Save additional node variables in SaveSolutionCallback

[DanielDoehring]

First attempt to save additional stuff in the solution callback. Not sure if the current implementation works for all cases already.

This could be extended to other quantities such as local Mach number, temperature, ...

[github-actions]

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[codecov]

Codecov Report

Attention: Patch coverage is 86.59794% with 13 lines in your changes missing coverage. Please review.

Project coverage is 96.69%. Comparing base (fdbc2dd) to head (a914f8e).
Report is 4 commits behind head on main.

Files with missing lines	Patch %	Lines
src/callbacks_step/save_solution_dg.jl	46.15%	7 Missing ⚠️
src/solvers/dg.jl	90.00%	2 Missing ⚠️
...4est_2d_dgsem/elixir_navierstokes_vortex_street.jl	94.12%	1 Missing ⚠️
examples/t8code_3d_dgsem/elixir_euler_ec.jl	91.67%	1 Missing ⚠️
...mples/tree_2d_dgsem/elixir_euler_blast_wave_amr.jl	92.86%	1 Missing ⚠️
examples/tree_2d_dgsem/elixir_euler_vortex_amr.jl	92.31%	1 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #2298      +/-   ##
==========================================
- Coverage   96.95%   96.69%   -0.26%     
==========================================
  Files         504      504              
  Lines       41721    41806      +85     
==========================================
- Hits        40448    40423      -25     
- Misses       1273     1383     +110     

Flag	Coverage Δ
unittests	96.69% <86.60%> (-0.26%)	⬇️

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[DanielDoehring]

Currently, the PR is somewhat inconsistent as for hyperbolic equations there is a dispatch based on the volume integral type, and for the parabolic equations we use an if-clause. This should be unified IMO.

[bennibolm]

In general, this looks good to me. Unfortunately, the correct export of the "limiting coefficient" is not CI tested extensively.
But, if you tested it locally and say it works properly, I'm fine with merging this after the one issue.

[DanielDoehring]

Maybe it also makes sense to add new functions get_derived_solution_variables ?

[DanielDoehring]

@JoshuaLampert could you maybe also take a look and leave your thoughts here?

[JoshuaLampert]

Thanks! I can image, this is a very useful feature. However, I would like to discuss the interface first, see my comment below.

[DanielDoehring]

I generalized the implementation such that now users can supply their own functions to be stored in the solution file.

I need to test the mpi-implementations, but from my side this is ready for review.

[bennibolm]

Looks very nice to me.

[bennibolm]

Suggested change

	Thus, in 1D this is a two integer tuple `indices = i, element`,
	in 2D a three integer tuple `indices = i, j, element`,
	and in 3D a four integer tuple `indices = i, j, k, element`.
	Thus, in 1D this is a two integer tuple `indices = (i, element)`,
	in 2D a three integer tuple `indices = (i, j, element)`,
	and in 3D a four integer tuple `indices = (i, j, k, element)`.

[DanielDoehring]

TODO: Change the if-clauses in the function get_node_variables! to really check for IDP and not only subcell vol integral (see also failing downstream tests)