L1 ⚛ L1-179 ⊙ Testnet

LES — large-eddy simulation

Fluid Dynamics · Subgrid-scale modeling for turbulence

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⬇ L1-179.md

# ⚛ L1 Principle — LES — large-eddy simulation **ID:** `L1-179` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Fluid Dynamics — *Subgrid-scale modeling for turbulence* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** filtered velocity field spacetime > **📡 Carrier:** mechanical · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 10 · **⛓ Block:** 41553966 --- ## 🧠 1. Introduction **LES — large-eddy simulation** is a **nonlinear inverse problem** whose unknown lives in **filtered velocity field spacetime** space, within the **Subgrid-scale modeling for turbulence** 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 · filter operator; L · sgs model operator; momentum balance (Navier-Stokes / Euler); detector accumulates flux over the exposure window. Observations are corrupted by additive Gaussian noise. Resolved scales > filter; SGS model for unresolved; expensive near walls. ## ⚙ 2. Forward Model Physical chain: **x** → L · sgs model → Momentum equation → Temporal integration → **y** (detector). ``` y = ∫_t dt ∂_t(ρv) + ∇·(ρv⊗v) `L.sgs_model` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.sgs_model` | L · sgs model operator | | `L.momentum` | Momentum balance (navier-stokes / euler) | | `int.temporal` | Detector accumulates flux over the exposure window | **🛰 Estimator components** _(used inside the solver, not in the forward equation)_: | Primitive | What it does | |---|---| | `L.filter` | L · filter operator | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Fluid Dynamics | | Sub domain | Subgrid-scale modeling for turbulence | | Carrier | mechanical | | Problem class | nonlinear_inverse | | Solution space | filtered_velocity_field_spacetime | | Noise model | gaussian | | Integration axis | temporal | | Difficulty delta | 10 | | L dag | 3.8 | ## 📡 4. Measurement Model Resolved scales > filter; SGS model for unresolved; expensive near walls. | Metric | Value | |---|---| | Metric | PSNR_dB | | Secondary | SSIM | ## 📏 5. Operating Range (Ω) **Center problem class:** `les` · **Forward operator:** `les_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 512 | | W | px | 512 | | Z | — | 128 | | Re | — | 100000 | | Snr db | dB | 30 | | N times | — | 1000 | | Sgs model error | — | 0 | | Filter width error | — | 0 | | Grid resolution error | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 64 – 8192 | | W | px | 64 – 8192 | | Z | — | 32 – 2048 | | Re | — | 1000 – 1000000000.0 | | Snr db | dB | 0 – 40 | | N times | — | 100 – 1000000 | | Sgs model error | — | 0.0 – 0.3 | | Filter width error | — | 0.0 – 0.3 | | Grid resolution error | — | 0.0 – 0.3 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 19.0 | Metric | Range | |---|---| | Psnr db | 10.0 – 45.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `800` and δ = `10`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x262b397bee7faadb6042e227dae9f0f6ded464d743d106be617fca15fd9b04ed` - **Chain tx hash:** `0x6847a81ed14976dff4180d385f8a2f68a3355bb40ad5bb3841497e2ad4626a9d` - **Chain block:** `41553966` --- ## File Mapping This bundle consists of: `L1-179.md`, `L1-179.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-179.md` | Source of truth — edit this | Human or LLM | | `L1-179.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 `L1-179`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-179.md).
Regenerate L1-179.json so every field matches the Markdown.
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Output each file in its own fenced code block tagged with the filename.

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L2-179-001 LES — large-eddy simulation Mismatch-Only Spec

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📋 JSON metadata

{
  "artifact_id": "L1-179",
  "chain_block": 41553966,
  "chain_hash": "0x262b397bee7faadb6042e227dae9f0f6ded464d743d106be617fca15fd9b04ed",
  "chain_tx_hash": "0x6847a81ed14976dff4180d385f8a2f68a3355bb40ad5bb3841497e2ad4626a9d",
  "domain": "Fluid Dynamics",
  "hardness_fn": {
    "delta": 10,
    "kappa": 800,
    "metric": "PSNR_dB",
    "type": "epsilon_fn"
  },
  "initiator_dataset": [
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      "ipfs_cid": null,
      "license_hash": null,
      "name": "primary",
      "weight": 1.0
    }
  ],
  "layer": "L1",
  "observable_profile": {
    "metric": "PSNR_dB",
    "regime": "Resolved scales \u003e filter; SGS model for unresolved; expensive near walls.",
    "secondary": "SSIM"
  },
  "physics_fingerprint": {
    "L_DAG": 3.8,
    "carrier": "mechanical",
    "difficulty_delta": 10,
    "domain": "Fluid Dynamics",
    "integration_axis": "temporal",
    "noise_model": "gaussian",
    "primitives": [
      "L.filter",
      "L.sgs_model",
      "L.momentum",
      "int.temporal"
    ],
    "problem_class": "nonlinear_inverse",
    "sensing_mechanism": "piv_hot_wire",
    "solution_space": "filtered_velocity_field_spacetime",
    "sub_domain": "Subgrid-scale modeling for turbulence",
    "title": "LES \u2014 large-eddy simulation"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "les_forward"
    ],
    "allowed_omega_dimensions": [
      "H",
      "W",
      "Z",
      "N_times",
      "Re",
      "SNR_dB",
      "sgs_model_error",
      "grid_resolution_error",
      "filter_width_error",
      "sgs_model_error",
      "grid_resolution_error",
      "filter_width_error"
    ],
    "allowed_problem_classes": [
      "les"
    ],
    "center_spec": {
      "epsilon_fn_center": "19.0",
      "forward_operator": "les_forward",
      "input_format": "measurement_only",
      "omega": {
        "H": 512,
        "N_times": 1000,
        "Re": 100000,
        "SNR_dB": 30,
        "W": 512,
        "Z": 128,
        "filter_width_error": 0.0,
        "grid_resolution_error": 0.0,
        "sgs_model_error": 0.0
      },
      "problem_class": "les"
    },
    "epsilon_bounds": {
      "psnr_db": [
        10.0,
        45.0
      ]
    },
    "omega_bounds": {
      "H": [
        64,
        8192
      ],
      "N_times": [
        100,
        1000000
      ],
      "Re": [
        1000,
        1000000000.0
      ],
      "SNR_dB": [
        0,
        40
      ],
      "W": [
        64,
        8192
      ],
      "Z": [
        32,
        2048
      ],
      "filter_width_error": [
        0.0,
        0.3
      ],
      "grid_resolution_error": [
        0.0,
        0.3
      ],
      "sgs_model_error": [
        0.0,
        0.3
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Subgrid-scale modeling for turbulence",
  "title": "LES \u2014 large-eddy simulation"
}

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