Given an explicit LES model τij a usual problem in postprocessing is the
evaluation of the explicit subgrid scale contribution, in other words to add or
not its contribution to the total predicted Reynolds stress. The advantages
of a zero-mean LES model could be explored. A simple approach could be
the following. Let us define the associated zero-mean LES model τ ∗ij as
τ ∗ij = λ(τij− < τij >)
where the brackets stand for the Reynolds average and λ is an appropriate
RANS independent factor. Could we discuss a little all that?
Let me add that λ could be chosen in order to reinforce for τ ∗ij
the same mean dissipation of τij
λ =< τij \bar(sij) >/(< τij\bar(sij )> − < τij >< \bar(sij)>)
where the overline stand for the LES average ans sij is the strain rate tensor.
In order to further discuss in a simple way, I would add the practical case of the solution of the Burgers equation in the 1D case, assuming that =U(x) do not vanish.
Recalling that
u(x,t) = U(x)+u'(x,t)
= u_bar(x,t)+u''(x,t)
we have:
d u_bar/dt + 0.5* d u_bar^2/dx -ni*d^2 u_bar/dx^2 = 0.5*d [u_bar^2-(u^2)_bar]/dx (LES)
d U^2/dx -2*ni*d^2 U/dx^2= d (U^2-)/dx (RANS)
where the proper closure model should be provided for the two RHS.
Dear Filippo
A good starting point. It could be interesting to test a simple LES model \tauij for forced Burgers 1D compared to the equivalent zero-mean LES model \tau*ij in order to see the difference. A detailed study of subgrid Burgers modeling has been conducted by Love, JFM 1980.
For people interested to this problem let me also suggest as a very
simple LES model the Wong-Lilly model. In the spirit of the question
what is important is the difference between it and the associated zero
mean model.
Dear Massimo,
I suppose you are talking about the scaling formulation proposed here
Article A comparison of two dynamic subgrid closure methods for turb...
I personally tested this SGS model in past years, both in channel flows (non vanishing mean flow) and on problems without a mean flow like here
Article A finite volume dynamic large-eddy simulation method for buo...
Article A new development of the dynamic procedure in large-eddy sim...
However, I always modified the dynamic procedure into the integral-based one.
Do you think some of these LES solutions can help you in your question?
Dear Filippo
Yes. In my opinion the WLM, both as such or in your dynamic version, is perfect for basic LES explorations. In my opinion it captures the essential, and scales correctly in the inertial region consistently with Kolmogorov. I recall that for this question the "essential" is the following: We would like in LES that
=
and a simple and pragmatic way is to impose that is
=0
Another point concerns Burgers turbulence. I must confess my inexperience.
Chaos develops in the Burgers' equation only when stochastically forced?
Many thanks Filippo for your activity and your enthusiasm.
Dear Massimo
yes, Burgers can be used also with forcing.
it produces a solution similar to the homogeneous isotropic decadying turbulence, only with a different slope of the inertial range.
From the point of view of the filtering approach a more theoretically founded analysis of the problem could be the following. More than proposing an empirical zero-mean model we could analyze the properties of a zero-mean filter given by
F*=F+E-EF
where E is the Reynolds average.
Obviously EF*= E. It was proposed by Yoshizawa a lot of time ago. I tried to publish something on that in the past, but without success.
Massimo Germano
Dear professor Germano,
For your information, we published a paper in JFM (703:1-28, 2012) and proposed the constrained large-eddy simulation for wall-bounded turbulence a few years ago. In that paper, we believed that the mean part of the subgrid-scale stress is more important for the mean statistics. The zero-mean fluctuating part was simply obtained through your dynamic process.
Dear Zhenhua
I know your paper. In my opinion represents the best hybrid Reynolds/DynamicLES formulation that I know. Your reference to the pioneering two part model of Schumann as regards the mean and the fluctuating part of a LES model is due: nothing new as always in what we do.
What I would like to see is a self constrained Reynolds/LES model, that does not rely on a RANS model, but is consistent with its own statistical values, the values that it produces. I think that the filtering approach is the best framework for that, and the Yoshizawa filter the best candidate for that.
I have added to my profile a preprint concerning the filtering properties of the Yoshizawa filter. It was refused in the past for the publication, so be careful.
Dear Massimo,
I am a little confused. My question is where the action of these filters really appear.
I mean, I can see that from DNS data you can do an explicit filter operation and you can use any type of filter you want.
But:
- How this post-processing can be compared to a real LES solution where the filter is only implicitly acted on by the discretization?
- How the filter you mentioned can be practically introduce in a real LES solver?
best regards
Dear Filippo
Implicit LES are very difficult to manage theoretically. One way is to derive
the numerical implicit filter subtended by the discretisation, you are an expert of that. For the moment I will only consider explicit filtered equations, with a clear sepration of filtering and numerics.
The Yoshizawa filter does not produce a zero-mean explicit model. It suggests a zero-mean model as a first approximation. Practical introduction in a LES solver of an explicit model based on a Yoshizawa filter remains a real challenge.
Dear Massimo,
ok, now I am sure you are referring to the theory for explicit filtering.
I would add that that means not only filtering explicitly the equations but also the BCs. Furthermore, in a dynamic procedure it should be carefully used some congruent test-filtering.
Very challenging task ...
Please, could somebody tell me if the equation (19) of the attached paper is correct ? It says that the LES subgrid stress of the Yoshizawa filter Y associated to a generic filter F is composed by three contributions. The first is the statistical fluctuation of the original subgrid stress, the second the difference between the Reynolds stree and the resolved Reynolds stress, while the third is related to the statistical fluctuations of the original velocity.
If this relation is correct, it could be the starting point for a possible implementation of the Yoshizawa filter
Dear Massimo,
before trying to give any answer, I first had to go back to the Yoshizawa filter since I never worked on.
I tried to write the relations with other classic decompositons, are they correct? If yes I will go ahead to your document.
Dear Filippo
I have read your note, everything seems correct. But why to introduce
all these new fluctuations? In my opinion the only fluctuations that are useful are the statistical fluctuations, the other ones very often only complicates the problem.....
Dear Massimo
you wrote before this filter should be applied explicitly. I have no idea how to apply that to the term:
(u_bar u_bar)_bar
for the Yoshizawa filter.
I am trying to think about the meaning of u’’ in terms of the statistical fluctuation u’” to get more insight.
At present I don’t have the original Yoshizawa paper on PoF and there is only a short paragraph on Sagaut book.
Dear Filippo
The term that you cite does not appear explicitly in my operational analysis of the Yoshizawa filter. It appears in the Leonard decomposition.
I have sent to you my private copy of the Yoshizawa paper. Frankly speaking I really hope that papers like this one could be open free for everybody.
- Badges
- Science topic