CST leading and trailing edge fixes and improvements

[sseraj]

Purpose

I made a few fixes and improvements to how the CST implementation handles leading and trailing edges:

1. Fixed the shape function coefficient fitting by subtracting the linear trailing edge thickness function from the y-coordinates before the least-squares solution
2. Tracked the upper and lower surface trailing edge y-coordinates separately. Some CST implementations only use one thickness variable, but tracking the upper and lower surfaces separately is more general and is consistent with the implementation in ESP.
3. Split the upper and lower surfaces for the CST fit based on LE and TE location instead of the spline projection method in _splitUpperLower. _splitUpperLower associates each point with either the upper or lower surface. This makes sense for addPointSet calls but not for the CST fit. When the airfoil has a single LE point or a sharp TE, those points should be included in both the upper and lower surfaces. This change ensures that symmetric airfoils have symmetric CST coefficients.
4. Fixed the chord normalization for calls to computeCSTCoordinates in the fit error check and in test_fitCST
5. Added trailing edge thickness arguments to plotCST

Expected time until merged

Not urgent, 2-3 weeks would be nice

Type of change

• [x] Bugfix (non-breaking change which fixes an issue)
• [ ] New feature (non-breaking change which adds functionality)
• [x] Breaking change (non-backwards-compatible fix or feature)
• [ ] Code style update (formatting, renaming)
• [ ] Refactoring (no functional changes, no API changes)
• [ ] Documentation update
• [ ] Maintenance update
• [ ] Other (please describe)

Testing

To verify the code changes, I:

1. Changed the existing trailing edge thickness tests to check the upper and lower surface y-coordinates
2. Added tests that check that coefficients for symmetric airfoils are symmetric (including symmetric airfoils with one LE point)
3. Verified the CST fit against the Kulfan class in pyESP and added regression tests for the coefficients (the reference is still DVGeometryCST)

Here is an example of how the CST coefficients change with this PR (for a NACA 0012 airfoil with leading edge at 0,0). The fit error computed by the internal check is lower, the upper and lower surface coefficients are symmetric, and the coefficients match pyESP.

naca0012_zeroLE.dat on main branch

Upper surface
    L2 norm of coordinates in dat file versus fit coordinates: 0.0006331960041569371
    Fit CST coefficients: [0.17289704 0.15522273 0.16084008 0.1639404  0.10807389 0.19881113
 0.08805734 0.19614525]
Lower surface
    L2 norm of coordinates in dat file versus fit coordinates: 0.0006288295041572267
    Fit CST coefficients: [-0.17253255 -0.15627056 -0.1586615  -0.16706265 -0.1049002  -0.20109143
 -0.08692161 -0.19651448]

naca0012_zeroLE.dat on PR branch

Upper surface
    L2 norm of coordinates in dat file versus fit coordinates: 3.476089168663822e-05
    Fit CST coefficients: [0.17309584 0.15072331 0.17568197 0.12476168 0.1680704  0.1238723
 0.14725536 0.13902121]
Lower surface
    L2 norm of coordinates in dat file versus fit coordinates: 3.4760891686639015e-05
    Fit CST coefficients: [-0.17309584 -0.15072331 -0.17568197 -0.12476168 -0.1680704  -0.1238723
 -0.14725536 -0.13902121]

naca0012_zeroLE.dat with pyESP

Upper surface coefficients [0.17309583808521334 0.15072330799759134 0.17568197194146518 0.12476168056503996 
0.1680704011542561 0.12387230726234683 0.14725535540361023 0.1390212120520205] dimensionless

Lower surface coefficients [-0.17309583807638124 -0.1507233079536379 -0.17568197237881203 -0.12476167919329707 
-0.16807040351349162 -0.12387230471899825 -0.14725535719212318 -0.13902121124037606] dimensionless

Checklist

• [x] I have run flake8 and black to make sure the Python code adheres to PEP-8 and is consistently formatted
• [ ] I have formatted the Fortran code with fprettify or C/C++ code with clang-format as applicable
• [x] I have run unit and regression tests which pass locally with my changes
• [x] I have added new tests that prove my fix is effective or that my feature works
• [ ] I have added necessary documentation

[codecov[bot]]

Codecov Report

Attention: Patch coverage is 96.00000% with 2 lines in your changes missing coverage. Please review.

Project coverage is 65.42%. Comparing base (3471013) to head (0a099fa). Report is 5 commits behind head on main.

Files with missing lines	Patch %	Lines
pygeo/parameterization/DVGeoCST.py	95.91%	2 Missing :warning:

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #252      +/-   ##
==========================================
+ Coverage   65.35%   65.42%   +0.06%     
==========================================
  Files          47       47              
  Lines       12286    12307      +21     
==========================================
+ Hits         8030     8052      +22     
+ Misses       4256     4255       -1     

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[eytanadler]

Is this ready to go and/or be reviewed by others?

[sseraj]

Is this ready to go and/or be reviewed by others?

Yes, this is ready for both

[sseraj]

Thanks for the reviews!