[Moreza7]

Hello,

I was reading the book "Unsteady TurbulentFlow Modelling and applications". They simulated the channel flow using LES with different meshes and different subgrid-scale models.

The weird thing is that in all cases, the simulations without a SGS model(iLES) give better results for dimensionless velocity profile and Reynolds stresses than the other models like dynamic Smagorinsky, WALE, and... . This is more significant in coarse grids.
The author claims that the same thing happens in this article:
https://www.researchgate.net/publica..._aero_vehicles .

I really don't understand why should the simulations without any subgrid-scale model give better results than the simulations with a complex subgrid-scale model?

The author also says that it is due to numerical diffusion, since the numerical errors are in the same order of magnitude with SGS stresses.
I can not cope with this! While the errors are working fine as a subgrid-scale model in iLES, then why should we sum SGS stresses to them and ruin the results?

If no model(iLES) works fine, then why should we waste computational power by defining a subgrid-scale model?

[FMDenaro]

your doubt is lawful, this is an issue debated in LES literature but without a clear and definitive conclusion.
First of all, speaking about LES without SGS model is not exactly as same as speaking about ILES. In the latter case we use some specific numerical method having as a result that the local truncation error has an effect similar to an SGS model, for example some dissipation effects acting at small scales.
More in general, speaking about LES without SGS model we can address any type of numerical formulation, not necessarily one containing a local truncation error mimicking a dissipation. For example, we can perform a runa using spectral methods without SGS model to assess the real effect superimposed when the model acts.


Thus, you can immagine that the general statement the a LES no-model or ILES performs better than a LES with an SGS model needs to be analysed deeper.


Finally, the term "better" is also misleading, what does it really mean? That you have a better agreement with DNS? But we are solving for a filtered variable that, in principle, is different from the DNS one on a mesh that produces an unresolved solution.

There is literature about such issues...

[Moreza7]

Originally Posted by FMDenaro

your doubt is lawful, this is an issue debated in LES literature but without a clear and definitive conclusion.
First of all, speaking about LES without SGS model is not exactly as same as speaking about ILES. In the latter case we use some specific numerical method having as a result that the local truncation error has an effect similar to an SGS model, for example some dissipation effects acting at small scales.
More in general, speaking about LES without SGS model we can address any type of numerical formulation, not necessarily one containing a local truncation error mimicking a dissipation. For example, we can perform a runa using spectral methods without SGS model to assess the real effect superimposed when the model acts.


Thus, you can immagine that the general statement the a LES no-model or ILES performs better than a LES with an SGS model needs to be analysed deeper.


Finally, the term "better" is also misleading, what do it really mean? That you have a better agreement with DNS? But we are solving for a filtered variable that, in principle, is different from the DNS one on a mesh that produces an unresolved solution.

There is literature about such issues...

Thank you, Professor.

The goal of the SGS model is to predict (some of) the effects of subgrid scales that can not be captured in LES. So, if the results are closer to DNS it means that the model is working better than the others.

The book is using a 2nd order FV solver for all models. No numerical method is used for ILES.
It's interesting that how can the truncation error give such accurate results for all statistics, not a particular one! I'm telling this because errors are random numbers and cannot give good results for all statistics.

Now my question is that in a no-model simulation we have:
Discretized equations + truncation errors

and in a simulation with an SGS model we have:
Discretized equations + truncation errors[same as the previous one] + SGS stresses.

Now while the truncation error is working well in the no-model simulation, then why should we add SGS stresses which cause the results to get worse?
Does the SGS model affect the truncation error's magnitude? [I don't think so, since the order of the solver is the same in both cases]

And finally, as a researcher, do you prefer no-model or ILES to SGS models?

Best Regards

[FMDenaro]

The goal of the SGS model is to predict (some of) the effects of subgrid scales that can not be captured in LES. So, if the results are closer to DNS it means that the model is working better than the others.


- No. Theoretically, an LES solution can be accurate even if it not close to a DNS one. That depends on the filter size and the LES tends to the DNS for vanishing mesh size because the SGS model vanishes, not because it works better.


The book is using a 2nd order FV solver for all models. No numerical method is used for ILES.


- What textbook? ILES is based on numerical methods!



It's interesting that how can the truncation error give such accurate results for all statistics, not a particular one! I'm telling this because errors are random numbers and cannot give good results for all statistics.


- No. Local truncation errors are well defined, they have nothing to do with a random distribution.



Now my question is that in a no-model simulation we have:
Discretized equations + truncation errors


- No. The discretized equation = original PDE + local truncation error = modified equation



and in a simulation with an SGS model we have:
Discretized equations + truncation errors[same as the previous one] + SGS stresses.


- No. You have discretized equation + discretized SGS model = Modified equation





Now while the truncation error is working well in the no-model simulation, then why should we add SGS stresses which cause the results to get worse?


- Because not all the type of local truncation error show a dissipative behavior



Does the SGS model affect the truncation error's magnitude? [I don't think so, since the order of the solver is the same in both cases]


- The SGS model is discretized and introduces a further ocal truncation error.





And finally, as a researcher, do you prefer no-model or ILES to SGS models?


- I always compare LES no-model to LES with SGS.

[Moreza7]

Thank you, dear Professor,

- What textbook? ILES is based on numerical methods!

Sorry, it was a mistake by me! It was no-model in the textbook, not ILES.

Because not all the type of local truncation error show a dissipative behavior

Why did you call it a dissipative behavior? Because it dissipates the grid-scale kinetic energy just like what the SGS model does?

I think a no-model simulation is a DNS simulation that does not have a DNS mesh. I don't know why do they call it LES!

Kind Regards.

[FMDenaro]

Originally Posted by Moreza7

Sorry, it was a mistake by me! It was no-model in the text book not ILES.


Why did you call it a dissipative behaviour? Because it dissipates the grid-scale kinetic energy just like what the SGS model does?


- yes, immagine the example of the simple FTUS scheme that shows a diffusive-like local truncation error.



I think a no-model simulation is a DNS simulation that does not have a DNS mesh. I don't know why do they call it LES.

Kind Regards.

- yes, it is also denoted as "coarse DNS", exactly the same as LES no-model.