Make volume integrals, indicators, etc dimension agnostic

[DanielDoehring]

Probably due to historical debt, the volume integrals have been implemented for every dimension. There is currently no reason to do so, as this results only in duplicated code and makes changes such as discussed in #2472 and #2149 unnecessary cumbersome.

Holds also true for some other functions (mostly create_cache)

[github-actions]

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[codecov]

Codecov Report

❌ Patch coverage is 88.88889% with 5 lines in your changes missing coverage. Please review.
✅ Project coverage is 96.77%. Comparing base (0821209) to head (cf6d461).

Files with missing lines	Patch %	Lines
src/solvers/dgsem/calc_volume_integral.jl	87.50%	4 Missing ⚠️
src/solvers/dg.jl	80.00%	1 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #2488      +/-   ##
==========================================
+ Coverage   96.76%   96.77%   +0.01%     
==========================================
  Files         518      519       +1     
  Lines       42400    42303      -97     
==========================================
- Hits        41027    40938      -89     
+ Misses       1373     1365       -8     

Flag	Coverage Δ
unittests	96.77% <88.89%> (+0.01%)	⬆️

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[ranocha]

Thanks for bringing this up. We have to discuss this in a larger group including @sloede and the other @trixi-framework/principal-developers

[JoshuaLampert]

If we want this (and I am in favor of it), I would propose to put the dimension agnostic functions into dimension-general files, e.g., moving the calc_boundary_flux! functions from src/solvers/dgsem_structured/dg_*d.jl to src/solvers/dgsem_structured/dg.jl. Otherwise it's hard to find the file if you are, e.g., working on 2D, but the function is in the 1D file.

[DanielDoehring]

If we want this (and I am in favor of it), I would propose to put the dimension agnostic functions into dimension-general files, e.g., moving the calc_boundary_flux! functions from src/solvers/dgsem_structured/dg_*d.jl to src/solvers/dgsem_structured/dg.jl. Otherwise it's hard to find the file if you are, e.g., working on 2D, but the function is in the 1D file.

That's an excellent idea!

[JoshuaLampert]

Following a similar idea, wouldn't it also make sense to put mesh-agnostic functions (at least the ones, which are the same of all mesh types) into mesh-general files like https://github.com/trixi-framework/Trixi.jl/blob/531ee91d0dbe93e8fb8bf9f675b34f7982b9077e/src/solvers/dg.jl. Currently, we have quite some functions, which also allow non-TreeMeshes in the dgsem_tree subfolder.

[DanielDoehring]

Following a similar idea, wouldn't it also make sense to put mesh-agnostic functions (at least the ones, which are the same of all mesh types) into mesh-general files like https://github.com/trixi-framework/Trixi.jl/blob/531ee91d0dbe93e8fb8bf9f675b34f7982b9077e/src/solvers/dg.jl. Currently, we have quite some functions, which also allow non-TreeMeshes in the dgsem_tree subfolder.

I like the idea and I would be fine with adding a file like volume_integrals.jl somewhere in the src/solvers directory.
However, this is maybe againts the following convention/code structure?

Trixi.jl/src/solvers/dg.jl

Lines 830 to 837 in 531ee91

	# Discretizations specific to each mesh type of Trixi.jl
	# If some functionality is shared by multiple combinations of meshes/solvers,
	# it is defined in the directory of the most basic mesh and solver type.
	# The most basic solver type in Trixi.jl is DGSEM (historic reasons and background
	# of the main contributors).
	# We consider the `TreeMesh` to be the most basic mesh type since it is Cartesian
	# and was the first mesh in Trixi.jl. The order of the other mesh types is the same
	# as the include order below.

[JoshuaLampert]

Yes, it would be against this code structure, but the question is, which code structure is easier to understand and work with. I was just last week talking to a Trixi.jl newcomer, who wants to contribute to Trixi.jl and was confused about seeing code relevant for the P4estMesh in the TreeMesh folder and therefore didn't find the relevant code. If we want to keep the current structure, I would at least highlight this structure more prominently in the docs, e.g., in the development section.

[DanielDoehring]

Yes, it would be against this code structure, but the question is, which code structure is easier to understand and work with. I was just last week talking to a Trixi.jl newcomer, who wants to contribute to Trixi.jl and was confused about seeing code relevant for the P4estMesh in the TreeMesh folder and therefore didn't find the relevant code. If we want to keep the current structure, I would at least highlight this structure more prominently in the docs, e.g., in the development section.

As a follow up: Maybe it also makes sense to bundle (in a different PR) identical rhs! functions, such as done for the parabolic solver:

Trixi.jl/src/solvers/dgsem_p4est/dg_2d_parabolic.jl

Line 52 in 9b51a54

function rhs_parabolic!(du, u, t, mesh::Union{P4estMesh{2}, P4estMesh{3}},

This way we can also reduce redundant code and re-do really only the stuff that is actually different, thus giving better code semantics.