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Computational effort of various LES models

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Old   November 9, 2021, 04:51
Default Computational effort of various LES models
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Is there a significant difference in compational effort between 0-equation and 1-equation LES models. For simulation a combustor for an aero engine I want to decide between the 0-equation models (Upwind LES model, Smagorinsky Model, Dynamic Smagorinsky Model, Sigma LES) and the 1-equation models (One-equation model/k-equation, Dynamic Structure model and Consistent Dynamic Structure model).
It seems that the Dynamic structure model and the Consistent Dynamic Structure model are most accurate however I also want to take the computational power into account for these models.
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Old   November 9, 2021, 06:19
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Originally Posted by velkon View Post
Is there a significant difference in compational effort between 0-equation and 1-equation LES models. For simulation a combustor for an aero engine I want to decide between the 0-equation models (Upwind LES model, Smagorinsky Model, Dynamic Smagorinsky Model, Sigma LES) and the 1-equation models (One-equation model/k-equation, Dynamic Structure model and Consistent Dynamic Structure model).
It seems that the Dynamic structure model and the Consistent Dynamic Structure model are most accurate however I also want to take the computational power into account for these models.



The dynamic procedure is generally more expensive than other SGS models.



PS: what do you mean for "Upwind LES model", the ILES formulation?
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Old   November 9, 2021, 06:49
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There are two factors here to consider, in my opinion.

The formal aspect is very simple. Assuming you use a segregated solver, the cost of a 1 eq. turb. model is similar to the one of any of your momentum equations. In any case, this is order of magnitudes higher than any algebraic model, however complex, for any reasonable implementation of the two.

Then there is the practical aspect. You mention better results, however "seems" might be a little weak to switch from an algebraic model to a 1 eq. model. One important aspect is also related to how such 1 eq models are used. If they still provide an eddy viscosity for the momentum equations, my personal opinion is that yes, they can give some additional insight for an eddy viscosity, but not much beyond what a simple wall distance function could give. Also, it is of paramount importance to understand the nature of the code where such models are implemented. The exact same models can behave differently, just with respect to each other, when implemented in different codes.

It is probable that 1 eq models might be somehow better in the so called VLES regime, maybe with strong recirculations; that is, where actual history effects might become important and more reliable than a grid dependent dissipation function. Or maybe you have a case where one of the two modeling approaches is simply wrong, while the other not: you don't really have choice then. But all in all, 1 eq. models haven't had great traction in LES, exactly because of the cost and the limited effect that they can have with respect to simple algebraic models.
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Old   November 9, 2021, 17:47
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Already answered but since I can perceive certain points to be still unclear, I write it again in my own words in hopes that it might benefit other readers.

Solving a transport equation is at least one order of magnitude more expensive than solving an algebraic equation.

In a stereotypical LES you solve 3 transport equations for the filtered velocities (one for each component). Then you have probably a subgrid model. If it is a 0-eqn algebraic model then it adds some cost which is generally small compared to how much it is to solve your 3 transport equations (because orders of magnitude) unless there is some really quirky implementation details you have to work around. If your subgrid model is a 1-eqn model then it solves another transport equation so your computational cost goes like 3+1=>4 (or 33% increase).

The Dynamic procedure in the Dynamic Smagorinsky approach involves solving the filtered velocities on both the test filter and the grid filter so you have to solve the 3 momentum equations twice. So 3+3=>6 and you dbl your computational cost. This is despite the underlying subgrid model still being an algebraic 0-eqn model.


So be careful where you put these dynamic procedure approaches in your ranking.

Actually in reality there are a lot of other overhead costs so the increase isn't 33% or 100% but a bit lower. The dynamic Smagorinsky approach for example is more like x1.8 compared to regular algebraic-only Smagorinsky and 1-eqn models about x1.2.
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Old   November 9, 2021, 17:57
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Originally Posted by LuckyTran View Post
Already answered but since I can perceive certain points to be still unclear, I write it again in my own words in hopes that it might benefit other readers.

Solving a transport equation is at least one order of magnitude more expensive than solving an algebraic equation.

In a stereotypical LES you solve 3 transport equations for the filtered velocities (one for each component). Then you have probably a subgrid model. If it is a 0-eqn algebraic model then it adds some cost which is generally small compared to how much it is to solve your 3 transport equations (because orders of magnitude) unless there is some really quirky implementation details you have to work around. If your subgrid model is a 1-eqn model then it solves another transport equation so your computational cost goes like 3+1=>4 (or 33% increase).

The Dynamic procedure in the Dynamic Smagorinsky approach involves solving the filtered velocities on both the test filter and the grid filter so you have to solve the 3 momentum equations twice. So 3+3=>6 and you dbl your computational cost. This is despite the underlying subgrid model still being an algebraic 0-eqn model.

So be careful where you put these dynamic procedure approaches in your ranking.
Everything perfect, except that the dynamic procedure doesn't actually implies solving on two grids, but filtering of some terms on your basic, and only, grid. The cost comes from the fact that, in general, the number of terms to be filtered is high (for a simple dynamic Smagorinsky model in a constant density isothermal flow, you shave to filter the 3 velocity components + 2x6=12 terms of two tensors, for a total of 15; for very general flows and more complex mixed models you can get up to 37 terms to filter!!!), and gradients of filtered variables are also needed. So, for a single constant, there is indeed a lot of work to do.

Last edited by sbaffini; November 10, 2021 at 03:09.
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Old   November 10, 2021, 09:06
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Thank you all for the replies. As I read that as the Dynamic Structure model is not a purely dissipative model like the dynamic Smagorinsky model it performs better in rotating turbulence, so also for the processes similar in combustion. However, when reading the above replies, is it true that the increase in performance in anisotropic flows for the dynamic structure model is marginal? In addition, how does the Dynamic Smagorinsky model and the Dynamic Structure model relate to each other in terms of computational effort?
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Old   November 10, 2021, 09:15
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Do you have a reference for the dynamic structure model? Because, over time, a lot of different approaches have been cast into that nomenclature
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Old   November 10, 2021, 09:39
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Thank you all for the replies. As I read that as the Dynamic Structure model is not a purely dissipative model like the dynamic Smagorinsky model it performs better in rotating turbulence, so also for the processes similar in combustion. However, when reading the above replies, is it true that the increase in performance in anisotropic flows for the dynamic structure model is marginal? In addition, how does the Dynamic Smagorinsky model and the Dynamic Structure model relate to each other in terms of computational effort?



In addition, consider also the scale similarity model, it is not dissipative and can be formulated in the dynamic procedure framework. It requires the cost of the explicit filtering.
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Old   November 10, 2021, 09:44
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Do you have a reference for the dynamic structure model? Because, over time, a lot of different approaches have been cast into that nomenclature
Rutland, Christopher. (2011). Large-eddy simulations for internal combustion engines - A review. International Journal of Engine Research. 12. 10.1177/1468087411407248.
The turbulence models are compared in the section from page 8 till page 12
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Old   November 10, 2021, 13:23
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Rutland, Christopher. (2011). Large-eddy simulations for internal combustion engines - A review. International Journal of Engine Research. 12. 10.1177/1468087411407248.
The turbulence models are compared in the section from page 8 till page 12
May take me some time to read it all (with the original references) but the model looks, indeed, exactly like a scale similar model, but scaled by k_sgs solved by its own transport equations. So, as costs, you have: 6 scalars to be filtered (from the symemtric L tensor) and a transport equation for k_sgs.

Note that the role of k_sgs (and its transport equation) here is pretty much different from the case where it is used in determining an eddy viscosity. Here it scales a pure scale-similar term, that has nothing to do with the eddy viscosity. In practice, k_sgs works like a sensor/reservoir for the model. In this sense, the additional equation might have more sense here.

Unless they use a dynamic procedure in the k_sgs equation (which is not clear from the paper), I think that the "dynamic" in the model name is pure marketing and highly misleading. It is dynamic in the same way that a pure scale similar model is... that is, no way.

With these details, I think it's up to you to decide if the costs are worth it or not. All considered, I think you should compare this model with a dynamic mixed model. Considering that the area of application seems to be combustion, the relative costs are indeed order 37 (if I did my math correctly) scalars to be filtered and gradients of 10 variables to be computed. So, the dynamic structure model might be really a winning option if it actually works as mentioned in the paper.

Note, however, that this is mostly a review and, in my opinion, these should be carefully scrutinized in LES because, as I said, the code is very important in LES and two codes using the same sgs model might give different results. You could basically do a whole Ph.D. on the implementation of scale similar terms in actual codes, so you might want to look carefully if the said dynamic structure model has specifications for the code you intend to use.

Also, I feel obliged to add that, the dynamic procedure numbers I used above are those of the classical, and most common, procedure. There are variants of this that greatly reduce such costs (say, around 12 scalars only to be filtered in the general case).
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Old   November 11, 2021, 09:30
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I just realized combustion is involved so some points can be reinforced.

Always you solve at least the momentum transport equations. In addition to this, you are solving also an energy equation if you have any type of compressible medium. In combustion you solve some type of mixture model and a reaction model (at the very minimum). You are going to have some type of oxidizer/fuel mixture fraction model or a bunch of additional species transport models. Then you have at least a reaction progress equation if you are not brute forcing the chemistry. So most of your computational cost is expended doing non subgrid things and the overall difference in computational time that you see in practice can indeed become quite marginal when you go from one LES model to the next.

So back to my old example. If I go from solving 3 momentum equations + 1 k-eqn then the cost goes like 3+1=>4. But a combustion problem might look more like 3 momentum equations, 1 energy equation, 1 mixture fraction, 1 progress variable, + my 1-eqn ksgs model so 6+1=>7 is a much less significant increase than before for a very very lean reacting LES.
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