I am unfamiliar with PANS, too... However, I think that PANS should be seen in terms of statistical RANS/URANS formulations. TFLES has a different background as you can see also in the textbook of Sagaut.

Maybe PANS could be related to DES.

(TF)LES should converge to DNS for sufficiently fine resolution whereas RANS (parts) and related methods do not. URANS on a fine grid does never recover DNS for example.

Markus J. Kloker , indeed they nominally converge to different results. However both methods, I believe, also allow for the specification of a filter/averaging width. Refinement in this scenario should give a converged result for the chosen filter width etc.

I suppose my question is geared more towards instances where both methods employ an explicit definition for the filter/averaging width that is independent of the grid size. In such a scenario, are TFLES/PANS equivalent or do they yield different interpretations as Filippo Maria Denaro suggested? Also, do they admit different types of modeling strategies?

Ok, I can't stop making some practical comments.

To "Refinement in this scenario should give a converged result for the chosen filter width etc": Theoretically maybe, but not in numerical practice. If you do not fully resolve, without modelling, you have to be lucky for a simple physical behavior of the filtered/averaged part. Sometimes this holds, and/or the error is not significant, and modelling works well for some aspects of the flow.

"... admit different types of modelling strategies?": Formally yes in my view, but eventually it is always about how to view/sell the result. There are many LES modellings (SGS, or with explicit or implicit filtering, or with designing the truncation error to 'exactly' model the missing parts, or ...), and still, no one is definitely superior in numerical practice other than for the cases shown by the designers for which they know what to do. Also, the numerical implementation may play a role especially for compressible flow.

So you see, I am a DNS guy, and methods with less resolution need

be stable and can be more or less acceptable; the reasonings for the behavior varies with the method.

The late J. Ferziger (Stanford) once said: "FDs of second order with Smagorinsky is the best", at a time where higher order was used already, so he was convinced of the method he used as a well reputated specialist. The same was said by a German group one decade later, comparing 2nd and higher-order FDs in a LES journal paper. At the same it turned out however that switching-off the model yielded virtually the same results in the latter case. Oops, but this is not untypical.

Markus J. Kloker

as you addressed, the real understanding of the LES formulation need to consider the mixed effect of the numerical implicit filtering induced by the discretization as well as the practical implementation of the SGS model. I always used to check what happens with and without SGS models in the LES results.

Time-filtering has to be seen in the framework of the time-space discretization.

However, the hystory you reported since from the Ferziger's statement has several corner stones, such as the introduction of the dynamic procedure and more complex models than the simply eddy viscosity one.

I would also address that for many years the FD discretization and the FV discretization were confused in a terrible manner.

Filippo Maria Denaro it is these types of nuances in interpretation (e.g., FD vs FV and their respective link to point solutions versus local averages -- also recently highlighted by Hiroaki Nishikawa) that I am wondering about regarding TFLES and PANS. While the approaches' mechanics may seem similar at a surface level, their true differences often reside in the derivations and assumptions of the final equations and thus the closure models they should admit. Hoping anybody familiar with either or both method could help make their distinctions more evident.