Add 3D multi-ion GLM-MHD equations for the TreeMesh solver

[amrueda]

This PR introduces the 3D multi-ion GLM-MHD equations. The implementation closely follows the 2D implementation (#2196), with the main difference being the inclusion of fluxes, non-conservative terms, and wave speeds for orientation == 3.

[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

Attention: Patch coverage is 99.65217% with 2 lines in your changes missing coverage. Please review.

Project coverage is 96.42%. Comparing base (f09a707) to head (0e4b390).

Files with missing lines	Patch %	Lines
src/equations/ideal_glm_mhd_multiion_3d.jl	99.65%	2 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #2215      +/-   ##
==========================================
+ Coverage   96.37%   96.42%   +0.05%     
==========================================
  Files         486      487       +1     
  Lines       39186    39761     +575     
==========================================
+ Hits        37764    38337     +573     
- Misses       1422     1424       +2     

Flag	Coverage Δ
unittests	96.42% <99.65%> (+0.05%)	⬆️

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.

[DanielDoehring]

Impressive work! I really do not want to imagine debugging this 💀 :D

[DanielDoehring]

Does it make sense to extract this, i.e.,

2^(k - 1) * (1 - 2) / (1 - 2^ncomponents(equations)) * rho

into an own variable with a descriptive name such that one has an idea what is going on here?

[DanielDoehring]

This is a little inconsistent as there is v_mag but no B_mag.