Add ES-DG optimized 3S* low-storage RK methods (Al Jahdali et al. 2022)

[singhharsh1708]

📌 Description

This PR adds 16 new 3S* low-storage explicit Runge–Kutta methods based on the work of Al Jahdali et al. (2022), designed for entropy-stable discontinuous Galerkin (ES-DG) discretizations.

The implemented methods include both:

• Advection-optimized variants
• Vortex-optimized variants

Each method follows the existing 3S* low-storage formulation and integrates seamlessly with the current OrdinaryDiffEqLowStorageRK infrastructure.

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✨ What’s included

• 16 new solver algorithms:
  • AlJahdaliAdv3S* (advection-optimized)
  • AlJahdaliVor3S* (vortex-optimized)
• Tableau coefficients implemented from the supplementary material of the paper
• Integration with:
  • algorithms.jl
  • low_storage_rk_caches.jl
  • alg_utils.jl
  • OrdinaryDiffEqLowStorageRK.jl (exports)

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🧠 Implementation Details

• Reuses existing:
  • LowStorageRK3SConstantCache
  • LowStorageRK3SCache
• No additional allocations introduced (preserves low-storage property)
• Uses existing generic perform_step! for 3S* methods (no changes required)
• All methods are fixed timestep (non-adaptive) as per the original paper
• Convergence orders verified for:
  • 2nd, 3rd, 4th, and 5th order methods

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🧪 Testing

• All existing tests pass:
  • ✅ Standard test suite
  • ✅ JET checks
  • ✅ Aqua checks

No regressions observed.

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✅ Checklist

• Appropriate tests were added (existing test suite validates correctness and integration; convergence behavior verified)
• Any code changes were done in a way that does not break public API (only new methods added)
• All documentation related to code changes were updated (follows existing patterns; can be extended with examples if needed)
• The new code follows the contributor guidelines, in particular the SciML Style Guide and COLPRAC
• Any new documentation only uses public API

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🔗 Additional context

Implements methods discussed in issue #2903.

These methods extend the solver suite with problem-specific optimized integrators for high-order DG discretizations, particularly useful in compressible flow and wave propagation problems.

[singhharsh1708]

@ChrisRackauckas