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: 48693600
num_examples: 200
download_size: 11977292
dataset_size: 48693600
- config_name: parameters
features:
- name: omega2_length
dtype: float64
- name: peclet
dtype: float64
splits:
- name: default
num_bytes: 3200
num_examples: 200
download_size: 4933
dataset_size: 3200
- config_name: snapshots
features:
- name: temperature
list: float64
splits:
- name: default
num_bytes: 8256800
num_examples: 200
download_size: 8181284
dataset_size: 8256800
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-*
Graetz Problem Dataset
Dataset Description
This dataset contains thermal simulations of the Graetz problem with varying geometric and flow parameters.
Dataset Summary
The Graetz dataset provides numerical simulations of heat transfer in a channel with developing thermal boundary layer. The problem is characterized by varying channel geometry (omega2_length) and Péclet number, making it suitable for parametric reduced-order modeling and thermal-fluid analysis.
Dataset Structure
Data Instances
The dataset consists of three configurations:
- geometry: Mesh information (nodes and connectivity) - varies with geometric parameter
- snapshots: Temperature field solutions
- parameters: Geometric and flow parameters 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
temperature: Temperature field at each node (float64)
Parameters Configuration
omega2_length: Geometric parameter defining the channel configuration (float64)peclet: Péclet number characterizing the heat transfer regime (float64)
Data Splits
default: Contains all simulations with varying parameters
Dataset Creation
Source Data
The dataset was generated using finite element simulations of the convection-diffusion equation representing the Graetz problem. The mesh geometry varies with the omega2_length parameter, making this a parametrized geometry problem.
Preprocessing
Each simulation has its own mesh corresponding to the geometric parameter value. Solutions are stored as 1D arrays corresponding to the nodal values on each respective mesh.
Usage
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/graetz", name="geometry")
# Load snapshots
ds_data = load_dataset("SISSAmathLab/graetz", name="snapshots")
# Load parameters
ds_params = load_dataset("SISSAmathLab/graetz", name="parameters")
# Visualize temperature distribution for simulation 16
idx = 16
pts_x = np.asarray(ds_geom['default']['node_coordinates_x'][idx]).flatten()
pts_y = np.asarray(ds_geom['default']['node_coordinates_y'][idx]).flatten()
connectivity = ds_geom['default']['connectivity'][idx]
temperature = ds_data['default']['temperature'][idx]
omega2_length = ds_params['default']['omega2_length'][idx]
peclet = ds_params['default']['peclet'][idx]
triang = mtri.Triangulation(pts_x, pts_y, connectivity)
plt.tripcolor(triang, temperature, cmap='coolwarm')
plt.colorbar(label='Temperature')
plt.title(f'Graetz Problem (ω₂={omega2_length:.2f}, Pe={peclet:.1f})')
plt.xlabel('x')
plt.ylabel('y')
plt.axis('equal')
plt.show()
Contact
For questions or issues, please contact SISSA mathLab.