Proposed Changes

Give a brief overview of your contribution here in a few sentences.

• Improve axisymmetric source-term behavior near the symmetry axis by smoothly transitioning between the standard v/r formulation and a L’Hôpital-consistent ∂v/∂r formulation as r→0.
• Apply a L’Hôpital-consistent treatment for axisymmetric auxiliary gradient terms at the axis instead of zeroing them.

Related Work

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

• Addresses nonphysical behavior observed in axisymmetric stagnation-region solutions where the 1/r terms become singular near the axis. This PR was prepared for review/discussion with SU2 developers.
• The standard formulation is preserved away from the axis; the near-axis modification only affects the r→0 limit.

PR Checklist

Put an X by all that apply. You can fill this out after submitting the PR. If you have any questions, don't hesitate to ask! We want to help. These are a guide for you to know what the reviewers will be looking for in your contribution.

• I am submitting my contribution to the develop branch.
• My contribution generates no new compiler warnings (try with --warnlevel=3 when using meson).
• My contribution is commented and consistent with SU2 style (https://su2code.github.io/docs_v7/Style-Guide/).
• I used the pre-commit hook to prevent dirty commits and used pre-commit run --all to format old commits.
• I have added a test case that demonstrates my contribution, if necessary.
• I have updated appropriate documentation (Tutorials, Docs Page, config_template.cpp), if necessary.