Add Akinci surface tension support to IISPH

[svchb]

Summary

• support CohesionForceAkinci and SurfaceTensionAkinci in ImplicitIncompressibleSPHSystem
• support AkinciFreeSurfaceCorrection with the current IISPH summation density
• enforce the required correction when the combined SurfaceTensionAkinci model is selected
• include Akinci surface tension and wall adhesion in the predicted velocity and final non-pressure momentum RHS
• update surface normals after summation densities are current and assemble predicted velocities before predicted densities
• add constructor, force-assembly, correction, wall-adhesion, and momentum regressions

Stack

Depends on #1266, which in turn depends on #1261. 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-normal-force-normalization...surface-tension/akinci-iisph-support

Verification

• complete unit test target passed
• IISPH system tests: 155/155
• aggregate surface-tension tests: 182/182
• standard IISPH behavior, Akinci prediction/RHS parity, correction assembly, and wall adhesion passed
• JuliaFormatter 2.1.1 and per-layer 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 94.15205% with 20 lines in your changes missing coverage. Please review.
✅ Project coverage is 79.69%. Comparing base (a720b1d) to head (f42b1fa).
⚠️ Report is 1 commits behind head on main.

Files with missing lines	Patch %	Lines
src/preprocessing/particle_packing/system.jl	16.66%	5 Missing ⚠️
src/schemes/fluid/fluid.jl	37.50%	5 Missing ⚠️
src/schemes/fluid/surface_normal_sph.jl	92.68%	3 Missing ⚠️
src/schemes/fluid/surface_tension.jl	94.91%	3 Missing ⚠️
src/general/semidiscretization.jl	81.81%	2 Missing ⚠️
src/io/io.jl	0.00%	2 Missing ⚠️

❗ There is a different number of reports uploaded between BASE (a720b1d) and HEAD (f42b1fa). Click for more details.

HEAD has 1 upload less than BASE

Flag	BASE (a720b1d)	HEAD (f42b1fa)
total	1	0

Additional details and impacted files

@@             Coverage Diff             @@
##             main    #1267       +/-   ##
===========================================
- Coverage   90.39%   79.69%   -10.70%     
===========================================
  Files         138      139        +1     
  Lines       11322    11581      +259     
===========================================
- Hits        10234     9230     -1004     
- Misses       1088     2351     +1263     

Flag	Coverage Δ
total	?
unit	79.69% <94.15%> (+2.21%)	⬆️

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