Add dimensionally consistent 2D Akinci kernels

[svchb]

Summary

• add dimension-specific cohesion and adhesion normalizations for the Akinci model
• preserve the published three-dimensional kernels exactly while using full-space integral matching in two dimensions
• dispatch fluid, wall, and rigid-body interactions by spatial dimension and reject unsupported dimensions explicitly
• document the normalization derivation and coefficient migration for existing 2D configurations

Stack

Depends on #1280. 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-normals/multicolor-thresholds...surface-tension/akinci-2d-kernels

Migration

To preserve an existing 2D pair contribution at compact-support radius h_c, multiply the previous surface-tension coefficient by 627 / (790 * h_c) and the previous adhesion coefficient by 42 / (65 * h_c). The resulting pair kernels are resolution-independent at a fixed smoothing-length-to-spacing ratio.

Verification

• surface-tension tests on this layer: 110/110 before the stack split
• complete unit test target passed with eight Julia threads before the stack split
• targeted 2D Akinci examples: 6/6, including zero RHS allocations
• JuliaFormatter checks pass on the rewritten branch

Stack Order

Focused merge 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 - 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:

• Draft: integrate focused Akinci surface tension PRs #1262 - aggregate implementation view
• Add Akinci model shootout with IISPH support #1263 - validation and resolution study
• Surface Tension Prototype V1  #1253 - 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 92.16867% with 13 lines in your changes missing coverage. Please review.
✅ Project coverage is 90.45%. Comparing base (a720b1d) to head (07ddec5).
⚠️ Report is 1 commits behind head on main.

Files with missing lines	Patch %	Lines
src/preprocessing/particle_packing/system.jl	50.00%	3 Missing ⚠️
src/schemes/fluid/surface_normal_sph.jl	92.30%	3 Missing ⚠️
src/schemes/fluid/surface_tension.jl	92.85%	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    #1259      +/-   ##
==========================================
+ Coverage   90.39%   90.45%   +0.06%     
==========================================
  Files         138      139       +1     
  Lines       11322    11446     +124     
==========================================
+ Hits        10234    10354     +120     
- Misses       1088     1092       +4     

Flag	Coverage Δ
total	90.46% <92.16%> (+0.06%)	⬆️
unit	77.74% <89.15%> (+0.26%)	⬆️

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