Add Carreau–Yasuda non-Newtonian viscosity model

[sherin-joseph]

modified:   src/TrixiParticles.jl
modified:   src/io/io.jl
modified:   src/schemes/fluid/viscosity.jl
modified:   test/schemes/fluid/viscosity.jl

[svchb]

Please don't close and reopen the same PR when fixing review comments.

[sherin-joseph]

Ready for review @efaulhaber

[codecov]

Codecov Report

❌ Patch coverage is 60.71429% with 11 lines in your changes missing coverage. Please review.
✅ Project coverage is 89.31%. Comparing base (06d4f42) to head (dd1e343).

Files with missing lines	Patch %	Lines
src/io/io.jl	0.00%	9 Missing ⚠️
src/schemes/fluid/viscosity.jl	89.47%	2 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #1010      +/-   ##
==========================================
- Coverage   89.40%   89.31%   -0.10%     
==========================================
  Files         121      121              
  Lines        8882     8910      +28     
==========================================
+ Hits         7941     7958      +17     
- Misses        941      952      +11     

Flag	Coverage Δ
total	89.31% <60.71%> (-0.10%)	⬇️
unit	65.42% <60.71%> (-0.02%)	⬇️

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[sherin-joseph]

Ready for re-review. @svchb

[LasNikas]

It would be nice to have an example file. Is there a corresponding validation in the literature to see the difference to Newtonian fluids?

[sherin-joseph]

It would be nice to have an example file. Is there a corresponding validation in the literature to see the difference to Newtonian fluids?

Yes—there's a corresponding validation case in the Vahabi paper mentioned in docs (bubble rise), which is used to highlight differences versus Newtonian behavior. I'm currently working on reproducing that setup and will share the example/inputs once it's in a clean, reusable form.