Add Akinci model shootout with IISPH support

[svchb]

Purpose

Add the validation-only layer on top of the focused Akinci implementation collected in #1262.

Changes

• add a parameterized 3D cube-to-sphere example for WCSPH, EDAC, and IISPH
• run a 21-case baseline shootout: the cohesion-only control uses all fourteen solver configurations, while the combined Akinci model runs the seven configurations with its required correction
• select five solver/density winners by late-time asphericity and study each at 4^3, 6^3, and 8^3 particles
• isolate nested resolution runs so requested particle counts and output metadata cannot be overwritten by the baseline include
• record shape, time-series, radial, spacing, center-of-mass, momentum, kinetic-energy, and resolution diagnostics
• mark unsupported no-correction full-Akinci plot cells explicitly and add reduced CI assertions

Stack

Depends on #1262. Fork branches cannot be selected as bases for pull requests into the upstream repository, so this PR targets main and temporarily includes the implementation stack.

Review-only diff: svchb/TrixiParticles.jlOpen@integration/akinci-models...validation/akinci-model-shootout

Validation Matrix

Models:

• CohesionForceAkinci as an uncorrected/corrected control across all fourteen configurations
• SurfaceTensionAkinci with its required AkinciFreeSurfaceCorrection across seven configurations

The configurations cover WCSPH with continuity or summation density, EDAC with both density calculators and both pressure formulations, and IISPH with summation density.

Verification

• reduced baseline matrix: 21/21 configurations successful
• reduced resolution matrix: 10/10 configurations successful with particle counts 2^3 and 3^3
• all reported diagnostics finite with center-of-mass and momentum tolerances satisfied
• shootout, final-shape, time-series, and resolution plotting scripts generated successfully
• JuliaFormatter 2.1.1 and validation-layer git diff --check passed

Stack Order

Focused merge order is #1258, #1279, #1280, #1259, #1261, #1266, then #1267. Supporting views are #1262, #1263, and historical umbrella #1253.

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 96.27507% with 13 lines in your changes missing coverage. Please review.
✅ Project coverage is 90.62%. Comparing base (a720b1d) to head (e61e5a5).
⚠️ 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	92.68%	3 Missing ⚠️
src/schemes/fluid/surface_tension.jl	94.91%	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    #1263      +/-   ##
==========================================
+ Coverage   90.39%   90.62%   +0.23%     
==========================================
  Files         138      139       +1     
  Lines       11322    11611     +289     
==========================================
+ Hits        10234    10523     +289     
  Misses       1088     1088              

Flag	Coverage Δ
total	90.63% <96.27%> (+0.23%)	⬆️
unit	79.71% <94.26%> (+2.22%)	⬆️

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