[Nijanthan]

Hi frds,
i wanna solve my problem with LARGE EDDY SIMULATION (LES). I wanna know some useful info. regarding LES n am in need of some tutorial files regarding LES. plz let me link possible. U can also mail me at nijaanthan@gmail.com

[Nijanthan]

I want to know what is LARGE EDDY SIMULATION. What is the use of this model when v hav other turbullence models in fluent. what is the use of deriving LES? to what king of problems v can use this LES turbulence models

[Ozora]

Every problem has different imputs. I prefer you to search for articles about your problem.

[sbaffini]

Take your previous simulation, make it 3D and unsteady. Make the grid such that in every space direction delta+ is around 15-30 (while still having y+ at wall below 1), take a time step such that the Courant number is below 1. Use a second order central scheme and a second order time advancement scheme. Use a SGS model at will. Proceed in time until the flow is statistically steady and then collect statistics for a sufficient time. If none of these make sense to you, then don't go LES; if they all do, then you're ready to go. Usually, in terms of computational costs, a good LES is around 1% of the relative DNS, a poor one is around 0.1% or below. With respect to RANS/URANS, it goes up with a power of the Re number and can be order of magnitudes more costy.

However, LES is not just grabbing a set of options in a solver. If you don't know how to do it your results can be a 100% off. There is no chance you can get LES in few posts, you need to go back to the books.

[Nijanthan]

Thank u Paolo Lampitella

[cfdmms]

Originally Posted by sbaffini

Take your previous simulation, make it 3D and unsteady. Make the grid such that in every space direction delta+ is around 15-30 (while still having y+ at wall below 1), take a time step such that the Courant number is below 1. Use a second order central scheme and a second order time advancement scheme. Use a SGS model at will. Proceed in time until the flow is statistically steady and then collect statistics for a sufficient time. If none of these make sense to you, then don't go LES; if they all do, then you're ready to go. Usually, in terms of computational costs, a good LES is around 1% of the relative DNS, a poor one is around 0.1% or below. With respect to RANS/URANS, it goes up with a power of the Re number and can be order of magnitudes more costy.

However, LES is not just grabbing a set of options in a solver. If you don't know how to do it your results can be a 100% off. There is no chance you can get LES in few posts, you need to go back to the books.

Hi sbaffini! I have some questions about LES as well.

In LES how filter separates large and small scale eddies?

And most of cases in LES, I have found they are using these resolved and unresolved scale motion terms, what is the physical meaning of it?

Thanks.

[sbaffini]

When you think about LES as reported in textbooks, you mostly have to think about it as just a mathematical model. You have the Navier-Stokes equations (NSE), you apply a filter on them, you get the filtered NSE. Now, still within this mathematical framework, according to your filter, you get different types of flow fields. In the vast majority of cases, these filters do not reduce the information content of the original NSE, but just modify it so that it has a very low energy content at scales below the cut-off length of the filter. The only exception to this is the so called spectral cut-off filter, which exactly removes all the information below its cut-off scale.

This is for what concerns the theoretical LES model. I want to stress again that here we are just talking about the Mathematical equations, the filtered NSE; we are not even remotely talking about a numerical simulation.

Now, let's go to the practice. What happens in general is that you have a certain grid which, more often than not, is not capable of correctly and fully represent the Whole range of scales as would be required by a DNS. If you are using a spectral code, instead of the grid you have some coefficients but, again, you can't solve for all the ones which would be required.

At this point, two questions arise:

1) What are we gonna do?

2) What is, if any, the theoretical model for our approximate computation (one with an insufficient number of grid points or coefficients)?

There are, of course, several possible answers (which is what typically confuse novice LES users). Let's start from the simpler one.

1a) I'm gonna do my simulation as it is; which means using the NSE on a coarse grid and, if needed, one of the two: employing a SGS model for the missing scales and a non dissipative scheme; no SGS and and some specific dissipative schemes.

2a) While the approach as suggested above is simple (indeed the most used one, including Fluent), it gives some problems in answering the second question. Indeed, what happens here is that:

- there is a first implicit filter determined by the grid. It acts as the spectral cut-off, in the sense that no information is retained below the grid resolution.

- there is a second implicit filter, determined by the fact that any numerical scheme (besides some exceptions discussed below) has a limited capability in representing numerical derivatives on a grid. Roughly speaking, a central scheme is very effective in computing derivatives of linearly varying functions (it is exact indeed) but gives 0 for checkerboard variations (i.e., 1 0 1 0 1...). Thus, the scheme doesn't work in the same way for all the scales and, actually, filters the smallest ones to a certain extent, depending on the accuracy of the scheme.

- if, in addition, the scheme is also dissipative or you are using a dissipative SGS model, there is an additional filter due to the added dissipation.

The consequence of these implicit filters is that you are certainly not resolving anything below the grid resolution but, for what concerns the scales above, there is a strong degree of uncertainty due to the implicitness of the various filters at play. In Fluent, for example, a rule of thumb is that you correctly resolve the scales down to 10 times the grid spacing; below that is all implicit filtering but the form of this filter is, in general, unknown.

What is important to note here is that, in (1a) you never do anything like filtering or similars. You just solve the equations as they were laminar and, possibly use a SGS model. Nothing else.

More generally speaking, with the approach (1a) you can be very far from the theoretical LES model discussed at the beginning. Let's go now to the less simple option.

1b) As (1a) looks so bad (in theory at least) why don't we try to recover our original theoretical model? This approach, known as explicitly filtered LES, is thus based on actually filtering the equations at each time step with a specific numerical procedure. There are several ways of doing this, each leading to a specific approach; however, in the simplest case it simply amounts (with respect to (1a)) to applying the filter to the convective term at each time step and, possibly, using a SGS model. So, the difference is not that much in terms of computational steps.

2b) While you would imagine that, by definition, (1b) satisfy our theoretical model, in practice it turns out that its underlying hypotheses are somehow difficult to meet in practical applications with the available computational filters at hand. Thus, the situation might be no more simple than in (1a). However, there are cases where these conditions are exactly met.

The distinguishing feature of (1b) is that you select the filter (including its cut-off length), so that you are exactly aware of what you are solving for. In practice, for this to be true, your filter has to cover the implicit filter of the grid and the implicit filter of the scheme, both of which are still present. This means that, for a given grid, (1b) solves less than (1a) but has strong correspondence with the theoretical model, so that you can possibly develop better (read appropriate) SGS models etc.

The exception to the above reasoning is for spectral codes (Fourier-Galerkin on single boxes and similar ones) as:

- cutting the resolution of some coefficients to a limited set is exactly a spectral cut-off filter. Thus, in a broader sense, the implicit grid filter coincides with the explicit filter. Also, because of the global nature of such codes and their expansions, they also fit the basic theoretical model without further assumptions.

- derivatives are cumputed analitically, thus no implicit filter due to the scheme is present (at least not for the derivatives part).

- de-aliasing with the 3/2 rules amounts exactly to filtering the convective term

As a consequence, LES with spectral codes is actually both (1a) and (1b). Indeed, as a matter of fact, (1b) has been mostly developed with spectral codes.

To give a more concise answer to your question: in LES you are solving what is allowed by your grid and anything built on it (schemes and filters). A filter effectively separates the scales by making some of them not available (completely canceling them). Not all the analytical filters have such property. However, in practice, there is Always one filter, at least, with such property (i.e., the grid).

[cfdmms]

Originally Posted by sbaffini

When you think about LES as reported in textbooks, you mostly have to think about it as just a mathematical model. You have the Navier-Stokes equations (NSE), you apply a filter on them, you get the filtered NSE. Now, still within this mathematical framework, according to your filter, you get different types of flow fields. In the vast majority of cases, these filters do not reduce the information content of the original NSE, but just modify it so that it has a very low energy content at scales below the cut-off length of the filter. The only exception to this is the so called spectral cut-off filter, which exactly removes all the information below its cut-off scale.

This is for what concerns the theoretical LES model. I want to stress again that here we are just talking about the Mathematical equations, the filtered NSE; we are not even remotely talking about a numerical simulation.

Now, let's go to the practice. What happens in general is that you have a certain grid which, more often than not, is not capable of correctly and fully represent the Whole range of scales as would be required by a DNS. If you are using a spectral code, instead of the grid you have some coefficients but, again, you can't solve for all the ones which would be required.

At this point, two questions arise:

1) What are we gonna do?

2) What is, if any, the theoretical model for our approximate computation (one with an insufficient number of grid points or coefficients)?

There are, of course, several possible answers (which is what typically confuse novice LES users). Let's start from the simpler one.

1a) I'm gonna do my simulation as it is; which means using the NSE on a coarse grid and, if needed, one of the two: employing a SGS model for the missing scales and a non dissipative scheme; no SGS and and some specific dissipative schemes.

2a) While the approach as suggested above is simple (indeed the most used one, including Fluent), it gives some problems in answering the second question. Indeed, what happens here is that:

- there is a first implicit filter determined by the grid. It acts as the spectral cut-off, in the sense that no information is retained below the grid resolution.

- there is a second implicit filter, determined by the fact that any numerical scheme (besides some exceptions discussed below) has a limited capability in representing numerical derivatives on a grid. Roughly speaking, a central scheme is very effective in computing derivatives of linearly varying functions (it is exact indeed) but gives 0 for checkerboard variations (i.e., 1 0 1 0 1...). Thus, the scheme doesn't work in the same way for all the scales and, actually, filters the smallest ones to a certain extent, depending on the accuracy of the scheme.

- if, in addition, the scheme is also dissipative or you are using a dissipative SGS model, there is an additional filter due to the added dissipation.

The consequence of these implicit filters is that you are certainly not resolving anything below the grid resolution but, for what concerns the scales above, there is a strong degree of uncertainty due to the implicitness of the various filters at play. In Fluent, for example, a rule of thumb is that you correctly resolve the scales down to 10 times the grid spacing; below that is all implicit filtering but the form of this filter is, in general, unknown.

What is important to note here is that, in (1a) you never do anything like filtering or similars. You just solve the equations as they were laminar and, possibly use a SGS model. Nothing else.

More generally speaking, with the approach (1a) you can be very far from the theoretical LES model discussed at the beginning. Let's go now to the less simple option.

1b) As (1a) looks so bad (in theory at least) why don't we try to recover our original theoretical model? This approach, known as explicitly filtered LES, is thus based on actually filtering the equations at each time step with a specific numerical procedure. There are several ways of doing this, each leading to a specific approach; however, in the simplest case it simply amounts (with respect to (1a)) to applying the filter to the convective term at each time step and, possibly, using a SGS model. So, the difference is not that much in terms of computational steps.

2b) While you would imagine that, by definition, (1b) satisfy our theoretical model, in practice it turns out that its underlying hypotheses are somehow difficult to meet in practical applications with the available computational filters at hand. Thus, the situation might be no more simple than in (1a). However, there are cases where these conditions are exactly met.

The distinguishing feature of (1b) is that you select the filter (including its cut-off length), so that you are exactly aware of what you are solving for. In practice, for this to be true, your filter has to cover the implicit filter of the grid and the implicit filter of the scheme, both of which are still present. This means that, for a given grid, (1b) solves less than (1a) but has strong correspondence with the theoretical model, so that you can possibly develop better (read appropriate) SGS models etc.

The exception to the above reasoning is for spectral codes (Fourier-Galerkin on single boxes and similar ones) as:

- cutting the resolution of some coefficients to a limited set is exactly a spectral cut-off filter. Thus, in a broader sense, the implicit grid filter coincides with the explicit filter. Also, because of the global nature of such codes and their expansions, they also fit the basic theoretical model without further assumptions.

- derivatives are cumputed analitically, thus no implicit filter due to the scheme is present (at least not for the derivatives part).

- de-aliasing with the 3/2 rules amounts exactly to filtering the convective term

As a consequence, LES with spectral codes is actually both (1a) and (1b). Indeed, as a matter of fact, (1b) has been mostly developed with spectral codes.

To give a more concise answer to your question: in LES you are solving what is allowed by your grid and anything built on it (schemes and filters). A filter effectively separates the scales by making some of them not available (completely canceling them). Not all the analytical filters have such property. However, in practice, there is Always one filter, at least, with such property (i.e., the grid).

Dear sbaffini, thanks for your long and wonderful illustration.
You have explained it very well and it really makes lots of things clear to me.
I have red marked some of portion that I dont have any idea or in other sense it can be said that I dont understand. If you shade some light on it would be a great help. Thanks again.

[sbaffini]

I don't know if it is possible for me to give you, at least, an overview of the topic. You should consult some book on these topics. However, very briefly (and roughly):

- in a spectral code you first assume your solution can be expressed as a truncated Fourier series (or any other suitable series), and then you solve for the coefficients of the series. Here you don't have the grid because, by definition, such series are good only for specific domains. For example, a Fourier series is only good for boxes with periodicity. As a consequence, instead of having Nx, Ny and Nz cells (or grid points) you have Nx, Ny and Nz coefficients.

- Now, for DNS, it doesn't change anything. If you need, say, Nx points along x, you roughly need Nx coefficients; etc. In LES, you would use a lower Nx number of grid points; the same is true for spectral codes, as you would use a lower number of coefficients (as you can't solve for all the ones required). The specific feature of such approach with a spectral code is that it has an exact analytical counterpart, the spectral cut-off filter (which actually means that you only solve for a limited set of coefficients).

- a dissipative (convective) scheme is one whose truncation error resembles a viscous terms. Using a dissipative scheme amounts to do a computation with an added artificial viscosity

- a dissipative SGS model is an additional term you put in your equations, as a model for the missing scales. Its form is explicitly that of a viscous term, hence it is dissipative.

- When you filter a signal you are actually smoothing its behavior so that the signal variations are more gentle. The larger the cut-off length of the filter, the smoother will be the resulting filtered signal. Now, if you Fourier transform such signals (original and filtered), they will mostly differ by the energy content at the smallest scales (higher frequencies), it being lower for the smoothed filtered signal. By no way filtering, in itself, means removing information. It is more of a transformation that only in specific cases (spectral cut-off filter) leads to a reduction of the information in the signal.

[cfdmms]

Originally Posted by sbaffini

I don't know if it is possible for me to give you, at least, an overview of the topic. You should consult some book on these topics. However, very briefly (and roughly):

- in a spectral code you first assume your solution can be expressed as a truncated Fourier series (or any other suitable series), and then you solve for the coefficients of the series. Here you don't have the grid because, by definition, such series are good only for specific domains. For example, a Fourier series is only good for boxes with periodicity. As a consequence, instead of having Nx, Ny and Nz cells (or grid points) you have Nx, Ny and Nz coefficients.

- Now, for DNS, it doesn't change anything. If you need, say, Nx points along x, you roughly need Nx coefficients; etc. In LES, you would use a lower Nx number of grid points; the same is true for spectral codes, as you would use a lower number of coefficients (as you can't solve for all the ones required). The specific feature of such approach with a spectral code is that it has an exact analytical counterpart, the spectral cut-off filter (which actually means that you only solve for a limited set of coefficients).

- a dissipative (convective) scheme is one whose truncation error resembles a viscous terms. Using a dissipative scheme amounts to do a computation with an added artificial viscosity

- a dissipative SGS model is an additional term you put in your equations, as a model for the missing scales. Its form is explicitly that of a viscous term, hence it is dissipative.

- When you filter a signal you are actually smoothing its behavior so that the signal variations are more gentle. The larger the cut-off length of the filter, the smoother will be the resulting filtered signal. Now, if you Fourier transform such signals (original and filtered), they will mostly differ by the energy content at the smallest scales (higher frequencies), it being lower for the smoothed filtered signal. By no way filtering, in itself, means removing information. It is more of a transformation that only in specific cases (spectral cut-off filter) leads to a reduction of the information in the signal.

Dear sbaffini, Thanks for the reply and your valuable times. It clears lots of things.

[cfdmms]

Originally Posted by sbaffini

I don't know if it is possible for me to give you, at least, an overview of the topic. You should consult some book on these topics. However, very briefly (and roughly):

- in a spectral code you first assume your solution can be expressed as a .............

Dear Sbaffini, I have a query about the graphical representation of energy spectrum (energy Vs wavenumbers). For LES what sort of information is carried out by this graphical representation? And what is the procedure to plot this for LES?

Eagerly waiting to hear from you.

[sbaffini]

Dear MMS,

the main thing you should consider is that, by definition, LES is based on a separation of spatial scales among large and small ones. As a consequence, the spatial spectrum which is usually considered in LES is a direct representation of the energy content at the different scales, classified by wavenumbers in a Fourier basis.

What you want to know from this spectrum, when applied to your results, is how the energy content is effectively distributed among the scales. E.g., are you capturing an inertial range? Is the filter evident? Which scales are effectively damped? Which ones are correctly resolved? Some of this questions, of course, require a reference DNS to be properly answered.

The way this spectrum is computed is indeed very easy. Consider a channel flow. For each wall normal coordinate y, you have two directions, x and z, along which you can compute this spectrum. They are different as, say, along x you have the mean motion while along z you don't.

So let's say you go over x. For each y then you have Nz vectors of Nx components, where Nx and Nz are the number of discretization points along x and z respectively.
To compute the spectrum along x you would first do the FFT of each of the Nz vectors distributed along x. For each of these FFT you compute the spectrum as the coefficients times their conjugates (you have to refer to specific routines for the required ordination of such coefficients and the possible multiplicative constants).

After you have done such Nz spectra along x you simply average them, coefiicient by coefficient.

[cfdmms]

Dear Sbaffini, In POPEs book, in Large eddy simulation chapter there is a graphical representation (DELTA*G(r) Vs r/DELTA) (may be fig 13.1) of comparison of different filters (box, gaussian, sharp spectral).
What sort of information this graph carrying?
How its possible to be r/DELTA= some negetive values (like -4,-2)?

[cfdmms]

What is Commutation errors and Aliasing errors in LES?

[Sandeep lamba]

I am facing issues in setting LES for turbulent combustion modelling.

Actually initially the LES is running fine but later after some time the solution doesn't shows Eddies.

Please see my results contours and animation https://drive.google.com/file/...vsh...w?usp=drivesdk

https://drive.google.com/file/...bu_...w?usp=drivesdk

https://drive.google.com/file/...Yaq...w?usp=drivesdk

Please comment what I am missing in setting LES.

Kind regards