Hi There,

I think you can help me here to understand filtering operation for LES.

There are some well known filter functions such as box, Gaussian, spectral, available in the literature to filter the NS/transport equation, in order to obtain the filtered version of the NS equation that would be solved.

My question is that, how does one know which filter function is used for filtering as the filtered NS equation remains always same? Even I could not see anything in the SGS part which says this one comes from this filter function.

Could you please help me here.

Thanks

SONAM

Nu_t = (Cs*Delta)^2 *|S| in an incompressible flow using the Smagorinsky model. The only information that this model, for example, has on the filter width is through the definition of Delta. The top-hat filter is usually defined as the cube-root of cell volume whilst other types of filter will define Delta in different ways.

Hi Andrew,

Thanks for your reply.

Do you know or any reference for the way Delta is defined in other filter functions?

Thanks

Actually this is not properly true.

First, in a formal approach (and also to be sure to remove some kind of error), the variables defined on your grid are not the filtered ones. So to obtain your filtered variables you should effectively perform the filtering. That is, in the formal approach the numerical variables are not the filtered ones.

However, the most common and inexpensive approach is to consider the numerical variables as the filtered ones. But this is a strong compromise with several issues on the behaviour of the solution.

For an interesting watch on this check the following paper:

Carati, Winckelmans, Jeanmart: On the modelling of the subgrid-scale and filtered-scale stress tensors in large-eddy simulation, J. Fluid Mech. (2001), vol. 441, pp. 119-138

Anyway, not considering this, we also have...

Second, even with a non-dynamic sgs model, the costant cs is formally dependent on the filter. That is, different filters will give you different cs. Actually the well known 0.17 value comes from the use of the sharp cut-off filter.

Anyway, with a more common dynamic sgs model, cs is directly dependent of the filter. That is, to compute the cs you have to filter some stuff.

Moreover, if you use a scale similar model (alone or combined with an eddy viscosity model) is the same model which requests some direct filtering.

This case is part of the more general case of the models which uses the deconvolution approach. This models actually require the approximate inversion of the filtering and so they require some direct filtering.

This is just to tell you about the more common cases in which you have to perform a direct filtering of the variables (to obtain double-filtered variables, triple-filtered and so on).

The ways in which the delta's value influences these and other computations are several but, in my knowledge, there is not a dependence of it's value from the kind of filter used. The only dependence that i knows is that of the grid. That is, the grid has some influence on the value of delta.

Dear Paolo,

Many thanks for your helpful explanation on this. I will get the JFM paper and read to learn more on this aspect.

SONAM