Using filters on NS equation for LES
 

Hi,
I am vishwa and am very new to LES. I use fluent for my simulation. My first question is how does the filtering operation work when we talk about resolved scales and subgrid scales. In fluent, i read that the filtered variable

phi_bar(x) = integral_volume(phi(x')G(x,x')dx_prime

where is G is the filter function and in FlUENT

G = 1/V*integral_volume(phi(x')dx', x' belongs to V

What does it actually mean.. Can anyone of you explain with an example.?

Regards,
vishwa

If you are not using dynamic models and since you are not explicitly filtering your data it may not mean anything for your numerical simulation. For details of LES, have a look at Pope or Saigaut or browse through the forum for exhaustive discussions on LES filters.

What it actually means is that fluent does not perform any explicit filtering and assumes that the volume average per each cell (because the code is a finite volume solver) acts as an implicit filter, which is in fact the case. This means that the filtering is not actually performed but assumed to be the result of the Finite Volume discretization.

However, in fluent the truncation error is of the same order of any of the LES models implemented so the use of any model is, at least, questionable.

Actually, when the finite volume approach is used as an implicit filtering in a consistent way (of course it's not the fluent case), the subgrid-scale stress tensor is not in its usual form as written in the books. Moreover, the same dynamic procedure turns out to be different because of this.

Because all these parts are 2nd order terms (as the truncation error), in fluent nothing is actually done and the equations solved are the same of the URANS equations but with a different turbulent model (actually a very simple one).

So the biggest part of the job is up to you: choosing a proper grid, time step and a centered convective scheme. Then just pick up the LES turbulent model and go.