[LES] How do Reynolds stresses exist in no model simulations?
 

Hello,

As I studied the concept of LES and SGS models, the Reynolds stresses are a part of the SGS stresses and are modeled by SGS model.

But how do they exist and plotted in simulations where no SGS model used?(implicit LES)
Regards

In ILES they are simply disregarded in the computation. It is supposed that the local truncation error acts as a model for them.

Tahnk you dear Prof.

In the following figure, the dashed-x plots (---x---x---x---) are the Reynolds stresses of a no model simulation. They also have bigger values than others!

You mean that all of them are caused by truncation errors?

Then why doesn't this error have a significant effect on the simulations with a SGS model?
https://s16.picofile.com/file/842217...121_091716.jpg

I should look at the details of the paper but, in general, what you typically see in these sort of plots is related to the solved reynolds stresses, which you can compute from any unsteady computation. Basically, they are computed as if the computation was a DNS. Because DNS and ILES actually solve the same continuous equations.

Thank you for your reply.
What I mean, is that while the Reynolds stresses are appeared and defined only when we use filtered or averaged equations, then I suppose that it does not have a meaning to have them in DNS or ILES.

Again, without the details of the paper it is impossible to know what those terms are but, why you think so? Can't I take, for example, a time average of any unsteady field u? Let's call it u_avg. Can't then I compute the instantaneous fluctuation u' = u - u_avg? Can't then I compute the average of the squared fluctuation (u' * u')_avg?

That's it, it makes total sense. How do you think people compare RANS models to DNS results if they can't compute such averages?

If you read some pure DNS paper you will find that there are a lot of such averages.

EDIT: of course, these terms are not, explicitly, part of the equations you are solving in DNS or ILES but, besides comparisons with models, they also have a relevant fluid dynamic role, that's another reason people want to look at them.

Paolo addressed the correct answer, what you see are the RMS evaluated from the time-averaged LES velocity field. Of course, they are not exactly the same fluctuations one would get from the DNS field.