[lucamirtanini]

Hi,
I have several question about the LES method:
1. I ve read several documents, also here , that Smagorinsky was the inventor of the LES method. Is this true?
I tried to read the paper of Smagorinsky (it is very complicated to me), I did not understand if the filter that He used is implicit or explicit.
I read that the implicit filter was the first one used. Is it true?

2. In a presentation some time ago I think to have understood that the implicit filter can be somehow associated to a top hat filter having extended in the interval from - to + (where is the grid). Is this true?

Thank you

[sbaffini]

Smagorinsky was probably the first to apply a certain approach in a certain context. But the approach was not new as artificial viscosities already existed as a mean to stabilize inviscid computations (especially in relation to shocks).

Smagorinsky and others were among the first to apply it for what would be later known as implicitly filtered LES. So, in this regard yes, Smagorinsky was the first. Yet, the exact first one, I think, is a blurred concept when there are several contributors in a narrow time window and the idea is not original per se.

It is only later that the filtering concept was introduced as a way to formalize LES and certain early implementations.

Unfortunately, in the years, this has been erroneously digested by the community as an analogous of the RANS formalism, disconnected from the implementation.

As soon you realize that implicitly filtered LES is just a plain code working on an under-resolved grid, possybly with a SGS model, you also see how a single LES formalism can't be correct for whatever code or method you use. Because all the interesting stuff happens near the grid cutoff, where all the methods mostly differ and impact a simulation.

So, no, there is no single, explicit, filter that can be related to all the implicitly filtered LES approaches. Even the top hat alone is only partially related to some practical approaches, as it totally lacks any reference to the grid.

[lucamirtanini]

Thank you for your answer. Do Smagorinsky use a implicit filter? I didn't noticed any mension about filter shapes.

Originally Posted by sbaffini

So, no, there is no single, explicit, filter that can be related to all the implicitly filtered LES approaches. Even the top hat alone is only partially related to some practical approaches, as it totally lacks any reference to the grid.

If we do not consider the effect of the SGS model or the truncation error of the numerical method used, the implicit method, for this can be related to the top hat having a cutoff at .?

[sbaffini]

I haven't read the Smagorinsky paper in a while but no, he doesn't use any explicit filter, just his famous SGS model.

A perfect numerical method alone isn't enough to completely specify the functional space where you seek for an LES solution. Imagine just how many variants there are of spectral methods.

However, for a straight spectral collocation method with a Fourier series expansion and proper dealiasing, the resulting implicit LES filter is a spectral cutoff. So not a top hat, not at all.

EDIT: Note that, actually, every dealiased spectral method does, in fact, imply a properly defined spectral cut off. Provided that you actually use the correct spectrum representation for the method.

[FMDenaro]

Originally Posted by lucamirtanini

Hi,
I have several question about the LES method:
1. I ve read several documents, also here , that Smagorinsky was the inventor of the LES method. Is this true?
I tried to read the paper of Smagorinsky (it is very complicated to me), I did not understand if the filter that He used is implicit or explicit.
I read that the implicit filter was the first one used. Is it true?

2. In a presentation some time ago I think to have understood that the implicit filter can be somehow associated to a top hat filter having extended in the interval from - to + (where is the grid). Is this true?

Thank you

1) Deardorff was also often referenced as one of the first scientists introducing to the world of the LES formulation. But do not forget that the concept of additional artificial viscosity at a certain lenght scale was introduced by Richtmyer at Los Alamos in 1948. At that time, the concept of filtering is only marginal and is not extended to the use of explicit filtering.
2) Only in some specific FD discretization or FV formulation that happens. But just think about spectral methods, they have nothing to do with the top-hat filtering.

[FMDenaro]

Originally Posted by lucamirtanini

If we do not consider the effect of the SGS model or the truncation error of the numerical method used, the implicit method, for this can be related to the top hat having a cutoff at .?

The cut-off you mentioned, is due to the grid size action, not to the scheme.

[sbaffini]

Originally Posted by FMDenaro

The cut-off you mentioned, is due to the grid size action, not to the scheme.

Nor, in case it was in doubt, it is due to the top-hat that, when relevant (i.e., finite volume scheme), has the first zero at twice the grid cut off wavenumber.

[FMDenaro]

Originally Posted by sbaffini

Nor, in case it was in doubt, it is due to the top-hat that, when relevant (i.e., finite volume scheme), has the first zero at twice the grid cut off wavenumber.

Yes, but I think that when one peron looks at the plot of the transfer function in any textbook (Sagaut to say one), he will be confused to see the continuous function represented also beyond the first zero. Thus, if you do not consider the superimposed action of the grid cut-off, you would really see on the filtered variable the effects of the negative sign in the transfer function. Conversely, that never happens in a real computation, at the least in using the main filter. A different example, wherein that effect can appear, is the test-filtered function.