Add parabolic RHS support for StructuredMesh{2}

[jlchan]

Non-Claude comments

• This was generated with assistance from Claude, which pretty much created a working draft on first try.
• The original PR was longer, so I tried to reduce the size of the PR by reusing more code.
• Claude sometimes stalls trying to test its changes (it seems to have issues with Julia's project and testing configurations), so I checked those manually. The plot of the solution looks qualitatively good if I run

trixi_include(joinpath(examples_dir(), "structured_2d_dgsem",
                                        "elixir_navierstokes_convergence.jl"), cells_per_dimension=(8,8),
                               tspan=(0.0, 0.2))

The oscillations disappear under mesh refinement. Different numbers of elements in x and y works as well.

Summary

• Extends the 2D parabolic solver (BR1 viscous formulation) to StructuredMesh{2} by adding it to Union type signatures in shared functions (create_cache_parabolic, transform_variables!, calc_viscous_fluxes!, calc_volume_integral!, calc_volume_integral_gradient!, apply_jacobian_parabolic!)
• Adds src/solvers/dgsem_structured/dg_2d_parabolic.jl with StructuredMesh{2}-specific implementations: prolong2interfaces!, calc_interface_flux!, prolong2boundaries!, calc_boundary_flux!, and the top-level rhs_parabolic!
• Adds a convergence test elixir examples/structured_2d_dgsem/elixir_navierstokes_convergence.jl on a curved periodic mesh (wavy mapping from elixir_euler_free_stream.jl) confirming order-4 L2 convergence (polydeg=3)
• Adds a regression test in test/test_parabolic_2d.jl

Convergence results (polydeg=3, cells_per_dimension doubled from 4×4 → 8×8 → 16×16)

Variable	Mean L2 EOC
rho	4.57
rho_v1	4.33
rho_v2	4.23
rho_e_total	4.87

Test plan

• CI passes

🤖 Generated with Claude Code

[github-actions]

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Testing

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Created with ❤️ by the Trixi.jl community.

[codecov]

Codecov Report

❌ Patch coverage is 98.92183% with 4 lines in your changes missing coverage. Please review.
✅ Project coverage is 97.06%. Comparing base (9d6e4b4) to head (c706074).
⚠️ Report is 1 commits behind head on main.

Files with missing lines	Patch %	Lines
src/solvers/dgsem_structured/dg_2d_parabolic.jl	98.24%	4 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #2862      +/-   ##
==========================================
+ Coverage   97.04%   97.06%   +0.01%     
==========================================
  Files         605      608       +3     
  Lines       47329    47695     +366     
==========================================
+ Hits        45930    46292     +362     
- Misses       1399     1403       +4     

Flag	Coverage Δ
unittests	97.06% <98.92%> (+0.01%)	⬆️

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