Provide document of numeric types and type stability

[huiyuxie]

Covers #1909. It is just a start and later I will add more documentation.

[github-actions[bot]]

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 :heart: by the Trixi.jl community.

[huiyuxie]

Please check again now :)

First, please check style, I try to keep consistency with the rest of the convention file. Second, concerning content, I think handling these cases on a case-by-case basis is acceptable for now (but I have no idea if this is good for other developers). Third, I suggest asking someone unfamiliar with these things to review it again. While you understand it clearly, it may not be as easy for others to grasp.

[huiyuxie]

Shall we merge this PR if it looks good to you, or should it be held until the main PR is ready to merge?

I think I should check the main PR again based on your provided notes. Please wait

[huiyuxie]

Thanks, these are good suggestions!