SA 2D axisymmetric source terms

[Corentinthomee]

Proposed Changes

Give a brief overview of your contribution here in a few sentences.
Additional source terms in the SA turbulence model have been added for the axisymmetric formulation.

In the baseline model, the only term that has an impact is:

Rewriting it in cylindrical coordinates, an additional source term is obtained:

In the Negative variant of the model, this source varies slightly due to the presence of $f_n$:

The compressibility correction also requires a new source. Rewriting

in cylindrical coordinates yields the new source

For the other model variants, it looks like the modification of strain magnitude (done for SST) takes care of the differences, but I might be mistaken.

Related Work

Resolve any issues (bug fix or feature request), note any related PRs, or mention interactions with the work of others, if any.
#1565

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• I am submitting my contribution to the develop branch.
• My contribution generates no new compiler warnings (try with --warnlevel=3 when using meson).
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• I have added a test case that demonstrates my contribution, if necessary.
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[bigfooted]

Great, we needed this! Do you have a testcase that we can use as a regression test to add to the PR?

[Corentinthomee]

I'm thinking about reusing the SST test case (axisymmetric_rans/air_nozzle) so that the same mesh can be used. Would that be fine ?

[bigfooted]

I'm thinking about reusing the SST test case (axisymmetric_rans/air_nozzle) so that the same mesh can be used. Would that be fine ?

That's a quite specific testcase. How did you test the implementation? Do you have some simple results for the turbulent axisymmetric jet? We know that the results for round jets are not super good for standard SA, but at least we know what the result should look like, here on p.32 - 35 they test SA for the round jet and compare to the Wygnanski & Fiedler measurements:
https://www.researchgate.net/publication/24296213_Turbulence_Modeling_Validation_Testing_and_Development

The domain is just a rectangle so pretty simple to set up.

You could also use the V&V test that we have, but it is a variable density jet:
https://su2code.github.io/vandv/SANDIA_jet/

[pcarruscag]

Nice work 👍 clean code

[pcarruscag]

Is it worth including the contribution to the Jacobian?

[Corentinthomee]

I'm thinking about reusing the SST test case (axisymmetric_rans/air_nozzle) so that the same mesh can be used. Would that be fine ?

That's a quite specific testcase. How did you test the implementation? Do you have some simple results for the turbulent axisymmetric jet? We know that the results for round jets are not super good for standard SA, but at least we know what the result should look like, here on p.32 - 35 they test SA for the round jet and compare to the Wygnanski & Fiedler measurements: https://www.researchgate.net/publication/24296213_Turbulence_Modeling_Validation_Testing_and_Development

The domain is just a rectangle so pretty simple to set up.

You could also use the V&V test that we have, but it is a variable density jet: https://su2code.github.io/vandv/SANDIA_jet/

I did some tests on a supersonic jet, since I already had the files, but it's a quite complex case so it's not that good to verify the implementation. I will look into the simpler cases you mentioned !

[bigfooted]

Any update on a testcase to add to the PR?

[Corentinthomee]

Sorry, I have been quite busy the past few weeks.
I will try to get it done in the next few days.