[gardener96]

Hello,
I have recently had a brief introduction about large eddy simulation. The teacher mentionned that convergence was tricky to verify in such a simulation, and that often times the way to verify it in a qualitative way was to look at mean and rms profiles (velocity, temperature etc) and check that the profiles were similar between mean and rms and that they were symmetric. I had a hard time understanding why convergence in LES was not as simple to verify as for instance in RANS. When I asked the teacher, I got a vague answer regarding the fact that there was no steady state in LES (or at least this is how I understood it, I could be wrong). I am also confused as to why there would be no steady state in LES. I understand it has to do with the nature of turbulence to be dependent of time, but I don't know is there is more to it?
I could not find any paper or review that explains this (possibly it is very obvious?).



I am looking for insights into the use of symmetric profiles to check convergence in LES, and why there is no steady state (or to correct me if I am wrong!). Fortunately this will not be at the exam, but I am still very curious about it Thanks in advance!

[FMDenaro]

Originally Posted by gardener96

Hello,
I have recently had a brief introduction about large eddy simulation. The teacher mentionned that convergence was tricky to verify in such a simulation, and that often times the way to verify it in a qualitative way was to look at mean and rms profiles (velocity, temperature etc) and check that the profiles were similar between mean and rms and that they were symmetric. I had a hard time understanding why convergence in LES was not as simple to verify as for instance in RANS. When I asked the teacher, I got a vague answer regarding the fact that there was no steady state in LES (or at least this is how I understood it, I could be wrong). I am also confused as to why there would be no steady state in LES. I understand it has to do with the nature of turbulence to be dependent of time, but I don't know is there is more to it?
I could not find any paper or review that explains this (possibly it is very obvious?).



I am looking for insights into the use of symmetric profiles to check convergence in LES, and why there is no steady state (or to correct me if I am wrong!). Fortunately this will not be at the exam, but I am still very curious about it Thanks in advance!

This is not a simle topic to clarify in few words. The key is that in LES we solve unsteady and 3D fields but the variables we solve are filtered, not statistically averaged as happens in RANS.

In turbulence we talk about "statistically steady state", that is the statistical means do not depend on time. But in LES we do not solve the statistical equations but the filtered equation. Having the LES solution for several time units, we can post-process the fields by computing the statistically averaged field. For this reason you can see that in a channel flow the rms and zero-th mean must be symmetric after the statistical post-processing.


Talking about the concept of convergence in LES, when the grid is used a implicit filtering, there is no convergence towards a LES solution. The LES variable is like


v=v(x,t:h)


therefore, for vanishing mesh size the LES variable has convergence towards the DNS variable.
But for each choice of the mesh h you get a filtered solution, in other
words a different resolved energy spectra.
Here are the files of my lectures about LES
https://www.researchgate.net/publica...VDb250ZW50In19


here a papers about what is resolved in LES


https://www.researchgate.net/publica...UNvbnRlbnQifX0

[LuckyTran]

When you run RANS, you get right away the statistical quantities and can tell if it is outright wrong, maybe right but not yet converged, never going to converge, or everything is 100% fine.

You cannot easily get the statistical quantities from LES (at least not right away). All the time when you look at LES results, you have no clue whether or not they make any sense because the instantaneous fields are a chaotic mess. You are forced to start sampling and averaging for a long long time and maybe after a few days of running you come back and and finally look at the mean fields and then find out that everything you've been doing so far was garbage.

You can step one iteration in a RANS, instantly see that the results have changed and then make a judgement on whether it looks any better or any worse. You take one time-step in an LES and it's one messy field followed by another messy field and you have no measure of whether or not any of them has converged.

Finally the average that you get is only the sampling average of the duration that you sample. So you never quite actually know whether or not you have run the LES long enough to get the true mean. Maybe if you keep running it longer it approaches the true mean. Or maybe if you keep running it, it diverges! In RANS, you see right away the mean and you can instantly say whether it is good or bad.

[gardener96]

Thank you very much for your replies, and for making them understandable! This is exactly what I was looking for