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fivos May 16, 2013 11:05

Question about LES
Hi to all,

I am currently trying to implement a LES model (simple Smagorinsky to begin with, later we shall see) in a CFD code. The code has capability of 3D and transient runs, of course and in its current state it is a pressure based RANS code (both compressible & incompressible).

First of all, it is my understanding that the algorithm should be more or less the same as it was in the former RANS form, with the main modification being the calculation of the subgrid turbulent viscosity; in other words it would be like a laminar solver with the viscosity increased by the subgrid viscosity. Is this true?

The main question I have is what is the treatment of the so called trace term of the SGS stress (the one mentioned as tkk in

What exactly is this term (I mean what is the equation of this term)? In a work ( it is mentioned that tkk is:

tkk = Ci * 2 * rho * Delta^2 * |S|^2

where Ci is a constant (0.09)
rho the density
Delta is the cell volume ^ (1/3)
and |S| = Sqrt(2*Sij:Sij), with Sij the element of the subgrid stress tensor.

Is the above correct?

I have seen also in several works and books (including Pope, Lesieur) that the tkk term is added to pressure. In others (including the Fluent manual, see also ), it is said that the term is omitted. What is your opinion on the treatment of this term?

Finally, do you have any book/reference to suggest for practical, application oriented LES implementation (I do not want another book pilling a ton pages on how LES is derived and when it comes to the implementation details of the LES equations it presents them in just 10 lines)?

Any comments are welcome
Thank you in advance

FMDenaro May 16, 2013 12:10

- for incompressible flows, the trace is considered into the pressure term, in practice you compute an elliptic equation for a modified pressure field.
- for compressible flows you have to somehow model also the isotropic term.

Note that generally RANS codes are quite low accurate in the time-space discretizations. Often in LES is necessary to build an ad-hoc high accurate code (choosing between implicit or explicit filtering).

fivos May 16, 2013 12:27

I see, thank you for your quick answer.

I understand that both spatial and temporal resolutions (and the relevant discretization schemes) should be appropriate in order:
- to properly resolve the larger eddies
- to reduce numerical viscosity/diffusion, which may mask/smooth eddies

What is your opinion about the omission of the term from the pressure equation? Have you tried working with it / without it?

Currently I have implemented the LES model for incompressible flow (I will see later for compressible) and I am testing it on the flow around a square cylinder at Re~21000. I have not implemented the pressure term but up to now subgrid viscosity has reasonable values, similar to the ones reported in literature. However the simulation is still running and it will need quite some time....

The solution of the modified pressure field baffles me ... what will be used to calculate it? The velocity divergence (i.e. the continuity imbalance) ? The imbalance + other terms ?


FMDenaro May 16, 2013 12:40

As I wrote before, for incompressible flows (Div V = 0) the isotropic SGS stress is simply disregarded in the filtered equations. As a consequence, the filtered pressure term that you solve from the elliptic equation contains also this term (a simple discussion can be read in the book of Sagaut). This is the reason for your good results without taking it into account.
For compressible flows this is not possible because you have the state equation for the pressure. However, it is somehow debated if the dilatation model improve the results.

fivos May 16, 2013 12:52

So (correct me if I am wrong), you imply that in incompressible when I include the subgrid viscosity term, I instantly get instead of pressure, the pressure + the isotropic SGS stress term without having to do anything else (such as include other terms in the SIMPLE or PISO pressure correction equations), right?

Ok, in that case I think I got it,
Thank you very much for your help.

FMDenaro May 16, 2013 13:12

yes, that's correct

sbaffini May 17, 2013 04:37

I just want to add that the reason for this is that for incompressible flows you solve for a scalar field (the pressure) whose gradient is used to correct the velocity and achieve a divergence free velocity field.

Now, in this framework, this scalar field is actually a lagrange multiplier more than just the pressure. So, it does not matter how many unknown gradient terms you have on your right hand side (pressure, SGS stress trace, gravity, etc.), in the exact moment you don't explicitly compute them they build up in the unique lagrange multiplier used to satisfy the divergence free condition for the velocity field.

I am working on a particular LES framework which also requires an explicit modeling term for the pressure itself. So i once tried, for an incompressible flow, to model this term and i also removed the trace free condition for the SGS stress. As a matter of fact i did not get any appreciable difference in the results. Of course, this mostly depends from the specific numerical method too and testing is always required.

fivos May 17, 2013 05:10

Thank you for your input too Paolo.

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