# ⚛  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`

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## 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._