Fix z-boundary backward FD stencil using fields(2) instead of fields(3)

[sbryngelson]

Summary

Severity: CRITICAL — produces wrong results in all 3D simulations using this routine.

File: src/common/m_finite_differences.fpp, line 53

The z-direction upper-boundary backward finite difference stencil at iz_s%end uses fields(2) (the y-component) instead of fields(3) (the z-component) in the third term of the second-order backward difference.

Before

divergence = divergence + (+3._wp*fields(3)%sf(x,y,z) &
    - 4._wp*fields(3)%sf(x,y,z-1) &
    + fields(2)%sf(x,y,z-2)) / (z_cc(z) - z_cc(z-2))
!   ^^^^^^^^^ should be fields(3)

After

divergence = divergence + (+3._wp*fields(3)%sf(x,y,z) &
    - 4._wp*fields(3)%sf(x,y,z-1) &
    + fields(3)%sf(x,y,z-2)) / (z_cc(z) - z_cc(z-2))

Why this went undetected

This is a copy-paste error in the x→y→z stencil chain where only the third term of the z-direction backward stencil is wrong — the first two terms correctly use fields(3). The bug only activates at the exact upper z-boundary cells (iz_s%end) where the one-sided backward stencil is used; the interior central-difference stencil and the lower-boundary forward stencil are both correct. This makes the error localized to a thin boundary layer that is easily masked by the correct values everywhere else.

Test plan

• Run 3D test case with non-trivial z-boundary divergence
• Verify divergence values at iz_s%end match the y-boundary analog

🤖 Generated with Claude Code

Fixes #1194

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📝 Walkthrough

Walkthrough

The s_compute_fd_divergence routine in the finite differences module was corrected to reference the proper field when computing the z-direction boundary divergence contribution. The affected term now accesses the third field instead of the second field.

Changes

Cohort / File(s)	Summary
Finite Differences Boundary Fix src/common/m_finite_differences.fpp	Corrected field index reference in z-direction boundary divergence computation from fields(2) to fields(3) for improved accuracy in boundary derivative calculations.

Estimated code review effort

🎯 2 (Simple) | ⏱️ ~5 minutes

Suggested labels

Review effort 2/5, size:XS

Poem

🐰 A whisker-twitch away from error
Field three now leads where two did stray
Boundaries fixed with finite precision
Divergence flows the proper way
Mathematics hops back on track!

🚥 Pre-merge checks | ✅ 3

✅ Passed checks (3 passed)

Check name	Status	Explanation
Title check	✅ Passed	The title accurately describes the bug fix: correcting a field index in the z-boundary finite difference stencil from fields(2) to fields(3).
Docstring Coverage	✅ Passed	No functions found in the changed files to evaluate docstring coverage. Skipping docstring coverage check.
Description check	✅ Passed	The PR description is comprehensive and well-structured, addressing severity, motivation, before/after code comparison, root cause analysis, and test plan.

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[codeant-ai]

Nitpicks 🔍

🔒 No security issues identified

⚡ Recommended areas for review Boundary-index safety The backward stencil at the upper z-boundary accesses z-1 and z-2. Ensure these indices are always valid for every call (ghost/halo cells or domain sizing). If the field arrays or z_cc do not include sufficient padding, this will read out-of-bounds or fetch invalid data. Consistency check Confirm there are no other places in the codebase that still use the y-component (fields(2)) for z-derivative boundary terms. The PR fixes one instance; any remaining occurrences will continue to corrupt divergence at the z-boundary. Performance / memory access The stencil reads multiple nearby entries from fields(3)%sf and z_cc repeatedly inside a tight GPU-parallel loop. This can harm memory coalescing and increase global memory traffic; caching neighbors into temporaries could reduce loads and improve throughput.

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[Copilot]

Pull request overview

Fixes an incorrect component reference in the z-direction upper-boundary backward finite-difference stencil inside the shared finite-differences module, preventing corrupted divergence results at the z-boundary for 3D runs.

Changes:

• Correct z-upper boundary backward-difference term to use fields(3) (z-component) rather than fields(2) (y-component).

[codecov]

Codecov Report

❌ Patch coverage is 0% with 1 line in your changes missing coverage. Please review.
✅ Project coverage is 44.05%. Comparing base (84c46e0) to head (dc4ebd7).
⚠️ Report is 4 commits behind head on master.

Files with missing lines	Patch %	Lines
src/common/m_finite_differences.fpp	0.00%	1 Missing ⚠️

Additional details and impacted files

@@           Coverage Diff           @@
##           master    #1173   +/-   ##
=======================================
  Coverage   44.05%   44.05%           
=======================================
  Files          70       70           
  Lines       20498    20498           
  Branches     1990     1990           
=======================================
  Hits         9030     9030           
  Misses      10329    10329           
  Partials     1139     1139           

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[sbryngelson]

Superseded by #1242 (batched HPC-sensitive fixes)