[hhy2022]

Description

Summary

The symmetry term of weakly enforced Dirichlet BCs (Nitsche) is now written like the bulk diffusion term in cylindrical and spherical coordinates:

Coordinate system	Before	After
cartesian	n·grad(v)	n·grad(v) (unchanged)
cylindrical	n·grad(v)	r n·grad(v / r)
spherical	n·grad(v)	r**2 n·grad(v / r**2)

This follows the diffusion term in HydrogenTransportProblem.create_formulation and festim.drift.drift_form. DirichletBCBase.weak_formulation takes a new coordinate_system argument (default cartesian), passed by both HydrogenTransportProblem and HydrogenTransportProblemDiscontinuous.

Related Issues

Fixes #1278

• Found in Enclosure cylindrical #1277.
• Same correction as for the drift terms in Drift terms #1231, where the divergence form needed -m c v·grad(w/m) instead of -c v·grad(w).
• Relevant to Move the coordinate system from the mesh to the volume subdomain #1243: besides the diffusion terms, the Nitsche symmetry term also needs the coordinate system.

Motivation and Context

In cylindrical coordinates, conservation comes from the test function v = r, which is in the P1 space. The bulk term r grad(u)·grad(v/r) vanishes for it, but the symmetry term n·grad(v) does not (grad(r) = 1), so particles are not conserved when a weakly enforced HenrysBC / SievertsBC is coupled to an enclosure.

With the MWE posted in #1278 (largest relative change of the total number of H atoms):

	Henry before	Henry after	Sieverts before	Sieverts after
cartesian	2.6e-11	2.6e-11	1.4e-16	1.4e-16
cylindrical	3.7e-06	5.3e-11	4.4e-07	2.8e-16
spherical	1.7e-04	1.8e-04	2.4e-05	2.6e-05

Type of Change

• 🐛 Bug fix (non-breaking change which fixes an issue)
• ✨ New feature (non-breaking change which adds functionality)
• 💥 Breaking change (fix or feature that would cause existing functionality to not work as expected)
• 🔨 Code refactoring (no functional changes, no API changes)
• 📝 Documentation update
• ✅ Test update (adding missing tests or correcting existing tests)
• 🔧 Build/CI configuration change

Testing

• All existing tests pass locally (pytest)
• I have added new tests that prove my fix is effective or that my feature works

Code Quality Checklist

• My code follows the code style of this project (Ruff formatted: ruff format .)
• My code passes linting checks (ruff check .)
• I have performed a self-review of my own code
• I have commented my code, particularly in hard-to-understand areas

Documentation

• I have updated the documentation accordingly (if applicable)
• I have added docstrings to new functions/classes following the project conventions

Additional Notes

Spherical is not exact, and cannot be with P1 elements. Conservation would need v = r**2 in the test space. The remaining drift is the same as with SurfaceReactionBC (no Nitsche) and is O(h^2):

n cells	Henry before	Henry after	SurfaceReactionBC
60	1.72e-04	1.83e-04	1.85e-04
120	4.29e-05	4.58e-05	4.63e-05
240	1.07e-05	1.14e-05	1.16e-05

The spherical symmetry term is changed for consistency with the bulk term.

With assistance from AI.

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 96.15%. Comparing base (1bd7a80) to head (2e567ff).

Additional details and impacted files

@@           Coverage Diff           @@
##             main    #1289   +/-   ##
=======================================
  Coverage   96.14%   96.15%           
=======================================
  Files          57       57           
  Lines        5165     5177   +12     
=======================================
+ Hits         4966     4978   +12     
  Misses        199      199           

Flag	Coverage Δ
dolfinx-v0.10.0	93.27% <100.00%> (+0.01%)	⬆️
dolfinx-v0.11.0	96.02% <100.00%> (+<0.01%)	⬆️

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