Sorry that language is a little convoluted I think, I'll try to rephrase.

On the one hand is the argument that I choose resolved fluctuations based on what I am modeling, On the other hand, is the idea that this gives me a metric where atleast x% of proper DNS behaviour is resolved. So my metric must naturally converge to how I define things in that DNS limit, not in what I am modeling in the intermediate level, right? And on the DNS level, there is no modelled component, just the total velocity with all its intricacies. But we are bifurcating things at that level into mean and fluctuations, and then coming backwards. Where does this differentiation occur between mean and fluctuation?

From a hand-wavy point of view it is fine for judging adequacy ... But what is the grounding argument behind the choice between the full field vs a representation of its oscillation..? Does that question make sense?

Thinking in terms of the stress tensor might lead somewhere...

Well, NSE are quite adequate in representing the mean features of the flow. One may argue that there is feedback from smaller-to-bigger scales (backscattering), which there is, but in principle such feedback is ignored in industrial CFD. Judging adequacy is loosely based in integral principles for a certain flow archetype, rather than an exact evaluation of the fields obtained. That is, you go and check mean + modelled features and compare these with integral quantities (Strouhal, Nusselt, correlations, integral times). A more "serious" verification may involve checking the turbulence cascade via energy power spectrum, and see whether LES is at least representing accurate decay in the phase space.

It is difficult to reconstruct a DNS signal from LES

I guess that's part of your question

You mean, LES+no model + "fine enough" grid will not approach DNS?

Right, I think we discussed something on these lines some time ago, about how to choose domain for FFT.

In reality, no. Only in very special cases. Some models (Smagorinsky dynamic) break down in the vicinity of walls, and some others may have inconsistencies. One of the main criticisms for iLES is exactly the difficulty to demonstrate that one can "reconstruct" DNS signals back. I've seen LES-to-DNS reconstructions via inverse deconvolution, but man, that's tricky

You can do a test, try to do a channel flow at Re_tau = 180, and set up any LES model. use a 200³ grid on a 2pi x pi x 1 domain (DNS theoretically) and you'll still see the model producing non-zero turbulence fluxes

Dammm and here I was thinking that in moving from RANS to LES I was going for an inherently more accurate formulation (because it will asymptotically go to DNS)

There are many intricacies when you pass from paper to algorithm to computation, that add to the problem. This also shows why the rule of Pope is so, "simple", (more of a guesstimation), because any step further in refining such metric involves also a deep revision of the code /methodology you're using

Bahhh, accuracy is used very loosely in CFD

Models do not define accuracy

I've gotten more "accurate" solutions with under-resolved DNS than with dynamicKEqn

Okay..Define an under resolved DNS, if its not a no model LES

Of course I assume it to be doable within openfoam.

This is a matter of taste, for me, "no model" LES is a pseudonim for "implicit" LES. That is, carefully crafted schemes that produce "meaningful" artificial viscosity. uDNS is DNS on a grid not appropriate for DNS.

Some other authors like to call "no model" LES, instead of uDNS. For me the former name is paradoxical when used in the context of under-resolved grids.

So would your DNS (u or not) is.... Laminar flow on very fine grid and very fine dt? Sorry if it sounds dumb, because you're telling me so many things are not-DNS, so I am wondering what approach is, grid adequacy apart. Simple central differencing, laminar flow on dense grid?

Maybe with some upwind bias

DNS doesnt mean laminar, the word 'laminar' in turbulenceProperties is an unfortunate mishap "imported" from Fluent. The correct word in FOAM should be 'noModel'. DNS is normally conducted with CD schemes, yes.

"on fine enough grids" not necessarily "dense"

Sooner or later Foundation will get around to changing this, I suppose.

Not really important

Agreed.. Also, thanks :)

if I'm only interested in averaged results, is there any point in running URANS/transient and then average? the case is inherently unsteady (so steady-state doesn't converge) but quantities I'm interested in converge quite nicely

probably yes because your solution still oscillate with circumferential position of your impeller. Maybe not by much but then that depends on you. foam-extend has a mixingPlane that would do best in this situation but it's tricky to make work

what about other cases, for example, drag of a blunt body or similar?