Add support for plotting 1D function

[JoshuaLampert]

Sometimes it might be of interest to not only plot the numerical solution, but also other functions on top of it, especially in a 1D plot. Often this is done with the initial condition/analytical solution as reference. Currently, as far as I know, there was no straightforward way to accomplish this in 1D (except for using the internal semi.cache.elements.node_coordinates).
This PR enables the possibility to call plot(func, semi), where func is a function accepting spatial coordinates x and the equations, i.e. it is called by func(x, equations). A common example would be (x, equations) -> initial_condition(x, last(tspan), equations).
If you agree that it would be nice to support this, I can clean up the PR a bit.

[github-actions]

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[codecov]

Codecov Report

Attention: Patch coverage is 88.23529% with 4 lines in your changes missing coverage. Please review.

Project coverage is 96.87%. Comparing base (06e8a20) to head (72cad15).
Report is 1 commits behind head on main.

Files with missing lines	Patch %	Lines
src/visualization/recipes_plots.jl	66.67%	4 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #2250      +/-   ##
==========================================
- Coverage   96.87%   96.87%   -0.00%     
==========================================
  Files         490      490              
  Lines       39427    39454      +27     
==========================================
+ Hits        38194    38220      +26     
- Misses       1233     1234       +1     

Flag	Coverage Δ
unittests	96.87% <88.24%> (-<0.01%)	⬇️

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[JoshuaLampert]

This is ready for a review from my point of view.

[SimonCan]

Looks good to me. Once the codecov is fine this can be merged.

[JoshuaLampert]

Once the codecov is fine this can be merged.

I think it will be hard to make codecov happy on this one because lines like this, i.e., the function definition lines of the plot recipes are just not caught by codecov. So we can't do much against it. The only two lines that are not covered are the error messages, but I think it's fine to not cover them.

[DanielDoehring]

I think it will be hard to make codecov happy on this one because lines like this, i.e., the function definition lines of the plot recipes are just not caught by codecov. So we can't do much against it. The only two lines that are not covered are the error messages, but I think it's fine to not cover them.

Yeah that is always with the case - ironically, code coverage punishes you for adding safety :D Would be nice to add comments for codecov s.t. some lines are tolerated to be skipped.

[ranocha]

Thanks! Nice feature to have 👍

[ranocha]

Could you please post the result of one or two examples? If that looks good, this PR should be ready to go 👍

[JoshuaLampert]

Could you please post the result of one or two examples? If that looks good, this PR should be ready to go 👍

Sure:

julia> include("examples/tree_1d_dgsem/elixir_euler_density_wave.jl")
[...]
julia> plot((x, equations) -> initial_condition(x, last(tspan), equations), semi)

julia> plot((x, equations) -> cons2prim(initial_condition(x, last(tspan), equations), equations), semi)

julia> plot!(sol)

julia> plot((x, equations) -> sinpi.(x), semi, nvisnodes = 5)

gives

and

and

The calls look the same for the StructuredMesh and the DGMultiMesh (with the differences that nvisnodes has no effect as it is the case for plotting the numerical solution on these mesh types).

[ranocha]

Thanks!