

There are two conclusions: the first is that using a time step smaller than 0.1 make surprisingly little difference to the results. Perhaps this is because the flow is steady-state? It is unclear to me what code-saturne uses to initialize the calculation: is it the initial value given in the setup.xml file, or a stokes calculation (the name STOKES appears in the listing).

The second conclusion is that refining the grid makes a small improvement, but with the means at my disposal, I can't say whether the code-saturne results would improve even further. The original Ghia et al., calculations were made on a 129-square grid.

To be clear the issue here is that at Reynolds numbers of 1000 or more, the vorticity near the center of either the plots in any pair should be constant (this was shown by Batchelor, 1956). So away from the boundary layers, u should behave like a linear function of y, and v like a linear function of x. In this regard code-saturne seems to be better at Re=1000 than 5000.

Of course I may be totally missing something, in which case many apologies
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Yvan Fournier
Posts: 2990
Joined: Mon Feb 20, 2012 3:25 pm

Re: Cavity flow for Re>1000

Post by Yvan Fournier » Sat Jun 27, 2020 1:19 pm

Hello,

Thanks for the feedback. I'll give it a look, but will also suggest some colleagues who have run quite a few tests on cavity variants while working on different new algorithms (CDO and steady) to take a look, as they may have more ideas than I do for this.

The main lid-driven cavity test case we use in our validation suite (similar to the one from the tutorial) uses a Reynlods number of 1000, and uses the data from the following article :

@article{Botella98,
author = "Botella, O. and Peyret, R.",
journal = "Computers \& Fluids, Vol. 27, No 4, pp. 421-433",
title = "Benchmark spectral results on the lid-driven cavity flow",
year = "1998"
}

But I do not think we usually test it at higher Reynolds (and for many higher Reynolds numbers, we use turbulence models, where turbulent viscosity will usually have a higher impact than the molecular viscosity, so the effects you observe might not be visible).

For both faster convergence and comparison purposes, it may be intersting to experiment also with the pseudo-steady time schemes.

Best regards,

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