scale similarity models and mixed models in OpenFOAM

backscatter · September 1, 2020, 04:52

HI all,

If anyone has had experience with implementation of dynamic mixed models in FOAM, please respond. I recently stumbled across such implementation of dynamic mixed smagorinksy by LEMOS,
https://github.com/LEMOS-Rostock/LEM...amicMixedModel

In the .C file, the authors have defined two filters- testFIlter_ and gridFilter_. If you look closely, you won't find any difference between the definitions of these two filters. Both are explicit filters. While we know that LES in FOAM is implicitly filtered LES, howcome the authors could be using an explicitly defined filter 'gridFilter_' to compute the quantities at the grid-level.
Any help/discussion is aprreciated.
Thanks.

clapointe · September 1, 2020, 17:54

For it to work the test filter is larger than the grid filter (and still in the inertial range). Presumably the filter size ratio is set in the case itself, as opposed to within the model (and the grid filter would be set to be the same size as the grid).

Caelan

backscatter · September 1, 2020, 21:36

Quote:

Originally Posted by clapointe

For it to work the test filter is larger than the grid filter (and still in the inertial range). Presumably the filter size ratio is set in the case itself, as opposed to within the model (and the grid filter would be set to be the same size as the grid).

Caelan

Thanks Caelan for your response. I doubt that is the case. It is not possible to filter anything at grid level explicitly in openfoam because if you look at the simpleFilter.C definition, you will find we can't define an explicit filter of width \delta. simpleFilter uses the interpolated values of the unfiltered variable from neighbor cells on the faces surrounding the cell, and then interpolates those face values on to the cell center, that in a sense is filtering with a width of 2\delta (the explicit test filter). To customize such an implementation for filtering at the grid level is not possible.
I think what they are doing is essentially applying the test filter twice, which is pretty much justifiable. Essentially to write,

$\tau_{ij} = \overline{\overline{u}_i \overline{u}_j} - \overline{\overline{u}}_i \overline{\overline{u}}_j$

for the second bar filter (which is supposed to represent the grid filter), they may be using a filter of larger width.
The second bar above the velocity components in the equation represents a second filter at a scale γΔ, where γ ≥ 1. The original model by Bardina used γ =1 while Liu et al. used γ = 2.
It is not wrong to do it but the authors have not mentioned it clearly in the model.

clapointe · September 1, 2020, 21:57

In my experience the test filter should be about double the actual/grid filter. And taking a look at their code I agree that the filter is applied twice to obtain the test-filtered velocity field. So this appears to implicitly incorporate the factor of 2 for (at least) the simple filter as you've noted. As for the grid-filter scale that's a different problem, but it's worth noting they have a variety of custom filters also in the repo.

Caelan

Santiago · September 2, 2020, 10:21

Quote:

Originally Posted by backscatter

HI all,

If anyone has had experience with implementation of dynamic mixed models in FOAM, please respond. I recently stumbled across such implementation of dynamic mixed smagorinksy by LEMOS,
https://github.com/LEMOS-Rostock/LEM...amicMixedModel

In the .C file, the authors have defined two filters- testFIlter_ and gridFilter_. If you look closely, you won't find any difference between the definitions of these two filters. Both are explicit filters. While we know that LES in FOAM is implicitly filtered LES, howcome the authors could be using an explicitly defined filter 'gridFilter_' to compute the quantities at the grid-level.
Any help/discussion is aprreciated.
Thanks.

I have made a thorough discussion of some mathematical inconsistencies in the smagorinsky LES models present in OF, plus I have proposed a lagrangian mixed model here:

HTML Code:

https://www.mdpi.com/2311-5521/4/3/171

I hope it offers clarity to your questions.

SIDE NOTE: the convolution model used in the LEMOS package (last time I checked, 4 years ago) is mathematically inconsistent (the Bardina model), in the sense that is not exactly a deconvolution but a truncated taylor expansion.

backscatter · September 2, 2020, 21:21

Quote:

Originally Posted by Santiago

I have made a thorough discussion of some mathematical inconsistencies in the smagorinsky LES models present in OF, plus I have proposed a lagrangian mixed model here:

HTML Code:

https://www.mdpi.com/2311-5521/4/3/171

I hope it offers clarity to your questions.

SIDE NOTE: the convolution model used in the LEMOS package (last time I checked, 4 years ago) is mathematically inconsistent (the Bardina model), in the sense that is not exactly a deconvolution but a truncated taylor expansion.

Thank you Santiago for your reply. Yes, I happened to find your paper on Mixed Lagragian model in openfoam a couple of days ago. Since you seem to have implemented the mixed lagragian model in FOAM, I still have the same question, in openfoam, how do you implement the scale-similar (SS) terms $\tau^{SS}_{ij} = \overline{\overline{u}_i \overline{u}_j} - \overline{\overline{u}}_i \overline{\overline{u}}_j$ in the expression of the mixed model at grid and test filter level?
If you have the source code of your mixed lagragian model handy, it would be great if you share it.
Any insights are appreciated. Thank you!

Santiago · September 3, 2020, 05:02

Quote:

Originally Posted by backscatter

Thank you Santiago for your reply. Yes, I happened to find your paper on Mixed Lagragian model in openfoam a couple of days ago. Since you seem to have implemented the mixed lagragian model in FOAM, I still have the same question, in openfoam, how do you implement the scale-similar (SS) terms $\tau^{SS}_{ij} = \overline{\overline{u}_i \overline{u}_j} - \overline{\overline{u}}_i \overline{\overline{u}}_j$ in the expression of the mixed model at grid and test filter level?
If you have the source code of your mixed lagragian model handy, it would be great if you share it.
Any insights are appreciated. Thank you!

All variables are assumed to be filtered in the context of finite volumes, and LES, by virtue of the Schumman hypothesis. The first thing that needs clarification is this "myth" that Openfoam implicitly filters: This has nothing to do with OF, it's an assumption made once you make use of the midpoint rule.

That being said, you need to apply a grid-level filter ONCE, to the residual stress tensor's terms.

backscatter · September 3, 2020, 05:21

Quote:

Originally Posted by Santiago

All variables are assumed to be filtered in the context of finite volumes, and LES, by virtue of the Schumman hypothesis. The first thing that needs clarification is this "myth" that Openfoam implicitly filters: This has nothing to do with OF, it's an assumption made once you make use of the midpoint rule.

That being said, you need to apply a grid-level filter ONCE, to the residual stress tensor's terms.

Yes, it is essentially the FV discretization that accounts for the 'implicit' grid filter in all of the FV codes, including OF. Nothing special about FOAM here, I agree.
When you say, I need to apply the grid-filter once to the tensors' terms, how is that possible because we don't have an explicit grid-filter. The top-hat filter that we have is an explicit (test) filter of twice the width of the grid size.
For clarity, a term like $\widehat{\overline{u}_i \overline{u}_j}$ can be implemented as

Code:

filter_( U() * U() )

.
Now, if we have a term like $\overline{\overline{u}_i \overline{u}_j}$ (which is one of the terms present in the scale-similar part of your mixed model at the grid level), how do we go about implementing it in FOAM?

Santiago · September 3, 2020, 06:25

Quote:

Originally Posted by backscatter

Yes, it is essentially the FV discretization that accounts for the 'implicit' grid filter in all of the FV codes, including OF. Nothing special about FOAM here, I agree.
When you say, I need to apply the grid-filter once to the tensors' terms, how is that possible because we don't have an explicit grid-filter. The top-hat filter that we have is an explicit (test) filter of twice the width of the grid size.
For clarity, a term like $\widehat{\overline{u}_i \overline{u}_j}$ can be implemented as

Code:

filter_( U() * U() )

.
Now, if we have a term like $\overline{\overline{u}_i \overline{u}_j}$ (which is one of the terms present in the scale-similar part of your mixed model at the grid level), how do we go about implementing it in FOAM?

1.
Nothing stops you to use/implement a filter with a kernel size equal to the grid size. Depending on the filter, this size may need to be defined explicitely. The simpleFilter, as an example, is only valid as a grid filter, not as test filter, because the kernel (the ball) is direct function of the size of the filter; that means, the bigger the filter size more "points" have to be used for averaging. The germano type of filters may offer a better approach to filtering in hexahedral grids.

2. Exactly the same as you present in your CODE, but in each case you have to use a different filter:

Code:

gridFilter_( U() * U() )

or

Code:

testFilter_( U() * U() )

.

Is up to the user to define the correct filter using dictionaries.

About the code: I share the code on a P2P basis, I don't fully release it to the general public. PM me, and we may discuss it further.

backscatter · September 3, 2020, 19:56

Quote:

Originally Posted by Santiago

1.
Nothing stops you to use/implement a filter with a kernel size equal to the grid size. Depending on the filter, this size may need to be defined explicitely. The simpleFilter, as an example, is only valid as a grid filter, not as test filter, because the kernel (the ball) is direct function of the size of the filter; that means, the bigger the filter size more "points" have to be used for averaging. The germano type of filters may offer a better approach to filtering in hexahedral grids.

2. Exactly the same as you present in your CODE, but in each case you have to use a different filter:

Code:

gridFilter_( U() * U() )

or

Code:

testFilter_( U() * U() )

.

Is up to the user to define the correct filter using dictionaries.

About the code: I share the code on a P2P basis, I don't fully release it to the general public. PM me, and we may discuss it further.

Dear Santiago,

Thank you for your responses. I have messaged you.
Thanks

September 1, 2020, 04:52	scale similarity models and mixed models in OpenFOAM	#1
backscatter Member Anonymous Join Date: Aug 2016 Posts: 75 Rep Power: 10	HI all, If anyone has had experience with implementation of dynamic mixed models in FOAM, please respond. I recently stumbled across such implementation of dynamic mixed smagorinksy by LEMOS, https://github.com/LEMOS-Rostock/LEM...amicMixedModel In the .C file, the authors have defined two filters- testFIlter_ and gridFilter_. If you look closely, you won't find any difference between the definitions of these two filters. Both are explicit filters. While we know that LES in FOAM is implicitly filtered LES, howcome the authors could be using an explicitly defined filter 'gridFilter_' to compute the quantities at the grid-level. Any help/discussion is aprreciated. Thanks.

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September 1, 2020, 17:54		#2
clapointe Senior Member Join Date: Aug 2015 Posts: 494 Rep Power: 15	For it to work the test filter is larger than the grid filter (and still in the inertial range). Presumably the filter size ratio is set in the case itself, as opposed to within the model (and the grid filter would be set to be the same size as the grid). Caelan

September 1, 2020, 21:57		#4
clapointe Senior Member Join Date: Aug 2015 Posts: 494 Rep Power: 15	In my experience the test filter should be about double the actual/grid filter. And taking a look at their code I agree that the filter is applied twice to obtain the test-filtered velocity field. So this appears to implicitly incorporate the factor of 2 for (at least) the simple filter as you've noted. As for the grid-filter scale that's a different problem, but it's worth noting they have a variety of custom filters also in the repo. Caelan