Fix Akinci free-surface correction with continuity density

[svchb]

Summary

• reconstruct the auxiliary kernel-summation density required by AkinciFreeSurfaceCorrection when WCSPH or EDAC uses ContinuityDensity
• use the reconstructed density for free-surface classification, corrected surface normals, and symmetric correction factors without replacing the integrated pressure density
• include dummy boundary masses so wall-adjacent particles are not misclassified as a free surface
• refresh the Akinci-specific EDAC correction data after density updates without importing unrelated cache changes
• require AkinciFreeSurfaceCorrection whenever the combined SurfaceTensionAkinci model is selected, while keeping cohesion-only use independent of normals and correction
• migrate affected examples and add constructor, reconstruction, wall, WCSPH, and EDAC regressions

Stack

Depends on #1259. Fork branches cannot be selected as bases for pull requests into the upstream repository, so this PR targets main and temporarily shows the preceding commits.

Review-only diff: svchb/TrixiParticles.jlOpen@surface-tension/akinci-2d-kernels...fix/akinci-free-surface-correction

Verification

• complete unit test target passed
• aggregate surface-tension tests: 175/175
• continuity-density reconstruction, wall classification, constructor rejection, and WCSPH/EDAC force assembly passed
• JuliaFormatter 2.1.1 and git diff --check passed

Stack Order

1. Harden surface tension model configuration #1258 - surface-tension configuration hardening
2. Clarify and visualize SPH surface normals #1279 - surface-normal scoping, explanation, and visualization
3. Implement multicolor surface normals and threshold handling #1280 - multicolor gradients and threshold handling
4. Add dimensionally consistent 2D Akinci kernels #1259 - dimensionally consistent 2D Akinci kernels
5. Fix Akinci free-surface correction with continuity density #1261 - required WCSPH and EDAC free-surface correction support
6. Use conservative Akinci pair forces across resolutions #1266 - conservative adaptive-resolution Akinci pair forces
7. Add Akinci surface tension support to IISPH #1267 - Akinci surface tension and correction support in IISPH

Supporting views: #1262 is the aggregate implementation view, #1263 is validation, and #1253 is the historical umbrella.

All focused PRs target upstream main because GitHub cannot use contributor-fork branches as upstream PR bases. Each PR links a fork comparison that isolates its own review layer.

[codecov]

Codecov Report

❌ Patch coverage is 94.75655% with 14 lines in your changes missing coverage. Please review.
✅ Project coverage is 90.53%. Comparing base (a720b1d) to head (8b326b4).
⚠️ Report is 1 commits behind head on main.

Files with missing lines	Patch %	Lines
src/schemes/fluid/surface_normal_sph.jl	90.24%	4 Missing ⚠️
src/preprocessing/particle_packing/system.jl	50.00%	3 Missing ⚠️
src/schemes/fluid/surface_tension.jl	93.47%	3 Missing ⚠️
src/general/semidiscretization.jl	81.81%	2 Missing ⚠️
src/schemes/fluid/fluid.jl	75.00%	2 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #1261      +/-   ##
==========================================
+ Coverage   90.39%   90.53%   +0.14%     
==========================================
  Files         138      139       +1     
  Lines       11322    11546     +224     
==========================================
+ Hits        10234    10453     +219     
- Misses       1088     1093       +5     

Flag	Coverage Δ
total	90.54% <94.75%> (+0.14%)	⬆️
unit	78.07% <92.88%> (+0.59%)	⬆️

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