LES, DNS and RANS
Would anyone please explain the basic discrete difference among the above three. What I understant is, in LES the smaller scale (smaller than the grid) are modeled using some turbulence model like Smagorinsky model or dynamic model, DMM etc and NS equations are directly solved on the grid level. In DNS, these models are not used and the NS equations are directly solved with any turbulence closure. To resolve the smallest eddy, one needs a fine mesh. What about RANS ??? What is the meaning of time average NS equations..? Any type of comments will be appreicated. Sas.......

Re: LES, DNS and RANS
All your description is good concerning DNS or LES.
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. Now your question will be: what is the difference with LES in this case? As mentioned above, the structures you capture are a mean of the ones occuring in the corresponding set of experiments. You have only representative space and time scales of the mean representative turbulent structures. With LES (ideally a perfect code), you get an exact turbulent structure solved on the grid given the EXACT initial and boundary conditions imposed in the code, something you can never achieve for applied simulations as it is inconsistent with the chaotic nature of turbulence. The solution is to carry out several LES simulations for a range of initial and boundary conditions (essentially changing the turbulence phase) and doing the mean. Something which is much easier (conceptually) done by URANS (Unsteady RANS). There is no use making all the efforts one can see to implement LES code for applied CFD (Fluent, StarCD...), excepted for marketing as LES is really sexy today. I am really persuaded that the priority should be the reliability of the RANS solvers which are currently sold. LES remains a very good laboratory tool for model developments as the isotropic scales may be decoupled from the coherent ones. But this is another story. 
Re: LES, DNS and RANS
Thanx Guillaume! But, what I do not understand is that " To discuss RANS,what kind of experiments you are talking about? Are you talking about the numerical experiments? In case of numerical experiments, if the initial conditions are same, the the results will be same, no matter how many time you repeat the numerical experiments. Would you please clarify about RANS more discretely.. Thanks in advance... Sas..

Re: LES, DNS and RANS
Of course!
The discussion for RANS is purely statistics of real experiments. The averaging is done with statistics in mind. For benchmarking, the rigorous way should be carrying thousands of real experiment and doing the mean. In practice, people do that in a single stationary experiment as, because of ergodicity, the averaging becomes time averaging if the experiment is timeindependent. Is this timeindependent benchmarking sufficient to make full URANS reliable is another question but it does not damage the intrinsic concept of the method. 
Re: LES, DNS and RANS
thank a lot ! But how does RANS differ than LES ? What is discrete difference? Like DNS does not use subgrid model as are used in LES? What about RANS?? Regards, Sas

Re: LES, DNS and RANS
Hi,
From a discrete point of view, the essential difference between LES and (U)RANS is that RANS turbulent viscosity does not tend toward zero as cell size tends towards zero (or more reasonnably towards Kolmogorov length scale), contrary to the LES turbulent viscosity (assuming of course that RANS and LES models are based on Boussinesq hypothesis, which is often true). Hope this helps, Lionel 
Re: LES, DNS and RANS
Hi ! Thanks for response. But , in LES does eddy viscosity ever become zero? or tend to become zero. I think if the fluid is more turbulent, the eddy viscosity will be larger and vice versa in less turbulent flow, am I right??
Also would you please explain the difference between the method in which both (LES and RANS) are computed? Thank again, regards, Sas 
Re: LES, DNS and RANS
I assume that you want to know the difference from a technical point of view.
RANS is averaging, thus the turbulent fluctuation (Reynolds tensor) is modelled for all the scales at one node. LES is spatial filtering, thus only the turbulent fluctuation (Leonard tensor) below the filter size is modelled. All the scales larger than this size are considered as `perfectly' (or directly in the sense of DNS) solved. This is the reason why Lionel has said that the smaller the grid size the lower the eddy viscosity. In the limit case your filter is below the Kolmogorov scale (the smaller eddies existing in the turbulent field), you have nothing more to model. All the scales are resolved. You are doing DNS. Usually, people claim that the scheme order should be larger for LES than RANS. If one has to consider that LES is DNS of a fraction of the turbulent scales (the largest ones), it may be consistent. 
Re: LES, DNS and RANS
Thank you very much Guillaume and Lionel !! I got the point !! Sas.

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Hi,
I understood the main difference between LES and DNS, but I found something which in my opinion seems strange. On the attached image there is a paragraph from "Computational Methods for Fluid Dynamics", 3rd Edition, J.H. Ferziger, M. Meric, p. 277. On scheme of Fig. 9.3 largescale eddies are solved with LES, but why smallscale eddies seem to be solved with DNS. Should they be solved with some subgridscale models instead of DNS? Here I should say that I am quite new with CFD... Thank you in advanced. 
Bringing up a very old thread but I will answer anyways. What that figure is trying to demonstrate is that the very smallscale details of the flow can only be resolved by DNS since these would be considered as "subgrid" in your LES simulations. I think your confusion is that they are not saying that you solve the smallscale eddies with DNS and feed that in to your LES model, rather they are modelled by your subgridscale model.

I suggest also to see the sketch of DNS, LES, RANS spectra in the Sagaut book, it is useful ...

Thank you for your replies.
So largescale eddies are solved directly with NS equations in both LES and DNS cases. Smallscale eddies are firstly modelled with some subgrid model then solved with NS equations in LES. In DNS these ones (smallscale eddies) are solved directly with NS equations without modelling. Am I right? So where does the benefit of the computational effort in LES come from? How is this optimization achieved with subgrid modelling? In both LES and DNS the grid size is smaller than the smallest eddies, isn`t it? I am trying to make the methods of LES and DNS clear to me so excuse me if my questions sound a bit silly :o 
You are close, however, the small scale turbulence is not *solved* at all in LES but its effects on the large scale eddies are accounted for using a subgrid scale model. It is called a "subgrid" model because it models things smaller than the grid size. If you solve a problem with LES you cannot get details about eddies smaller than the grid scale, which is why they need to be modelled. The reason LES takes less time than DNS is that the grid can be quite a bit more coarse because you don't need to capture the small turbulent fluctuations.

Quote:
no, the issue is quite different ... Assume you have some turbulent flow that you want to solve in a case with DNS and in a second case in LES. The flow has a Kolmogorov scale eta (the smallest scale where a vortical structure is dissipated) that is a physical lenght depending on the problem. Performing DNS means that you use the (unfiltered) NS equation solved over a computational grid having all mesh sizes (dx, dy,dz) smaller than eta. You simply must solve all time and space components of the flow, this drive to a large number of computational unknowns. Performing LES means that you will compute the solution of the "filtered" NS equations. The filter width, say delta (K_delta = pig/Delta), is greater than eta and lies in the inertial region of the energy spectra. Very often, the filter width is only implicitly assumed by the computational mesh size. In conclusion, the optimization in LES is in the fact that you have a smaller computational number of unknowns than DSN. That part of the energy spectrum that you cut away by filtering is NOT resolved but modelled. The effect of the model (SGS) acts on the resolved field, but mainly near the highest resolved wavenumber components of the flow. The low wavenumber components are not practically altered neither by the filter or the SGS model, in this sense they are directly solved. 
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