0.10_Fluid_Dynamics_Chaos

layout	article
title	UET Topic 0.10: Fluid Dynamics and Chaos
description	Structured documentation for the fluid-dynamics topic in the UET repository.

0.10 Fluid Dynamics and Chaos

Problem

This topic studies whether UET-based fluid solvers can provide useful internal benchmark behavior relative to repository Navier-Stokes comparators and canonical fluid references.

Assumptions and scope

• Scope: internal speed, stability, and benchmark comparisons
• Out of scope: claiming closure of the Navier-Stokes Millennium problem
• Current topic materials mix solver engineering claims, mathematical interpretation, and benchmark comparisons; public summaries must keep those categories separate

Conceptual Diagram

flowchart LR
    A["embedded grid config"] --> B["simplified NS comparator"]
    A --> C["UET master-equation step"]
    B --> D["runtime trials"]
    C --> D
    C --> E["stress field finite check"]
    D --> F["speedup gate"]
    E --> F
    G["external CFD datasets"] --> H["future validation gate"]
    I["theorem assumptions"] --> J["future proof package"]

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Evidence Matrix

Layer	Current status	Evidence / artifact	Claim allowed
Embedded speed benchmark	Runnable internal gate	Result/artifacts/fluid_benchmark_validation.json	implementation speed comparison
Stress finite-output check	Runnable internal gate	same artifact	stress-test diagnostic
UET fluid formulas	Formula-audited	FORMULA_AUDIT.md	model/component description
External CFD validation	Not yet packaged	DATA_MANIFEST.md	future validation target
Millennium proof target	Not part of current gate	LIMITATIONS.md	no mathematical-proof claim

Data sources

• Canonical reference citation: Reynolds 1883 in docs/references.bib
• Topic benchmark configs and result folders under Data/ and Result/

Method summary

• 2D solver: Code/01_Engine/Engine_UET_2D.py
• 3D solver: Code/01_Engine/Engine_UET_3D.py
• Benchmark proof script: Code/02_Proof/Proof_Turbulence_Benchmarks.py
• Additional research scripts under Code/03_Research/

Supporting standard files:

• METHOD.md
• DATA_MANIFEST.md
• VERIFICATION_SPEC.md
• BASELINE_COMPARISON.md
• LIMITATIONS.md

Parameters and fitting status

• Current topic wording should describe speed and stability as internal benchmark outputs
• Public summaries should not claim global smoothness or Millennium-problem closure unless a separate proof package is documented and independently reviewed

Metrics and thresholds

• Internal metrics currently include runtime speedup and stability checks
• Proof_Turbulence_Benchmarks.py uses an internal benchmark target of speedup greater than 2.0x together with finite stress-test output

Baselines

• Comparator model: simplified Navier-Stokes solver in the benchmark proof script
• Supporting references: classical fluid-dynamics literature listed in repository citations

Limitations and open risks

• Benchmark comparator is simplified and should be described honestly as such
• Internal speedups are implementation-specific and environment-sensitive
• Topic claims about proof-level consequences remain far stronger than the current repository benchmark evidence

Reproducibility

• Verification command: python docs/topics/0.10_Fluid_Dynamics_Chaos/Code/02_Proof/Proof_Turbulence_Benchmarks.py
• Artifact contract: see VERIFICATION_SPEC.md

Current readiness status

Structured