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 2.31481% with 422 lines in your changes missing coverage. Please review.
✅ Project coverage is 95.91%. Comparing base (1c5ed24) to head (16bca95).
⚠️ Report is 3 commits behind head on main.

Files with missing lines	Patch %	Lines
...ization/semidiscretization_artificial_viscosity.jl	0.00%	155 Missing ⚠️
examples/tree_2d_dgsem/elixir_ecav_2d.jl	0.00%	75 Missing ⚠️
src/solvers/dgsem_tree/dg_2d.jl	0.00%	63 Missing ⚠️
src/solvers/dgsem_tree/dg_1d.jl	0.00%	50 Missing ⚠️
examples/tree_1d_dgsem/elixir_ecav_1d.jl	0.00%	48 Missing ⚠️
src/solvers/dgmulti/dg.jl	0.00%	16 Missing ⚠️
...c/equations/laplace_diffusion_entropy_variables.jl	0.00%	6 Missing ⚠️
src/solvers/solvers_parabolic.jl	0.00%	6 Missing ⚠️
src/equations/compressible_euler_1d.jl	0.00%	1 Missing ⚠️
src/equations/compressible_euler_2d.jl	0.00%	1 Missing ⚠️
... and 1 more

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #2700      +/-   ##
==========================================
+ Coverage   88.24%   95.91%   +7.67%     
==========================================
  Files         550      553       +3     
  Lines       43421    43853     +432     
==========================================
+ Hits        38313    42058    +3745     
+ Misses       5108     1795    -3313     

Flag	Coverage Δ
unittests	95.91% <2.31%> (+7.67%)	⬆️

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