Add function to calculate optimal CFL number for PERK2 integrator and related updates

[warisa-r]

This PR introduces a new function to compute the optimal CFL number based on the optimal time step for the PairedExplicitRK2 (PERK2) integrator.

• Added dt_opt as a new attribute of PairedExplicitRK2 to store the optimal time step.
• Implemented calculate_cfl function to compute the CFL number from the optimal time step.
• Created a new example demonstrating how to use the calculate_cfl function with the PERK2 integrator.
• Added a test to validate the new example showing the usage of the calculate_cfl function with the PERK2 integrator.

TODO:

• Update the values in the test to match the ones in CI workflow.

Please let me know if there are any suggestions or improvements!

[github-actions]

Review checklist

This checklist is meant to assist creators of PRs (to let them know what reviewers will typically look for) and reviewers (to guide them in a structured review process). Items do not need to be checked explicitly for a PR to be eligible for merging.

Purpose and scope

• The PR has a single goal that is clear from the PR title and/or description.
• All code changes represent a single set of modifications that logically belong together.
• No more than 500 lines of code are changed or there is no obvious way to split the PR into multiple PRs.

Code quality

• The code can be understood easily.
• Newly introduced names for variables etc. are self-descriptive and consistent with existing naming conventions.
• There are no redundancies that can be removed by simple modularization/refactoring.
• There are no leftover debug statements or commented code sections.
• The code adheres to our conventions and style guide, and to the Julia guidelines.

Documentation

• New functions and types are documented with a docstring or top-level comment.
• Relevant publications are referenced in docstrings (see example for formatting).
• Inline comments are used to document longer or unusual code sections.
• Comments describe intent ("why?") and not just functionality ("what?").
• If the PR introduces a significant change or new feature, it is documented in NEWS.md with its PR number.

Testing

• The PR passes all tests.
• New or modified lines of code are covered by tests.
• New or modified tests run in less then 10 seconds.

Performance

• There are no type instabilities or memory allocations in performance-critical parts.
• If the PR intent is to improve performance, before/after time measurements are posted in the PR.

Verification

• The correctness of the code was verified using appropriate tests.
• If new equations/methods are added, a convergence test has been run and the results
  are posted in the PR.

Created with ❤️ by the Trixi.jl community.

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 96.34%. Comparing base (288d41d) to head (9ab373d).
Report is 1 commits behind head on main.

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #2077      +/-   ##
==========================================
+ Coverage   96.32%   96.34%   +0.02%     
==========================================
  Files         470      470              
  Lines       37485    37494       +9     
==========================================
+ Hits        36106    36121      +15     
+ Misses       1379     1373       -6     

Flag	Coverage Δ
unittests	96.34% <100.00%> (+0.02%)	⬆️

Flags with carried forward coverage won't be shown. Click here to find out more.

☔ View full report in Codecov by Sentry.
📢 Have feedback on the report? Share it here.

[ranocha]

This changed the interface here since it requires an additional argument, so it is a breaking change. Is this stuff declared as experimental so that we can just do it?

[DanielDoehring]

Yeah, I somehow forgot that I added the breaking label. We should revert this and merge with 0.9. #1997

[warisa-r]

Would you like me to open this PR again?

[DanielDoehring]

Would you like me to open this PR again?

Yes, sorry for this hazzle! My bad.