README.md

---
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---
# Lid-Driven Cavity Flow Dataset

## Dataset Description

This dataset contains computational fluid dynamics simulations of the classic lid-driven cavity problem with varying lid velocity parameters.

### Dataset Summary

The Lid-Driven Cavity dataset provides numerical simulations of viscous fluid flow in a square cavity with a moving lid. The dataset includes velocity magnitude and pressure fields, representing a fundamental benchmark problem in computational fluid dynamics suitable for validation of numerical methods and machine learning applications.

## Dataset Structure

### Data Instances

The dataset consists of three configurations:

- **geometry**: Mesh node coordinates
- **snapshots**: Flow field solutions (velocity magnitude and pressure)
- **parameters**: Lid velocity values for each simulation

### Data Fields

#### Geometry Configuration
- `node_coordinates_x`: Sequence of x-coordinates of mesh nodes (float64)
- `node_coordinates_y`: Sequence of y-coordinates of mesh nodes (float64)

#### Snapshots Configuration
- `velocity_magnitude`: Velocity magnitude at each node (float64)
- `pressure`: Pressure field at each node (float64)

#### Parameters Configuration
- `velocity`: Lid velocity parameter for each simulation (float64)

### Data Splits

- `default`: Contains all simulations

## Dataset Creation

### Source Data

The dataset was generated using numerical simulations of the incompressible Navier-Stokes equations in a square cavity with a moving top lid. This is a classic benchmark problem used for validating CFD codes.

### Preprocessing

Solutions are stored as 1D arrays corresponding to the nodal values. The geometry uses a structured or unstructured mesh representation of the square cavity domain.

## Usage

```python
from datasets import load_dataset
import numpy as np
import matplotlib.pyplot as plt

# Load geometry
ds_geom = load_dataset("SISSAmathLab/lid-cavity", name="geometry")

# Load snapshots
ds_data = load_dataset("SISSAmathLab/lid-cavity", name="snapshots")

# Load parameters
ds_params = load_dataset("SISSAmathLab/lid-cavity", name="parameters")

# Visualize velocity magnitude for first simulation
pts_x = np.asarray(ds_geom['default']['node_coordinates_x']).flatten()
pts_y = np.asarray(ds_geom['default']['node_coordinates_y']).flatten()
velocity_mag = ds_data['default']['velocity_magnitude'][0]

plt.scatter(pts_x, pts_y, c=velocity_mag, cmap='jet', s=1)
plt.colorbar(label='Velocity Magnitude')
plt.title('Lid-Driven Cavity Flow')
plt.xlabel('x')
plt.ylabel('y')
plt.axis('equal')
plt.show()
```


## Contact

For questions or issues, please contact SISSA mathLab.