[vesp]

Originally Posted by FMDenaro

For example you can read the approach for LES


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


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

Thank you for the list. I quickly glanced over the first manuscript - it does state that

Running LES supplied with the perfect SGS stress, we recover exactly
the same energy spectra of filtered DNS solution, regardless of the filter
used.

So this statement and the link I provided below show for LES, the issues observed for RANS do not appear - or did I miss something?

[FMDenaro]

Originally Posted by vesp

Thank you for the list. I quickly glanced over the first manuscript - it does state that
So this statement and the link I provided below show for LES, the issues observed for RANS do not appear - or did I miss something?

The definition of a "perfect model" strictly depends on the definition of the LES filter. In case you apply an explicit filtering procedure, you can really have a congruent coupling with the DNS (filtered) fields. On the other hand, the common use of an implicit filtering makes more complicated to define the correct unresolved field and insert into LES.



What is intriguing is the RANS is based on a well defined statistical averaging and the "perfect model" should be well suited.

[vesp]

Originally Posted by FMDenaro

The definition of a "perfect model" strictly depends on the definition of the LES filter. In case you apply an explicit filtering procedure, you can really have a congruent coupling with the DNS (filtered) fields. On the other hand, the common use of an implicit filtering makes more complicated to define the correct unresolved field and insert into LES.

yes, I agree. So for LES, we have a number of cases where this perfect closure approach has been demonstrated to work, and no proof that an issue as in RANS has occurred.

What is intriguing is the RANS is based on a well defined statistical averaging and the "perfect model" should be well suited.

I am not a RANS expert, but I wonder if the blow up reported in the paper is due to an inconsistent discretization of the Tau terms and to convective term. I would also like to see the analysis repeated wir an explicit time stepping to steady state and not an implicit solve for the steady solution. I csn easily see how else small scale errors explode in the perfect RANS approach. I must say that the paer is interesting, but that I remain sceptical.

[FMDenaro]

From DNS you could compute the "exact" unresolved terms to be included in a steady RANS, so I don't see a theoretical reason for which it can not work....

[vesp]

Originally Posted by FMDenaro

From DNS you could compute the "exact" unresolved terms to be included in a steady RANS, so I don't see a theoretical reason for which it can not work....

Since tau is a nonlinear function of the DNS, one has to be careful a) how to compute it and how to project it onto the RANS grid
b) how to discretize tau, i.e. how to apply die divergence operatot consistently.

If one of the two steps is not done correctly, the solution of the DNS and the perfect RANS should differ.

[FMDenaro]

Originally Posted by vesp

Since tau is a nonlinear function of the DNS, one has to be careful a) how to compute it and how to project it onto the RANS grid
b) how to discretize tau, i.e. how to apply die divergence operatot consistently.

If one of the two steps is not done correctly, the solution of the DNS and the perfect RANS should differ.

You could compute div Tau directly on the DNS grid so that you have a fully resolved and accurate term to be inserted into the RANS solver.

[vesp]

Originally Posted by FMDenaro

You could compute div Tau directly on the DNS grid so that you have a fully resolved and accurate term to be inserted into the RANS solver.

Then div tau would be exact - but shouldnt the divergence operator be the discrete one then? The one on the left side is. For the terms in tau and the convective term to cancel (otherwise the solution to the equation is no linger the filtered DNS), not only the terms themselves must match, but also their discretizations.

[FMDenaro]

Originally Posted by vesp

Then div tau would be exact - but shouldnt the divergence operator be the discrete one then? The one on the left side is. For the terms in tau and the convective term to cancel (otherwise the solution to the equation is no linger the filtered DNS), not only the terms themselves must match, but also their discretizations.

You could also think to solve the RANS over the DNS grid, just a 2D plane of the DNS grid is sufficient. I don't see a theoretical reason to not get a convergence.

[vesp]

Originally Posted by FMDenaro

You could also think to solve the RANS over the DNS grid, just a 2D plane of the DNS grid is sufficient. I don't see a theoretical reason to not get a convergence.

I think I have to disagree - from the paper they solve the equations on the RANS grid, and then averaging / filtering and discretization errors mingle. It is possible to account for that (this is why in the paper you cited, the LES is filtered explicitly and the equations are solved on a fine grid), but it is unclear / not mentioned in the paper. I find it curious that they note the discrepancy fir increasing Re on a fixed grid - this is exactly what would happen as a consequence of what I have outlined here.

[vesp]

Originally Posted by FMDenaro

The real issue that has not been highlighted is that we already know from DNS solutions that extracting from those data the unresolved fields and inserting them in a practical computations still produce not satisfactory solutions.
Thus, I don't think that a ML algorithm can change this framework.

Dear FMDenaro,

having gone through the literature you provided and others, I found that the picture is different for RANS than it is for LES. For LES, the general observation is that inserting the closure from DNS works - as one would expect from a mathematical point of view. For RANS, the picture is not so clear, there might be something going on there.



So for RANS, this would pose a problem for ML methods, while not for LES.

Thanks again for providing these insightful literature links!

[sbaffini]

Originally Posted by vesp

Dear FMDenaro,

having gone through the literature you provided and others, I found that the picture is different for RANS than it is for LES. For LES, the general observation is that inserting the closure from DNS works - as one would expect from a mathematical point of view. For RANS, the picture is not so clear, there might be something going on there.



So for RANS, this would pose a problem for ML methods, while not for LES.

Thanks again for providing these insightful literature links!

One possible explanation for this would be the unsteady nature for LES, versus the steady one for RANS.

LES might be forgiving because the unsteady term can accomodate anything unbalanced.

In contrast, RANS can't; moreover, it also needs that the equilibrium found among all the terms is actually stable (which seems to be the real issue here, if I read correctly some of the material you all posted here).

[vesp]

Originally Posted by sbaffini

One possible explanation for this would be the unsteady nature for LES, versus the steady one for RANS.

LES might be forgiving because the unsteady term can accomodate anything unbalanced.

Hm, interesting thought, but I am not sure about that: Wouldn't this mean that the perfect LES solution and the filtered DNS solution would have to differ at certain timesteps? From e.g. https://journals.aps.org/pre/abstrac...RevE.75.046303 Fig 1. this is not the case.

[FMDenaro]

Originally Posted by vesp

Hm, interesting thought, but I am not sure about that: Wouldn't this mean that the perfect LES solution and the filtered DNS solution would have to differ at certain timesteps? From e.g. https://journals.aps.org/pre/abstrac...RevE.75.046303 Fig 1. this is not the case.

Actually, filtering a DNS field at a certain time does not represent exactly the LES solution at the same time under the evolution of the filtered equations.

[vesp]

Originally Posted by FMDenaro

Actually, filtering a DNS field at a certain time does not represent exactly the LES solution at the same time under the evolution of the filtered equations.

No, but if - like in the paper I posted - the filtered equations are started from a filtered DNS and then evolved with the closure terms (derived by filtering the DNS), then these two quantities are and remain identical (within rounding error limits).

[FMDenaro]

Originally Posted by sbaffini

One possible explanation for this would be the unsteady nature for LES, versus the steady one for RANS.

LES might be forgiving because the unsteady term can accomodate anything unbalanced.

In contrast, RANS can't; moreover, it also needs that the equilibrium found among all the terms is actually stable (which seems to be the real issue here, if I read correctly some of the material you all posted here).

I am not sure. I don’t know of existing studies that performed analyses for a perfect model in both LES and RANS on the same flow problem...and I doubt about a good accordance when implicit filter is used.

[FMDenaro]

Originally Posted by vesp

No, but if - like in the paper I posted - the filtered equations are started from a filtered DNS and then evolved with the closure terms (derived by filtering the DNS), then these two quantities are and remain identical (within rounding error limits).

The problem is 1) identify the LES filter to use on DNS. 2) using the LES equations with the perfect model but on the DNS grid or not?

[sbaffini]

Originally Posted by vesp

Hm, interesting thought, but I am not sure about that: Wouldn't this mean that the perfect LES solution and the filtered DNS solution would have to differ at certain timesteps? From e.g. https://journals.aps.org/pre/abstrac...RevE.75.046303 Fig 1. this is not the case.

Unfortunately I have no access to this work, and time has passed since the last time I read the De Stefano-Vasyliev. Yet, what I read from the abstract seems to contradict what you wrote:

"We demonstrate, in the context of implicit-filtering large eddy simulations (LESs) of geostrophic turbulence, that while the attractor of a well-resolved statistically stationary turbulent flow can be reached in a coarsely resolved LES that is forced by the subgrid scale (SGS) terms diagnosed from the well-resolved computation, the attractor is generically unstable: the coarsely resolved LES system forced by the diagnosed SGS eddy terms has multiple attractors. This points to the importance of interpreting the diagnosed SGS forcing terms in a well-resolved computation or experiment from a combined physical-numerical point of view rather than from a purely physical point of view."

As I remember of different works actually trying this (not only these 2), it may actually depends from the specific details of the implementation (as, btw, it is typically the case in LES).

[sbaffini]

Originally Posted by Argyris

I am a postgraduate student, so I dont have any experience with AI in CFD but I see some serious research regarding data-driven turbulence modeling from NASA, University of Michigan, ONERA etc.

http://turbgate.engin.umich.edu/symp.../Duraisamy.pdf


http://turbgate.engin.umich.edu/symp...2/Fabbiane.pdf


From what I understand they use data from DNS and experiments to optimize the coefficients in Spalart-Allmaras model.They also suggest a similar procedure can be implemented in Reynolds Stress models, which are more difficult to calibrate to be applicable in a wide range of flows.


I am really interested in doing some research in this area, but I have doubts over its future (good funding or will it be abandoned?).

Soon or later it is going to be abandoned for the new kid on the block, just like everything else in research. If funding is available now, you should go now. Why caring about tomorrow? I think it is highly unprobable that you can get funding for the rest of your life just working on a single topic.

[vesp]

Originally Posted by FMDenaro

The problem is 1) identify the LES filter to use on DNS. 2) using the LES equations with the perfect model but on the DNS grid or not?

1) What is done in two papers I mentioned is independent of the filter used on the DNS - it clearly gives a different solution u_filtered, but the overall perfect LES is independent of that.

2) In both publications, the perfect LES is actually solved on the LES grid, so discretization errors have to be balanced out by a term in the closure, see EQ 6 in the Nadiga paper.

[vesp]

Originally Posted by sbaffini

Unfortunately I have no access to this work, and time has passed since the last time I read the De Stefano-Vasyliev. Yet, what I read from the abstract seems to contradict what you wrote:

"We demonstrate, in the context of implicit-filtering large eddy simulations (LESs) of geostrophic turbulence, that while the attractor of a well-resolved statistically stationary turbulent flow can be reached in a coarsely resolved LES that is forced by the subgrid scale (SGS) terms diagnosed from the well-resolved computation, the attractor is generically unstable: the coarsely resolved LES system forced by the diagnosed SGS eddy terms has multiple attractors. This points to the importance of interpreting the diagnosed SGS forcing terms in a well-resolved computation or experiment from a combined physical-numerical point of view rather than from a purely physical point of view."

As I remember of different works actually trying this (not only these 2), it may actually depends from the specific details of the implementation (as, btw, it is typically the case in LES).

Ok, I understand how this summary might be misinterpreted. What they are doing in the paper is:
a) show that with the filtered DNS as a closure, the solution remains the filtered solution for all times. BTW, this is also shown in the paper about the ML I mentioned earlier that somewhat started this discussion.
b) They then perturb the closure term and observe a deviation.
Here is the Fig. 1 from the paper I was talking about
https://ibb.co/jx9O59

This last point is what they refer to in their summary.