[WIP] Implementation of Amplification Factor Transport(AFT) 2019b tranistion model

[sun5k]

Proposed Changes

Hi, all.

This PR is for implementing well known subsonic transition model (SA-AFT2019b).

Coder's SA-AFT2019b model is composed of the amplification factor and the logarithmic intermittency transport equation as shown below.

Current State

The primary implementation of the model has been completed and is now in the validation. The validation problems are refer : https://doi.org/10.2514/6.2023-3530 and https://doi.org/10.2514/6.2019-0039.

The transition onset location and the amplification factor field are slightly different. I'm still debugging and checking various things.

Validation Problem of Current State

Firstly, I'm trying the validation problem for 2-D problems (flat plate and NLF-0416 airfoil). The current results are shown below.

S&K Flat plate from https://doi.org/10.2514/6.2023-3530

NLF-0416 airfoil from https://doi.org/10.2514/6.2023-3530

PR Checklist

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• [ ] I have added a test case that demonstrates my contribution, if necessary.
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[sun5k]

Thanks 👍 Looks good but we can re-use a lot of code from the LM solver and see the question about the aux var gradient which looks suspicious.

Thank you for comment @pcarruscag. I'll try to address each of your comments one by one.

For now, the SA-AFT2017b model is for testing purposes, so I'll delete the relevant parts.

[sun5k]

The original plan was to finish it before the new version (v8.2.0) was released, but I was busy and couldn't manage it. Now that I have some spare time, I'll start working on it again next week!