fix TS adjoint

[SichengHe]

Purpose

Fix the time spectral (TS) adjoint, which was completely broken because the case (timeSpectral) block in initres_block (src/solver/residuals.F90) was wrapped inside #ifndef USE_TAPENADE, so Tapenade never generated adjoint code for the spectral time derivative terms. The generated AD code only handled case (steady), completely missing the TS contributions.

Changes:

• Exposed case (timeSpectral) in residuals.F90 to Tapenade by moving the #endif boundary, with #ifdef USE_TAPENADE blocks to replace pointer access with direct flowDoms array access (required since Tapenade cannot differentiate through Fortran pointers)
• Added reverse mode adjoint for TS in residuals_b.f90
• Added forward mode tangent for TS in residuals_d.f90
• Added state-only reverse mode for TS in residuals_fast_b.f90
• Added test script tests/test_ts_adjoint.py for verification

Expected time until merged

Non-urgent. A week or two is fine.

Type of change

• Bugfix (non-breaking change which fixes an issue)
• New feature (non-breaking change which adds functionality)
• 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

Run with 2 MPI ranks on the NACA 64A010 Euler time spectral case (3 time intervals, pitching oscillation):
mpirun -np 2 python tests/test_ts_adjoint.py

Three tests are performed:

1. Dot product test (forward vs backward consistency): relative error = 1.06e-15 (machine precision)
2. Forward AD vs finite difference: residual derivative relative error = 4.03e-05; function derivatives (cl, cd, cmz) match to 1e-7 — 1e-8
3. Adjoint sensitivity (evalFunctionsSens): all three adjoint solves (cd, cl, cmz) converge

Checklist

• I have run ruff check and ruff format 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
• I have run unit and regression tests which pass locally with my changes
• I have added new tests that prove my fix is effective or that my feature works
• I have added necessary documentation

[A-CGray]

Thanks for these fixes @SichengHe , can you please update your tests to use ADflow's existing RegTest class. See this file for an example.

Also, which version of Tapenade did you use to generate the new derivative code? I think the failing Tapenade check is probably due to a version mismatch, the test uses 3.16

[A-CGray]

Please put this file in the reg_tests directory

[A-CGray]

Shouldn't need this once file is moved

[SichengHe]

should be all good now.
Thanks for all the feedback! They are very helpful.

[SichengHe]

@A-CGray