L1 ⚛ L1-194 ⊙ Testnet

Fluid-Structure Interaction (FSI) — coupled fluid + solid

Fluid Dynamics · Partitioned / monolithic FSI

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⬇ L1-194.md

# ⚛ L1 Principle — Fluid-Structure Interaction (FSI) — coupled fluid + solid **ID:** `L1-194` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Fluid Dynamics — *Partitioned / monolithic FSI* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** coupled flow and deformation > **📡 Carrier:** mechanical · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 10 · **⛓ Block:** 41553978 --- ## 🧠 1. Introduction **Fluid-Structure Interaction (FSI) — coupled fluid + solid** is a **nonlinear inverse problem** whose unknown lives in **coupled flow and deformation** space, within the **Partitioned / monolithic FSI** sub-domain of **Fluid Dynamics**. Measurements consist of mechanical vibrations or strain signals via a **piv dic** sensing mechanism. The forward operator applies, in order: L · fluid solver operator; L · solid solver operator; L · interface coupling operator; detector accumulates flux over the exposure window. Observations are corrupted by additive Gaussian noise. Strong coupling for low mass ratios; added-mass instability in partitioned schemes. ## ⚙ 2. Forward Model Physical chain: **x** → L · fluid solver → L · solid solver → L · interface coupling → Temporal integration → **y** (detector). ``` y = ∫_t dt `L.interface_coupling` `L.solid_solver` `L.fluid_solver` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.fluid_solver` | L · fluid solver operator | | `L.solid_solver` | L · solid solver operator | | `L.interface_coupling` | L · interface coupling operator | | `int.temporal` | Detector accumulates flux over the exposure window | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Fluid Dynamics | | Sub domain | Partitioned / monolithic FSI | | Carrier | mechanical | | Problem class | nonlinear_inverse | | Solution space | coupled_flow_and_deformation | | Noise model | gaussian | | Integration axis | temporal | | Difficulty delta | 10 | | L dag | 4 | ## 📡 4. Measurement Model Strong coupling for low mass ratios; added-mass instability in partitioned schemes. | Metric | Value | |---|---| | Metric | PSNR_dB | | Secondary | SSIM | ## 📏 5. Operating Range (Ω) **Center problem class:** `fsi` · **Forward operator:** `fsi_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | Snr db | dB | 25 | | N times | — | 1000 | | N fluid dof | — | 100000 | | N solid dof | — | 10000 | | Added mass error | — | 0 | | Mesh motion error | — | 0 | | Solid damping error | — | 0 | | Interface mapping error | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | Snr db | dB | 0 – 40 | | N times | — | 100 – 1000000 | | N fluid dof | — | 1000 – 10000000 | | N solid dof | — | 100 – 1000000 | | Added mass error | — | 0.0 – 0.5 | | Mesh motion error | — | 0.0 – 0.3 | | Solid damping error | — | 0.0 – 0.3 | | Interface mapping error | — | 0.0 – 0.3 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 18.0 | Metric | Range | |---|---| | Psnr db | 10.0 – 45.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `1000` and δ = `10`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x68a53b397e965b367cb1e532c2148a725e89e68f0d272a22b72c1b5f375c148b` - **Chain tx hash:** `0xfc3d39f87822ca048d6b6d9be0febdb08bba044a25e442938395fdc03d062548` - **Chain block:** `41553978` --- ## File Mapping This bundle consists of: `L1-194.md`, `L1-194.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-194.md` | Source of truth — edit this | Human or LLM | | `L1-194.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 `L1-194`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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L2-194-001 Fluid-Structure Interaction (FSI) — coupled fluid + solid Mismatch-Only Spec

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📋 JSON metadata

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  "chain_block": 41553978,
  "chain_hash": "0x68a53b397e965b367cb1e532c2148a725e89e68f0d272a22b72c1b5f375c148b",
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  "domain": "Fluid Dynamics",
  "hardness_fn": {
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    "kappa": 1000,
    "metric": "PSNR_dB",
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    "regime": "Strong coupling for low mass ratios; added-mass instability in partitioned schemes.",
    "secondary": "SSIM"
  },
  "physics_fingerprint": {
    "L_DAG": 4.0,
    "carrier": "mechanical",
    "difficulty_delta": 10,
    "domain": "Fluid Dynamics",
    "integration_axis": "temporal",
    "noise_model": "gaussian",
    "primitives": [
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      "L.interface_coupling",
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    ],
    "problem_class": "nonlinear_inverse",
    "sensing_mechanism": "piv_dic",
    "solution_space": "coupled_flow_and_deformation",
    "sub_domain": "Partitioned / monolithic FSI",
    "title": "Fluid-Structure Interaction (FSI) \u2014 coupled fluid + solid"
  },
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      "SNR_dB",
      "interface_mapping_error",
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      "solid_damping_error",
      "mesh_motion_error",
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      "solid_damping_error",
      "mesh_motion_error"
    ],
    "allowed_problem_classes": [
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    "center_spec": {
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      "forward_operator": "fsi_forward",
      "input_format": "measurement_only",
      "omega": {
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        "N_solid_DOF": 10000,
        "N_times": 1000,
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        "mesh_motion_error": 0.0,
        "solid_damping_error": 0.0
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    "omega_bounds": {
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        1000,
        10000000
      ],
      "N_solid_DOF": [
        100,
        1000000
      ],
      "N_times": [
        100,
        1000000
      ],
      "SNR_dB": [
        0,
        40
      ],
      "added_mass_error": [
        0.0,
        0.5
      ],
      "interface_mapping_error": [
        0.0,
        0.3
      ],
      "mesh_motion_error": [
        0.0,
        0.3
      ],
      "solid_damping_error": [
        0.0,
        0.3
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Partitioned / monolithic FSI",
  "title": "Fluid-Structure Interaction (FSI) \u2014 coupled fluid + solid"
}

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