Update to OrdinaryDiffEq.jl v7 and related SciML packages

[github-actions]

This pull request changes the compat entry for the RecursiveArrayTools package from 3.37 to 3.37, 4.
This keeps the compat entries for earlier versions.

Note: I have not tested your package with this new compat entry.
It is your responsibility to make sure that your package tests pass before you merge this pull request.

Closes #2918, closes #2919, closes #2949, closes #2950, closes #2960, closes #2961, closes #2962, closes #2963, closes #2965, closes #2966, closes #2967, closes #2968, closes #2969, closes #2970, closes #2971, closes #2972, closes #2973, closes #2981, closes #2983, closes #2984.

Also closes #2938 and closes #2941.

The required changes, which keep backwards compatibility with older versions from the SciML ecosystem are:

• Replacing u_modified! by derivative_discontinuity!. Done in Replace u_modified! by derivative_discontinuity! #2996.
• Stage limiters are not allowed anymore as positional arguments, but need to be keyword arguments. Done in Make stage_limiter! a kwarg #2995.
• Iterating over a VectorOfArray of SVectors now returns the underlying floating values, not the SVector, fixed by replacing u by parent(u)
• thread is now passed as FastBroadcast.Serial()/FastBroadcast.Threaded() instead of True()/False(). Done in Replace Trixi.True() by Trixi.Threaded() #2997.
• Changing a few sol.destats to sol.stats (sol.destats is already deprecated from some time and we changed almost all occurrences already in follow SciMLBase update destats -> stats #1372). Done in Replace deprecated destats by stats #2994.
• Adapting the new controller interface for loading and saving the controller (now in an extension for OrdinaryDiffEqCore.jl)
• The PIDController constructor, which only accepts beta1, beta2, beta3, has (accidentally) another default value for (the algorithm dependent) qsteady_max. We can go back to the previous behavior by also passing the ode algorithm to the constructor of the PIDController. See below for a discussion about this.
• Changing a reference value due to Fix spurious tiny final step for fixed-dt methods SciML/OrdinaryDiffEq.jl#3441

Note that I used Claude to help me with refactoring some parts, but I reviewed the code and adapted it.

[codecov]

Codecov Report

❌ Patch coverage is 48.14815% with 28 lines in your changes missing coverage. Please review.
✅ Project coverage is 97.08%. Comparing base (2e5ed0b) to head (d624e9e).

Files with missing lines	Patch %	Lines
ext/TrixiOrdinaryDiffEqCoreExt.jl	33.33%	24 Missing ⚠️
src/callbacks_step/save_restart.jl	63.64%	4 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #2910      +/-   ##
==========================================
- Coverage   97.13%   97.08%   -0.06%     
==========================================
  Files         625      626       +1     
  Lines       48514    48557      +43     
==========================================
+ Hits        47122    47137      +15     
- Misses       1392     1420      +28     

Flag	Coverage Δ
unittests	97.08% <48.15%> (-0.06%)	⬇️

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.

🚀 New features to boost your workflow:

• ❄️ Test Analytics: Detect flaky tests, report on failures, and find test suite problems.

[JoshuaLampert]

Needs dependencies like SummationByPartsOperators.jl to be updated first.

[JoshuaLampert]

We need jlchan/StartUpDG.jl#219 to be merged and released before.

[JoshuaLampert]

Finally, we probably still want to figure out why elixir_advection_restart_amr.jl has a slightly different result. I can try to find that out.

I bisected this discrepancy to this PR: SciML/OrdinaryDiffEq.jl#3441, which first landed in OrdinaryDiffEqCore.jl v3.33.0. Using the commit directly before that PR:

julia> include("examples/tree_2d_dgsem/elixir_advection_restart_amr.jl");
[...]
julia> analysis_callback(sol)
(l2 = [8.018497923389368e-5], linf = [0.0007307237754662355])

(run_v3_32) pkg> st
Status `~/.julia/dev/Trixi/run_v3_32/Project.toml`
  [7d9f7c33] Accessors v0.1.44
  [bbf590c4] OrdinaryDiffEqCore v3.32.0 `https://github.com/SciML/OrdinaryDiffEq.jl.git:lib/OrdinaryDiffEqCore#97f41902`
⌃ [b0944070] OrdinaryDiffEqLowStorageRK v1.15.0
  [a7f1ee26] Trixi v0.16.8-DEV `..`
Info Packages marked with ⌃ have new versions available and may be upgradable.

With the commit from the PR:

julia> include("examples/tree_2d_dgsem/elixir_advection_restart_amr.jl");
[...]
julia> analysis_callback(sol)
(l2 = [8.018498574373939e-5], linf = [0.0007307237754662355])

(run_v6) pkg> st
Status `~/.julia/dev/Trixi/run_v6/Project.toml`
  [7d9f7c33] Accessors v0.1.44
  [bbf590c4] OrdinaryDiffEqCore v3.32.0 `https://github.com/SciML/OrdinaryDiffEq.jl.git:lib/OrdinaryDiffEqCore#1864296`
⌃ [b0944070] OrdinaryDiffEqLowStorageRK v1.15.0
  [a7f1ee26] Trixi v0.16.8-DEV `..`
Info Packages marked with ⌃ have new versions available and may be upgradable.

These L2-error values are exactly the two values in https://github.com/trixi-framework/Trixi.jl/pull/2910/changes#diff-0d913e7961860bd3a9c595d68dbd7a7b09ea17758afc8c814b9e45a454a04796R77. So this has nothing to do with restarting, controllers, or the v7 updates of the SciML packages, but is simply a coincidence. It didn't surface before since we currently restrict OrdinaryDiffEqCore.jl to v3.31. Looking at the changes of that PR, I think we can simply use the new value. Do you agree, @ranocha?

[JoshuaLampert]

Coverage reports are relatively bad with this PR, but that is expected because there are some error messages, which are not covered and the OrdinaryDiffEqCore.jl <v4 paths are not reported to be covered by codecov and coveralls because they are only covered by the Downgrade job, which does not contribute to the coverage reports since it is in a different actions file. I double-checked that the downgrade job indeed goes into the methods it should by introducing debug statements.

[vchuravy]

Are there any changes that would make sense to pull out into its own PR? I wish stacked PRs would be in general availability https://github.github.com/gh-stack/

[JoshuaLampert]

Yes, I think we could if it helps reviewing since many changes are related to fixing deprecations, but it would also be a bit of work to split the PR manually now.

[ranocha]

Finally, we probably still want to figure out why elixir_advection_restart_amr.jl has a slightly different result. I can try to find that out.

I bisected this discrepancy to this PR: SciML/OrdinaryDiffEq.jl#3441, which first landed in OrdinaryDiffEqCore.jl v3.33.0. Using the commit directly before that PR:

julia> include("examples/tree_2d_dgsem/elixir_advection_restart_amr.jl");
[...]
julia> analysis_callback(sol)
(l2 = [8.018497923389368e-5], linf = [0.0007307237754662355])

(run_v3_32) pkg> st
Status `~/.julia/dev/Trixi/run_v3_32/Project.toml`
  [7d9f7c33] Accessors v0.1.44
  [bbf590c4] OrdinaryDiffEqCore v3.32.0 `https://github.com/SciML/OrdinaryDiffEq.jl.git:lib/OrdinaryDiffEqCore#97f41902`
⌃ [b0944070] OrdinaryDiffEqLowStorageRK v1.15.0
  [a7f1ee26] Trixi v0.16.8-DEV `..`
Info Packages marked with ⌃ have new versions available and may be upgradable.

With the commit from the PR:

julia> include("examples/tree_2d_dgsem/elixir_advection_restart_amr.jl");
[...]
julia> analysis_callback(sol)
(l2 = [8.018498574373939e-5], linf = [0.0007307237754662355])

(run_v6) pkg> st
Status `~/.julia/dev/Trixi/run_v6/Project.toml`
  [7d9f7c33] Accessors v0.1.44
  [bbf590c4] OrdinaryDiffEqCore v3.32.0 `https://github.com/SciML/OrdinaryDiffEq.jl.git:lib/OrdinaryDiffEqCore#1864296`
⌃ [b0944070] OrdinaryDiffEqLowStorageRK v1.15.0
  [a7f1ee26] Trixi v0.16.8-DEV `..`
Info Packages marked with ⌃ have new versions available and may be upgradable.

These L2-error values are exactly the two values in https://github.com/trixi-framework/Trixi.jl/pull/2910/changes#diff-0d913e7961860bd3a9c595d68dbd7a7b09ea17758afc8c814b9e45a454a04796R77. So this has nothing to do with restarting, controllers, or the v7 updates of the SciML packages, but is simply a coincidence. It didn't surface before since we currently restrict OrdinaryDiffEqCore.jl to v3.31. Looking at the changes of that PR, I think we can simply use the new value. Do you agree, @ranocha?

Thanks for debugging this! I agree that we can modify the value in this case.

[JoshuaLampert]

Can this be reverted again now that #2993 has been merged, @vchuravy?