---
dataset_info:
- config_name: geometry
  features:
  - name: node_coordinates_x
    list: float64
  - name: node_coordinates_y
    list: float64
  - name: connectivity
    list:
      list: int32
  splits:
  - name: default
    num_bytes: 75692
    num_examples: 1
  download_size: 48029
  dataset_size: 75692
- config_name: parameters
  features:
  - name: viscosity
    dtype: float64
  splits:
  - name: default
    num_bytes: 4000
    num_examples: 500
  download_size: 5460
  dataset_size: 4000
- config_name: snapshots
  features:
  - name: velocity_x
    list: float64
  - name: velocity_y
    list: float64
  - name: pressure
    list: float64
  splits:
  - name: default
    num_bytes: 19674000
    num_examples: 500
  download_size: 19644566
  dataset_size: 19674000
configs:
- config_name: geometry
  data_files:
  - split: default
    path: geometry/default-*
- config_name: parameters
  data_files:
  - split: default
    path: parameters/default-*
- config_name: snapshots
  data_files:
  - split: default
    path: snapshots/default-*
---
# Navier-Stokes Flow Around Cylinder Dataset

## Dataset Description

This dataset contains computational fluid dynamics simulations of incompressible flow around a cylinder with varying viscosity parameters.

### Dataset Summary

The Navier-Stokes Cylinder dataset provides numerical simulations of viscous fluid flow around a circular cylinder. The dataset includes velocity fields (x and y components) and pressure fields, making it ideal for fluid dynamics research, reduced-order modeling, and machine learning applications in CFD.

## Dataset Structure

### Data Instances

The dataset consists of three configurations:

- **geometry**: Mesh information (nodes and connectivity)
- **snapshots**: Flow field solutions (velocity and pressure)
- **parameters**: Viscosity 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)
- `connectivity`: Sequence of element connectivity (triangular elements, int32)

#### Snapshots Configuration
- `velocity_x`: Velocity field in x-direction at each node (float64)
- `velocity_y`: Velocity field in y-direction at each node (float64)
- `pressure`: Pressure field at each node (float64)

#### Parameters Configuration
- `viscosity`: Kinematic viscosity parameter for each simulation (float64)

### Data Splits

- `default`: Contains all simulations

## Dataset Creation

### Source Data

The dataset was generated using finite element simulations of the incompressible Navier-Stokes equations with varying viscosity parameters. The flow configuration represents flow around a circular cylinder, a classic benchmark problem in computational fluid dynamics.

### Preprocessing

Solutions are stored with velocity components and pressure as separate 1D arrays corresponding to the nodal values on the mesh. The raw data is reshaped from column-major (Fortran) order.

## Usage

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

# Load geometry
ds_geom = load_dataset("SISSAmathLab/navier-stokes-cylinder", name="geometry")

# Load snapshots
ds_data = load_dataset("SISSAmathLab/navier-stokes-cylinder", name="snapshots")

# Load parameters
ds_params = load_dataset("SISSAmathLab/navier-stokes-cylinder", 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()
connectivity = ds_geom['default']['connectivity'][0]

vel_x = np.asarray(ds_data['default']['velocity_x'][0])
vel_y = np.asarray(ds_data['default']['velocity_y'][0])
velocity_magnitude = np.sqrt(vel_x**2 + vel_y**2)

triang = mtri.Triangulation(pts_x, pts_y, connectivity)
plt.tripcolor(triang, velocity_magnitude, cmap='viridis')
plt.colorbar(label='Velocity Magnitude')
plt.title('Navier-Stokes - Flow Around Cylinder')
plt.xlabel('x')
plt.ylabel('y')
plt.axis('equal')
plt.show()
```


## Contact

For questions or issues, please contact SISSA mathLab.