Draft of entropy correction artificial viscosity

[jlchan]

This PR is mainly intended as experimentation and brainstorming on how to implement ECAV in Trixi.

Ideally we would like to reuse the gradient calculations between rhs_parabolic! and rhs!. Two assumptions:

• SplitODEProblem calls rhs_parabolic! first, then rhs! so that the viscous gradients are available to rhs!, which would now need to take in a cache_parabolic or viscous_container argument.
• the AV is implemented in rhs! and should not be overly stiff.

Since the rhs! call signature changes, this probably requires a new Semidiscretization?

Questions:

• how would one run with no parabolic terms? Maybe have a dummy parabolic equation which is set by default if the parabolic equation is not specific. This would just trigger rhs_parabolic! to calculate gradients

[github-actions]

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Created with ❤️ by the Trixi.jl community.

[codecov]

Codecov Report

❌ Patch coverage is 1.20968% with 490 lines in your changes missing coverage. Please review.
✅ Project coverage is 90.36%. Comparing base (16e465f) to head (56815c8).
⚠️ Report is 43 commits behind head on main.

Files with missing lines	Patch %	Lines
...ization/semidiscretization_artificial_viscosity.jl	0.00%	176 Missing ⚠️
...c/solvers/dgsem_tree/dg_2d_artificial_viscosity.jl	0.00%	122 Missing ⚠️
src/solvers/dgsem_tree/dg_1d_parabolic.jl	1.69%	58 Missing ⚠️
examples/tree_1d_dgsem/elixir_ecav_1d.jl	0.00%	50 Missing ⚠️
examples/tree_2d_dgsem/elixir_ecav_2d.jl	0.00%	37 Missing ⚠️
src/solvers/dgmulti/dg.jl	0.00%	27 Missing ⚠️
...c/equations/laplace_diffusion_entropy_variables.jl	0.00%	6 Missing ⚠️
src/solvers/dgsem_tree/dg_2d_parabolic.jl	14.29%	6 Missing ⚠️
src/solvers/solvers_parabolic.jl	14.29%	6 Missing ⚠️
src/equations/compressible_euler_1d.jl	0.00%	1 Missing ⚠️
... and 1 more

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #2700      +/-   ##
==========================================
- Coverage   97.08%   90.36%   -6.71%     
==========================================
  Files         611      615       +4     
  Lines       47580    48058     +478     
==========================================
- Hits        46189    43427    -2762     
- Misses       1391     4631    +3240     

Flag	Coverage Δ
unittests	90.36% <1.21%> (-6.71%)	⬇️

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