L1 ⚛ L1-176 ⊙ Testnet

RANS k-epsilon — turbulence closure

Fluid Dynamics · Standard k-epsilon RANS

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⬇ L1-176.md

# ⚛ L1 Principle — RANS k-epsilon — turbulence closure **ID:** `L1-176` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Fluid Dynamics — *Standard k-epsilon RANS* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** reynolds stress mean velocity > **📡 Carrier:** mechanical · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41553966 --- ## 🧠 1. Introduction **RANS k-epsilon — turbulence closure** is a **nonlinear inverse problem** whose unknown lives in **reynolds stress mean velocity** space, within the **Standard k-epsilon RANS** sub-domain of **Fluid Dynamics**. Measurements consist of mechanical vibrations or strain signals via a **piv hot wire** sensing mechanism. The forward operator applies, in order: L · mean flow ns operator; L · k eq operator; L · eps eq operator; pixel-level spatial averaging on the detector. Observations are corrupted by additive Gaussian noise. Conditional stability; mismatch parameters dominate at Omega bounds. ## ⚙ 2. Forward Model Physical chain: **x** → L · mean flow ns → L · k eq → L · eps eq → Spatial integration → **y** (detector). ``` y = ∫_A dA `L.eps_eq` `L.k_eq` `L.mean_flow_ns` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.mean_flow_ns` | L · mean flow ns operator | | `L.k_eq` | L · k eq operator | | `L.eps_eq` | L · eps eq operator | | `int.spatial` | Pixel-level spatial averaging on the detector | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Fluid Dynamics | | Sub domain | Standard k-epsilon RANS | | Carrier | mechanical | | Problem class | nonlinear_inverse | | Solution space | reynolds_stress_mean_velocity | | Noise model | gaussian | | Integration axis | spatial | | Difficulty delta | 5 | | L dag | 3.5 | ## 📡 4. Measurement Model Conditional stability; mismatch parameters dominate at Omega bounds. | Metric | Value | |---|---| | Metric | PSNR_dB | | Secondary | SSIM | ## 📏 5. Operating Range (Ω) **Center problem class:** `rans_kepsilon` · **Forward operator:** `rans_kepsilon_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 256 | | W | px | 256 | | Z | — | 128 | | Snr db | dB | 30 | | C mu error | — | 0 | | C eps error | — | 0 | | Sigma k error | — | 0 | | Wall fn error | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 32 – 2048 | | W | px | 32 – 2048 | | Z | — | 16 – 1024 | | Snr db | dB | 0 – 40 | | C mu error | — | 0.0 – 0.2 | | C eps error | — | 0.0 – 0.3 | | Sigma k error | — | 0.0 – 0.3 | | Wall fn error | — | 0.0 – 0.3 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 20.0 | Metric | Range | |---|---| | Psnr db | 10.0 – 45.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `500` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x9c0900d0c3b59974796ede94c0737f780bf457a0a52674292a10fca7a79a9a69` - **Chain tx hash:** `0x37f21bdb20d24bcd165a6cc7bf04062af723aae8607ffa59f82acb9f01589db1` - **Chain block:** `41553966` --- ## File Mapping This bundle consists of: `L1-176.md`, `L1-176.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-176.md` | Source of truth — edit this | Human or LLM | | `L1-176.json` | Structured metadata for the registry | LLM regenerates from the sections above | **Prompt for your LLM after editing this Markdown:** > Read the attached Markdown. Regenerate the sibling `.json` so every field matches. > Preserve the schema documented in the rows above. > Output each file in its own fenced code block tagged with the filename. > Output only the JSON object. _This Markdown was auto-synthesized from the catalog row for `L1-176`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-176.md).
Regenerate L1-176.json so every field matches the Markdown.
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📋 JSON metadata

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  "artifact_id": "L1-176",
  "chain_block": 41553966,
  "chain_hash": "0x9c0900d0c3b59974796ede94c0737f780bf457a0a52674292a10fca7a79a9a69",
  "chain_tx_hash": "0x37f21bdb20d24bcd165a6cc7bf04062af723aae8607ffa59f82acb9f01589db1",
  "domain": "Fluid Dynamics",
  "hardness_fn": {
    "delta": 5,
    "kappa": 500,
    "metric": "PSNR_dB",
    "type": "epsilon_fn"
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  "initiator_dataset": [
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      "name": "primary",
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  "layer": "L1",
  "observable_profile": {
    "metric": "PSNR_dB",
    "regime": "Conditional stability; mismatch parameters dominate at Omega bounds.",
    "secondary": "SSIM"
  },
  "physics_fingerprint": {
    "L_DAG": 3.5,
    "carrier": "mechanical",
    "difficulty_delta": 5,
    "domain": "Fluid Dynamics",
    "integration_axis": "spatial",
    "noise_model": "gaussian",
    "primitives": [
      "L.mean_flow_ns",
      "L.k_eq",
      "L.eps_eq",
      "int.spatial"
    ],
    "problem_class": "nonlinear_inverse",
    "sensing_mechanism": "piv_hot_wire",
    "solution_space": "reynolds_stress_mean_velocity",
    "sub_domain": "Standard k-epsilon RANS",
    "title": "RANS k-epsilon \u2014 turbulence closure"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "rans_kepsilon_forward"
    ],
    "allowed_omega_dimensions": [
      "H",
      "W",
      "Z",
      "SNR_dB",
      "C_mu_error",
      "sigma_k_error",
      "C_eps_error",
      "wall_fn_error",
      "C_mu_error",
      "sigma_k_error",
      "C_eps_error",
      "wall_fn_error"
    ],
    "allowed_problem_classes": [
      "rans_kepsilon"
    ],
    "center_spec": {
      "epsilon_fn_center": "20.0",
      "forward_operator": "rans_kepsilon_forward",
      "input_format": "measurement_only",
      "omega": {
        "C_eps_error": 0.0,
        "C_mu_error": 0.0,
        "H": 256,
        "SNR_dB": 30,
        "W": 256,
        "Z": 128,
        "sigma_k_error": 0.0,
        "wall_fn_error": 0.0
      },
      "problem_class": "rans_kepsilon"
    },
    "epsilon_bounds": {
      "psnr_db": [
        10.0,
        45.0
      ]
    },
    "omega_bounds": {
      "C_eps_error": [
        0.0,
        0.3
      ],
      "C_mu_error": [
        0.0,
        0.2
      ],
      "H": [
        32,
        2048
      ],
      "SNR_dB": [
        0,
        40
      ],
      "W": [
        32,
        2048
      ],
      "Z": [
        16,
        1024
      ],
      "sigma_k_error": [
        0.0,
        0.3
      ],
      "wall_fn_error": [
        0.0,
        0.3
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Standard k-epsilon RANS",
  "title": "RANS k-epsilon \u2014 turbulence closure"
}

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