L1 ⚛ L1-178 ⊙ Testnet

Spalart-Allmaras — one-eq turbulence model

Fluid Dynamics · Single-eq SA for external aerodynamics

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⬇ L1-178.md

# ⚛ L1 Principle — Spalart-Allmaras — one-eq turbulence model **ID:** `L1-178` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Fluid Dynamics — *Single-eq SA for external aerodynamics* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** nu tilde field > **📡 Carrier:** mechanical · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41553966 --- ## 🧠 1. Introduction **Spalart-Allmaras — one-eq turbulence model** is a **nonlinear inverse problem** whose unknown lives in **nu tilde field** space, within the **Single-eq SA for external aerodynamics** 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 · nu tilde transport operator; L · damping fn 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 · nu tilde transport → L · damping fn → Spatial integration → **y** (detector). ``` y = ∫_A dA `L.damping_fn` `L.nu_tilde_transport` `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.nu_tilde_transport` | L · nu tilde transport operator | | `L.damping_fn` | L · damping fn operator | | `int.spatial` | Pixel-level spatial averaging on the detector | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Fluid Dynamics | | Sub domain | Single-eq SA for external aerodynamics | | Carrier | mechanical | | Problem class | nonlinear_inverse | | Solution space | nu_tilde_field | | Noise model | gaussian | | Integration axis | spatial | | Difficulty delta | 3 | | L dag | 3.2 | ## 📡 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:** `sa` · **Forward operator:** `sa_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 256 | | W | px | 256 | | Z | — | 128 | | Snr db | dB | 30 | | C b error | — | 0 | | Wall error | — | 0 | | Damping error | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 32 – 2048 | | W | px | 32 – 2048 | | Z | — | 16 – 1024 | | Snr db | dB | 0 – 40 | | C b error | — | 0.0 – 0.3 | | Wall error | — | 0.0 – 0.3 | | Damping error | — | 0.0 – 0.2 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 22.0 | Metric | Range | |---|---| | Psnr db | 10.0 – 45.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `400` and δ = `3`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x38e139678c0c3b8c84aec6ad5292680de1ca10fc74369f607305c46693179335` - **Chain tx hash:** `0xbdc793eb065e21591197093d606635e4a4f6e99f1db3262174e2b0e1c9104ef4` - **Chain block:** `41553966` --- ## File Mapping This bundle consists of: `L1-178.md`, `L1-178.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-178.md` | Source of truth — edit this | Human or LLM | | `L1-178.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 `L1-178`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-178.md).
Regenerate L1-178.json so every field matches the Markdown.
Preserve the schema documented in the File Mapping footer at the bottom of the MD.
Output each file in its own fenced code block tagged with the filename.

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L2-178-001 Spalart-Allmaras — one-eq turbulence model Mismatch-Only Spec

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📋 JSON metadata

{
  "artifact_id": "L1-178",
  "chain_block": 41553966,
  "chain_hash": "0x38e139678c0c3b8c84aec6ad5292680de1ca10fc74369f607305c46693179335",
  "chain_tx_hash": "0xbdc793eb065e21591197093d606635e4a4f6e99f1db3262174e2b0e1c9104ef4",
  "domain": "Fluid Dynamics",
  "hardness_fn": {
    "delta": 3,
    "kappa": 400,
    "metric": "PSNR_dB",
    "type": "epsilon_fn"
  },
  "initiator_dataset": [
    {
      "ipfs_cid": null,
      "license_hash": null,
      "name": "primary",
      "weight": 1.0
    }
  ],
  "layer": "L1",
  "observable_profile": {
    "metric": "PSNR_dB",
    "regime": "Conditional stability; mismatch parameters dominate at Omega bounds.",
    "secondary": "SSIM"
  },
  "physics_fingerprint": {
    "L_DAG": 3.2,
    "carrier": "mechanical",
    "difficulty_delta": 3,
    "domain": "Fluid Dynamics",
    "integration_axis": "spatial",
    "noise_model": "gaussian",
    "primitives": [
      "L.mean_flow_ns",
      "L.nu_tilde_transport",
      "L.damping_fn",
      "int.spatial"
    ],
    "problem_class": "nonlinear_inverse",
    "sensing_mechanism": "piv_hot_wire",
    "solution_space": "nu_tilde_field",
    "sub_domain": "Single-eq SA for external aerodynamics",
    "title": "Spalart-Allmaras \u2014 one-eq turbulence model"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "sa_forward"
    ],
    "allowed_omega_dimensions": [
      "H",
      "W",
      "Z",
      "SNR_dB",
      "damping_error",
      "C_b_error",
      "wall_error",
      "damping_error",
      "C_b_error",
      "wall_error"
    ],
    "allowed_problem_classes": [
      "sa"
    ],
    "center_spec": {
      "epsilon_fn_center": "22.0",
      "forward_operator": "sa_forward",
      "input_format": "measurement_only",
      "omega": {
        "C_b_error": 0.0,
        "H": 256,
        "SNR_dB": 30,
        "W": 256,
        "Z": 128,
        "damping_error": 0.0,
        "wall_error": 0.0
      },
      "problem_class": "sa"
    },
    "epsilon_bounds": {
      "psnr_db": [
        10.0,
        45.0
      ]
    },
    "omega_bounds": {
      "C_b_error": [
        0.0,
        0.3
      ],
      "H": [
        32,
        2048
      ],
      "SNR_dB": [
        0,
        40
      ],
      "W": [
        32,
        2048
      ],
      "Z": [
        16,
        1024
      ],
      "damping_error": [
        0.0,
        0.2
      ],
      "wall_error": [
        0.0,
        0.3
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Single-eq SA for external aerodynamics",
  "title": "Spalart-Allmaras \u2014 one-eq turbulence model"
}

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