Validation Carreau Yasuda Model

[sherin-joseph]

Please note that this is more of a steady-profile preservation check than a full convergence-from-rest validation, because the default and high-resolution runs use analytical initial conditions. . For a stronger transient validation, we need to use initial_condition_mode = zero or newtonian and verify convergence of the velocity profile toward the analytical solution.

The relative L2 velocity-profile error remains below 3% for all tested Carreau-Yasuda indices at ny = 200. The largest error occurs for n = 0.25, the strongest shear-thinning case, while the Newtonian limit n = 1 is recovered with about 1.4% relative L2 error.

The reference Poiseuille validation from Section 3.1 of Coclite et al. (2020) is shown below for comparison.

[svchb]

For validation cases we want to have the following structure:

1. example file that is trixi_include'd into the validation_run file
2. the validation run file contain some kind of error bounds
3. Additionally a plot file to plot the results of the validation run.

So you just need to create this additional example file and figure out an error bound for the validation to get to that structure.

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 90.04%. Comparing base (b3f0e7d) to head (6f08372).

Additional details and impacted files

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Flag	Coverage Δ
total	90.05% <ø> (ø)
unit	70.77% <ø> (ø)

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[sherin-joseph]

@svchb
The PR now includes:

examples/fluid/poiseuille_carreau_2d.jl as the example file
validation/poiseuille_carreau_2d/validation_poiseuille_carreau_2d.jl as the validation runner using trixi_include
relative L2 error bounds in the validation runner
plot_carreau_comparison.jl for plotting the validation results

I hope this follows the expected structure now. Please let me know if any further changes or corrections are needed.

Thanks for the guidance!