DGMulti shock capturing part 2: SBP approximation types

[jlchan]

This splits off implementation of shock capturing for SBP types from #2872 into a smaller PR. Part 1 is #2940 and should be merged first.

The main functionality implemented here is volume_integral_kernel! for DGMultiFluxDiffSBP types on tensor product element types. Previously, there was only an implementation for GaussSBP types, which involved one additional projection step.

[github-actions]

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[jlchan]

CI results differ pretty significantly from local results in this PR: https://github.com/trixi-framework/Trixi.jl/actions/runs/24645680499/job/72057804271?pr=2942#step:7:11928

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 97.13%. Comparing base (237cca1) to head (04d0210).
⚠️ Report is 1 commits behind head on main.

Additional details and impacted files

@@           Coverage Diff           @@
##             main    #2942   +/-   ##
=======================================
  Coverage   97.13%   97.13%           
=======================================
  Files         623      624    +1     
  Lines       48384    48439   +55     
=======================================
+ Hits        46995    47050   +55     
  Misses       1389     1389           

Flag	Coverage Δ
unittests	97.13% <100.00%> (+<0.01%)	⬆️

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[jlchan]

CI results differ pretty significantly from local results in this PR: https://github.com/trixi-framework/Trixi.jl/actions/runs/24645680499/job/72057804271?pr=2942#step:7:11928

Still trying to track down CI differences. Rerunning with Julia v1.10.11 on my laptop doesn't change test results.

Edit: it seems to be an Apple Silicon issue. Using julia +1.12~x86 matches CI results, while julia+1.12 on aarch64 results in different values...

[jlchan]

Found the issue: it's the discontinuous initial condition from initial_condition_weak_blast_wave. Floating point differences on aarch64 and x86 resulted in different initial conditions when using SBP approximation types with points on the boundary.

This issue doesn't arise for other approximation types because they initialize the solution using an L2 projection at interior quadrature points and never evaluate the solution exactly at the discontinuity.

Edit: maybe not, CI still seems to be having issues still

Edit 2: ah, the issue is discontinuity of atan around x=0.

[jlchan]

Thanks for the review @DanielDoehring!

[DanielDoehring]

LGTM! Thanks for making these PRs easier digestible Jesse :)