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DNS - necessary Discretization

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Old   December 2, 2009, 09:50
Default DNS - necessary Discretization
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Volker Pawlik
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As far as I know it is necessary to use a central differencing type of discretization together with LES in order to avoid too much dissipation or numerical diffusion by Upwind schemes.

The same is valid for DNS if I remember the talks of several scientists at ERCOFTAC seminar. Now I am not sure anymore, after I have red the answer from Paolo Lampitella ( who mentioned that Upwind is ok too for natural convection flows ?

Is that the same for forced convection? Hence can I use Fluent's 3rd Order MUSCL?
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Old   December 3, 2009, 19:19
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Paolo Lampitella
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Hi Volker,

i'm glad that you question ERCOFTAC scientists because of me but at that time i was focusing on a different aspect (and i was also a little bit upset by someone saying that there is no DNS in Fluent) so i didn't cleared it too much.

When i say "even an upwind scheme is ok for the DNS but you need a VERY VERY VERY VERY fine grid" it is correct but it does not means that it is the most reasonable choice.

To be more specific, in DNS you have to be sure that all the relevant scales of the flow are CORRECTLY resolved. It is always possible, whatever the scheme is, but different schemes requires different resolutions to achieve this.

For example, in the DNS of the turbulent channel flow at Re_tau = 180 (on a domain 4 pi x 2 x 4/3 pi) a spectral method would require a grid of 128x129x128 points.

I performed the same test case with fluent on the same grid and the central 2nd order scheme. However the resolution was already insufficient because of the spatial discretization error. Probably a resolution 192x143x128 (or even higher, that's why i said it's pointless and insane) would have been required to properly perform a DNS with such a scheme.

With a resolution 6-8 times higher (hence several million cells) even an upwind scheme would probably give the same result of the 2nd order central scheme, that is a correct DNS. This is because both schemes would have the error concentrated in a spectral band which for such a grid is strongly affected by the physical viscous dissipation.

However this does not means that it is a feasible choice and a spectral method is the best candidate for DNS. In that post i was just making my point, that is: "not only Fluent can do DNS but it could do it even with a first order upwind". I gave for granted what DNS means, that is all the relevant scales need to be CORRECTLY resolved and not just resolved, which requires different resolutions according to the specific numerical method used.

In conclusion, if you have to perform a DNS, use a central scheme.

I hope i've been more clear about it
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