Can someone tell me where (apart from theoretical definition) does the difference come in writing a FVM code when we use LES instead of RANS. Particularly how will we switch to space averaging instead of time averaging in Navier Stokes Equations? Thanks

The process of discretizing the continuous Navier-Stokes onto a discete domain is usually used as the filtering (spatial averaging) process and the sub-grid scale models are added to the stress tensor.

When simulating turbulent flows (computationally) there really is no change to the Navier-Stokes, whether you're using RANS or LES, except for a modification to the stress tensor on the RHS of the equation.

Altough some schemes commonly used in RANS are not recommended to LES. For instance, upwinding...

How abnut use hybrid differencing scjeme?

I dont have much experience yet. I am a begginer, but as I could read in the literature, any hibrid scheme would also contain an "upwind percentage" and this is not good for LES. What I see people doing is setting those upwinding (or artificial dissipation) to a minimum level, so that a stabilized algorithm is still obtained, with the least demage to your spectrum, and consequently to the accuracy of your solution.

Why is Upwinding not recommended for LES and ok to use for RANS? Can you name a paper which deals with why upwinding is not good for LES?

Also, you say that what you "see people doing is setting those upwinding (or artificial dissipation) to a minimum...with the least damage to your spectrum". Can you explain this comment further please. Do you know of a paper which discusses this concept? How would upwinding damage the spectrum? Why would central differencing not?

Why is Upwinding not recommended for LES and ok to use for RANS? Can you name a paper which deals with why upwinding is not good for LES?

Ans: because it is dissipative. Piomelli, 1999. Large eddySimulation: achievements and challanges. Progress in Aerospace Sciences 35

Also, you say that what you "see people doing is setting those upwinding (or artificial dissipation) to a minimum...with the least damage to your spectrum". Can you explain this comment further please. Do you know of a paper which discusses this concept? How would upwinding damage the spectrum? Why would central differencing not?

Ans: for instance in a paper from T.T. Bui, 2000- Computers&Fluids 29. If you combine a central diferences scheme (non dissipative) with a upwind (dissipative), given each one adjustable weights "a" and "b"

u = a*u(CentDiff) + b*u(UpWind)

you will find out that the lower the "b", the better. But since sometimes you need some dissipation to stabilize your algorithm, you cant set b=0.

Some recent advances (Mahesh, Moin, etc... in 2004) showed how to implement a numerical schem that is stable even for righ Re, with no upwinding at all.

I hope this helps. Luiz

Hi,

Thank you Luiz. I have some further questions.

Why does the dissipative nature of Upwinding effect RANS more than LES? I assume it is something to do with swamping the sgs term, but is it not better to swamp a small proportion of the energy (information/sgs) in LES than to swamp an entire simulation (RANS)?

Also, you say upwinding may be needed to stabilise the simulation. Why does introducting some error (i.e., using upwinding to stabilise) result in a better solution? What is it about upwinding that makes it acceptable to within a specific order of accuracy rather than simply destroying a solution?

How bad is a high reynolds (Peclet high) number flow solved using upwinding? Is it at all accepatble in LES?

Thank you for your comments and the papers recommened. I shall look into them immediately.

"Why does the dissipative nature of Upwinding effect RANS more than LES? I assume it is something to do "

Actually it is the other way around. They are acceptable for RANS, but not suitable for LES.

"with swamping the sgs term, but is it not better to swamp a small proportion of the energy (information/sgs) in LES than to swamp an entire simulation (RANS)? "

This is a question I am always trying to get think about and makeup my mind. I dont have the complete answer yet, but I suspect it is the following: altough the dissipative effect of upwinding acts on small scales which contains little energy, the problem is that many sgs models use exactly the information contained in these scales (close to cutoff) to compute the subgrid tensor. Then if dont reproduce well the spectrum close to cutoff, you can spoil the subgrid term, eventough there is not so much energy in this part of spectrum. That is what I think...

" Also, you say upwinding may be needed to stabilise the simulation. Why does introducting some error (i.e., using upwinding to stabilise) result in a better solution? "

The easiest way to explain that is: whenever you add a dissipative term you are getting closer to laminar flows, which we know are very stable. Not necessarily you get a better solution by stabilising your algorithm, but at least you get some solution, which is better than none. In some algorithms if you dont stabilise it by artifitial means you may get overflows in your variables... Read the lasts papers of Mahesh on Combustion using LES... He explains how to write, or what is the requirements a stable algorithm sould comply with. (Essentialy it must conserve cinetic energy in the convective discrete form, apart from boundary effects).

"What is it about upwinding that makes it acceptable to within a specific order of accuracy rather than simply destroying a solution? "

With upwinding you know you are spoiling your solution. But without it, you may not even get one solution (only overflows - nan). So if you dont have a good algorithm (like the one developed by Mahesh) you will need upwinding to at least have a solution. But, since upwinding spoils the solution, try to use the minimun amount of upwind possible, and you should get the "least worst" solution...

" How bad is a high reynolds (Peclet high) number flow solved using upwinding? Is it at all accepatble in LES? "

It will depend on what you consider an acceptable solution for your particular problem. It will also depend on your mesh, since the coarse it is, the bigger the dissipative effect of upwinding. I suggest you do have a look in those papers, to get an idea of how much...

" Thank you for your comments and the papers recommened. I shall look into them immediately. "

Best of luck, luiz

I think your discussion of "upwinding" is too vague. I assume you mean 1st order upwinding because you speak of dissipation. There are higher order upwinding schemes which yield much better results than any central scheme could. Some of them are TVD, ENO, WENO schemes of order 2 and greater - in fact I have a paper where an 11th order WENO scheme is used.

Harten and Osher are the fathers of higher order upwinding schemes using polynomial reconstruction.

I agree with you, basically the problem is when you have shocks (or strong discontinuities in general), where central differences create a mess. Basically any discretization scheme with constant coefficents (doesn 't matter the order) is not better than a first order scheme close to a discontinuity (Godunovs theorem). TVD schemes, or WENO (probably not ENO), MP-WENO behave much better. Basically reverting to some up-winding close to the discontinuity. Anyway,as always, some schemes are better than others depending on the particular case. There are papers doing LES with TVD schemes specially at high speed flows. And at low speed flows, TVD schemes are generally used in the passive scalar transport equations.

Hi, i am trying to switch from Fortran based RANS code to LES for my FVM code. Q1. I am bit stuckup with the use of space fiter..how to actually use it in Navier Stokes equations? Q2.In what respect i shall be switching from my time averaged Navier Stokes eqautions? I have studied it theoratically but am not still clear about how to implement it actually in the code. Q3. From where are we inputting the unsteady velocity and pressure etc as in comparison with time averaged ones in RANS? I highly appreciate you for your comments

Hi,

The main difficulty is that the intrinsic numerical dissipation of upwind schemes, even the high order ones (for instance 5th order WENO), could be higher than the turbulent viscosity related to the "classical" LES models.

That's a reason why people prefer to use centered (possibly high order) schemes with no intrinsic dissipation. However such scheme generally lead to spurious oscillations in compressible LES, and it is a common pratice to use filtering in order to stabilize the computation when no strong shock waves are expected (note that this filtering create numerical dissipation too). Use of hybrid scheme is also an option, possibly with some kind of "oscilation sensor" acting as a blending function between the upwind and centered part. The goal is to retain the dissipative upwind component in the region where numerical oscillations are encountered only.

If strong shock waves exist in the flowfield, a similar strategy can be applied, with a sensor to detect the shock location and then apply some kind of TVD regularization only in the region of the shock. However, LES for supersonic flows is still a challenge and an active research area.

The problem of upwind scheme dissipation is by far less important in RANS computations because the turbulent viscosity of the RANS models is several orders of magnitude higher that its LES counterpart. Moreover, implicit time integration with high CFL numbers are generally used (for both steady and unsteady computations) that also add some dissipation and tend to hide the one coming from the space scheme.

Regards

Lionel

Sorry, I was talking about incompressible LES, which is my research topic... I forgot to specify...