1D Linearized Euler

[DanielDoehring]

This adds the linearized Euler equations in 1D. This comes with 3 examples: The usual convergence test, a somewhat nontrivial example with walls and an elixir that illustrates the computation of the analytical solution using the eigensystem.

[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.

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.

[codecov[bot]]

Codecov Report

Attention: Patch coverage is 83.75000% with 13 lines in your changes are missing coverage. Please review.

Project coverage is 74.79%. Comparing base (641fde8) to head (10a2d72).

Files	Patch %	Lines
src/equations/linearized_euler_1d.jl	76.60%	11 Missing :warning:
...em/elixir_linearizedeuler_characteristic_system.jl	93.10%	2 Missing :warning:

Additional details and impacted files

```diff @@ Coverage Diff @@ ## main #1867 +/- ## =========================================== - Coverage 96.32% 74.79% -21.54% =========================================== Files 445 448 +3 Lines 35926 35947 +21 =========================================== - Hits 34605 26883 -7722 - Misses 1321 9064 +7743 ``` | [Flag](https://app.codecov.io/gh/trixi-framework/Trixi.jl/pull/1867/flags?src=pr&el=flags&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=trixi-framework) | Coverage Δ | | |---|---|---| | [unittests](https://app.codecov.io/gh/trixi-framework/Trixi.jl/pull/1867/flags?src=pr&el=flag&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=trixi-framework) | `74.79% <83.75%> (-21.54%)` | :arrow_down: | Flags with carried forward coverage won't be shown. [Click here](https://docs.codecov.io/docs/carryforward-flags?utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=trixi-framework#carryforward-flags-in-the-pull-request-comment) to find out more.

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[DanielDoehring]

Thanks @lchristm for your review!

[DanielDoehring]

Thanks @andrewwinters5000 for the review! The CI failures are solely due to codevov, so this should also be ready to merge.

[andrewwinters5000]

@lchristm Are we good to merge?

[lchristm]

@andrewwinters5000 Yes, looks good to me! Thanks again for adding this feature, @DanielDoehring

[andrewwinters5000]

The only failures are from CodeCov strangeness, is it okay to merge this @sloede @ranocha ?

[ranocha]

Yes. Thanks!