LES vs RANS
Please help me to understand the difference between LES and RANS.
I'd read some article in this forum, but I still confused about them. The point is this, 1) What is the exact difference between LES that uses box filter and RANS. 2) Is it true that RANS does not use time averaging? Then why it's named after ReynoldsAveraging? Thanks, YE 
Dear Ye;
Consider a turbulent flow doamin. RANS can only give a time averaged mean value for velocity field. since it is based on time averaging. in fact velocity field in this method is averaged over a time period of "t" which is considerably higher than time constant of velocity flucctuations. therefore within the period of "t" we have only a constant mean velocity and could not monitor its timedependent variations. for example, suppose that you can take successive pictures of velocity vector in a specific point of a turbulent flow during "t". clearly you can see that this velocity vector varies with the time. but if you use RANS you can only see a constant velocity vector which is an average of pictures you have already taken!. On the other hand, LES is based on filtering rather than averaging. in this method you need to choose a filter size first. all flow scales larger than the filter size specified will be exactly calculated and the scales smaller than filter size will be modeled. now consider the picture taking again. if you use LES you can clearly see the variation of velocity vector at that specific point. smaller the filter size, more exact the time variation resolution of velocity vector. as filter size reaches to zero, LES results turns to DNS ones. regards 
I'm also confused by RANS and LES.
If the grid size is the same, then what's the difference? It seems that everybody says that LES need higher resolution grid than RANS, but I did not get a criterion. 
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hope it helps teguh 
I think you have to read a course on turbulence modeling like (Moin, Sagaut, Poinsot ...) because it is more complex than what is exposed in the answers.
The main point is than RANS methods model all the turbulence spectrum and on the other hand, LES model only high frequency while computing the smaller ones (high frequency = small scales, which are supposed to be independent to the configuration of the flow). The choice of the mesh depends directly of the geometry, the Reynolds number etc ... and will drive the quality of the LES (with a given model of course). To conclude my post, the best advise I can give is to read a book !! 
Thanks for your explanation.
I guess the main problem for me is that for all the books I have read, "LESs grid must be better than RANs". But for some journal articles I have read, say, somebody use RANS with grid size A, while some others do LES with grid size B, and B >> A (order of magnitudes). I'm confused by this fact. So my question is that, is there any universal criterion about the grid size between LES and RANS, if the grid size is larger than a specific value, one should use RANS, if the grid size is smaller than a specific value, one should use LES? or the grid size is dependent on specific phenomenon, which allow the grid size for some LES simulations larger than (orders of magnitude) that for some RANS simulation? 
To answer your question, their is no universal criterion ! That's why I advise you to read interesting papers and books (I have forgotten Pope work also).
What you have to keep in mind is that for a theoretical view point, using LES require to use a mesh and a model that provide a cutoff in the inertial range of the turbulence spectrum. And most of the time (for practical applications), you just don't known these scales before doing the computation. That's why, you have to check the quality of your computation after doing the computation and check the sensitivity of the results to the resolution. From a practical point of view, most of the time when people do RANS computations and want to go further, the first idea is to use the same mesh (in order to keep a low cost computation and compare the results given with the same mesh). This is only due to practical reasons. Then, when you have a certain experience with LES, you can feel before computation the mesh resolution needed by the physics. But never forget to check if the resolution is sufficient. To conclude:  their is not any universal criterion, most of the time LES meshes are more fine that RANS meshes,  one have to check the quality of his mesh after the computation (Pope criterion for example),  finally, the quality of the mesh largely depends on the price you can pay for you computation: CPU !!!! Normally, a good LES model goes to 0 when the resolution is increase ... 
Thanks Florent for your explanation.
LES is the field I have never tried, but on my todo list in the near future. Surely I have to do more reading. Your post helps me a lot. From the limited reading I have done, I just have the impression that in journal articles, the authors just write they use LES because it's better than RANS, while they do not give explanation for the reason why the specific grid resolution they choose is fit for LES, while not RANS. From my limited knowledge now , I could not figure it out. Perhaps I have igored something. Thanks for kind post again. 
Thanks for everyone.
Actually, I've read an article in here. http://www.cfdonline.com/Forums/mai...dnsrans.html In this article, one said that For RANS, there is no time averaging (this is a common misunderstanding). The average is done  virtually  on a large number of the same experiment. Hence, as turbulence is chaotic, all the experiments are slightly different and RANS captures the mean. You are thus able to capture  if grid size is fine enough  some structures, for instance VonKarman street eddies. It makes me confused. If he is right, RANS do ensemble by itself? I mean, if I operate RANS one time, it done several time and output the ensembled one? If he is incorrect, please notice me which is correct. Thanks! 
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I recommend you to read the mathematical deduction of the RANS, it is simpler than you imagine and it can help you to understand it. It is much difficult LES's one. Hope it helps 
Thank you, Davahue!

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But in LES models, results have grid dependency. less sizes more accuracy. in very fine meshes your results can be reach to DNS results. in this situation you solve all of your flow instead of modelling. 
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The main problem for me now is , for a specific simulation, how to determine if the grid size I choose is suitable for RANS, LES, or DNS? The limited papers I have read just present the the grid and the method they choose, without giving the reasons why the grid they choose is suitable for LES or DNS. I need more reading to solve this issue. Surely I appreciate your help if you could give more idea. 
In fact, the mathematic equations don't know if they are RANS or LES.
Actually, the equations are same to some extend! Imagine you use a same uniform mesh to do two simulations, one URANS with mixing length model and with the Lm chosen to be Cs*dx, and the other LES, with Smagorinsky model. You should get exact same results. 
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Often this aspect leads to confusion... URANS and LES equations can be quite similar in the appearence. The key is in the way in which you model the unresolved terms: it is different. In URANS the unresolved part is related to a time averaging field while in LES is related to a spatial filtering. Consequently, is the model that creates the difference between LES and URANS, and the resolved fields have different meaning. 
Although the physics of RANS and LES are different (as explained by Florent), the equations are basically the same. The Reynolds stresses are simply replaced by the SGS stresses. Frohlich makes the following distinction between RANS and LES: If the turbulence model depends on the grid size, you have a LES model. If it does not, then you have a RANS model. You can see how people turned classic RANS turbulence models such as SpalartAllamaras or kwSST into DES models by simply introducing a mesh dependency. It does not make a lot of sense physically (again, because the physics of RANS is not the same as LES), but that is pretty elegant... :D
Fröhlich, Jochen, and Dominic von Terzi. "Hybrid LES/RANS methods for the simulation of turbulent flows." Progress in Aerospace Sciences 44.5 (2008): 349377. 
In my opinion LES and RANS equations can not be confused, simply because the RANS equations have no time derivative by definition.
Conversely URANS and LES can have a similar formulation, as a matter of fact URANS can be seen as a form of LES with timefiltering 
This is a very useful document in simple language provided by Prof. Lars Davidson. You can find several fundamental points related to turbulence and fluid dynamics in it, and ansewer of most of these questions were asked in the threat.
"Fluid mechanics, turbulent ﬂow and turbulence modeling"; you can download it from: http://www.tfd.chalmers.se/˜lada/MoF/lecture notes.html and http://www.tfd.chalmers.se/˜lada/comp turb model/lecture notes.html if you have problem in downloading it, send me an email. I 'll willingly send it to you. 
Hi sorry to bring this up as I have some queries regarding RANS and LES.
I just want to sum up the above dicsussion from what I have learnt. please correct me if i am wrong. RANS  The equations to be solved are obtained by applying a timeaveraging and reynolds decomposition technique on the NS equations.  Time averaging is to obtain the mean quantity over a certain time interval (i.e. timestep?).  I also read that RANS equations is also ensemble averaging, which is averaging over a large number of the same experiment? Why would the result be different if they are all numerical experiments (shouldn't the result be always the same)?  The unsteady RANS equations has a time dependent term (URANS and LES equations look almost identical actually). Does that mean that the resolved time dependent term give unsteady behaviour of the mean quantities? Does that also mean if my time interval (i.e. timestep?) goes very small, solving RANS would give a accurate time series result? 
LES
I also have a quesition on the grid size on LES. So the advantage of LES over DNS is that the grid size of LES can be larger, thus reducing computation time. LES equations are obtained by a spatial filter of the NS equations. The filter width should be larger than Kolmogorov scale (smallest length scale in the problem). LES is then performed on the filtered NS equations. The scales which are smaller than the filter width are modelled by a SubGrid Scale (SGS) model, and the effects are therefore accounted in the solution. If I understand LES correctly, filter width = grid size? I have started off with steady RANS and moved to unsteady simulation. Now, I am confused whether LES or URANS is giving me a correct representation. 
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