Add Laplace diffusion in terms of entropy variables

[jlchan]

Adds the symmetrized version of Laplacian diffusion using the gradient of entropy variables and a change of variables to the conservative variables. For now, the change of variables uses ForwardDiff.jacobian, but can be specialized if the analytical formula is known to improve speed.

This formulation is provably entropy dissipative unlike LaplaceDiffusion.

[github-actions]

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[codecov]

Codecov Report

Attention: Patch coverage is 72.09302% with 12 lines in your changes missing coverage. Please review.

Project coverage is 96.92%. Comparing base (4238b89) to head (b2b2757).

Files with missing lines	Patch %	Lines
...c/equations/laplace_diffusion_entropy_variables.jl	36.84%	12 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #2406      +/-   ##
==========================================
- Coverage   96.95%   96.92%   -0.03%     
==========================================
  Files         504      508       +4     
  Lines       41721    41764      +43     
==========================================
+ Hits        40448    40479      +31     
- Misses       1273     1285      +12     

Flag	Coverage Δ
unittests	96.92% <72.09%> (-0.03%)	⬇️

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[jlchan]

I don't think the test failures are related to this PR...

[DanielDoehring]

I have two main suggestions:

1. For the standard Laplace we have the 3 files for the dimensions. Maybe do this also here?

2. Would it be possible to implement the Laplace operator similar to the Gradients for Navier-Stokes, i.e., with distinction between
   GradientVariablesPrimitive and GradientVariablesEntropy?
   

   Trixi.jl/src/equations/compressible_navier_stokes_1d.jl

   Lines 9 to 10 in 5acf73a

   	CompressibleNavierStokesDiffusion1D(equations; mu, Pr,
   	gradient_variables=GradientVariablesPrimitive())

[jlchan]

Thanks, @DanielDoehring!

1. For the standard Laplace we have the 3 files for the dimensions. Maybe do this also here?

I'm not opposed to this, but is there an advantage of having multiple files for a single equation? I sometimes find it harder to navigate code split across multiple files compared with just scrolling through a single file.

2. Would it be possible to implement the Laplace operator similar to the Gradients for Navier-Stokes, i.e., with distinction between
   `GradientVariablesPrimitive` and `GradientVariablesEntropy`?
   https://github.com/trixi-framework/Trixi.jl/blob/5acf73a96f4d4e72cb72169ede148c8d106838fb/src/equations/compressible_navier_stokes_1d.jl#L9-L10

I thought of implementing it this way. However, I was worried that LaplaceDiffusion also serves as a template for anyone trying to implement their own custom diffusion model and didn't want to necessarily clutter the "default" parabolic equations.

@ranocha, @sloede, any thoughts on this?

[ranocha]

Thanks, @DanielDoehring!

1. For the standard Laplace we have the 3 files for the dimensions. Maybe do this also here?

I'm not opposed to this, but is there an advantage of having multiple files for a single equation? I sometimes find it harder to navigate code split across multiple files compared with just scrolling through a single file.

I don't have a strong opinion here but @sloede often favored many files.

2. Would it be possible to implement the Laplace operator similar to the Gradients for Navier-Stokes, i.e., with distinction between
   `GradientVariablesPrimitive` and `GradientVariablesEntropy`?
   https://github.com/trixi-framework/Trixi.jl/blob/5acf73a96f4d4e72cb72169ede148c8d106838fb/src/equations/compressible_navier_stokes_1d.jl#L9-L10

I thought of implementing it this way. However, I was worried that LaplaceDiffusion also serves as a template for anyone trying to implement their own custom diffusion model and didn't want to necessarily clutter the "default" parabolic equations.

I agree with you 👍

[jlchan]

Sorry @DanielDoehring, forgot to format some new files. Can you reapprove?

[ranocha]

Thanks! I just have a few minor suggestions.

[jlchan]

Thanks for the review @ranocha!

[ranocha]

Thanks!

[ranocha]

Sorry, I forgot: Could you please add a NEWS.md entry?

[jlchan]

Ah! Of course, will add that in a bit.