| --- |
| 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 |
| |
| ```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/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. |
| |
