NurshatMenglik/Paired_Compressible_Boussinesq_Flow_Simulation_with_Random_Temperature_BCs

Paired Compressible / Boussinesq Flow with Random Temperature BCs

📄 Paper: A Neural Surrogate Approach for Simulating Natural Convection Problems (arXiv:2606.25259) — Nurshat Menglik, Alex Shao, David Hyde.

10,000 matched pairs of 2D natural-convection simulations of the differentially heated square cavity under randomized wall-temperature boundary conditions. Each sample solves the same problem twice — once with the Boussinesq model and once with the fully compressible model — producing aligned low-fidelity/high-fidelity field pairs.

Both solves use a monolithic, fully implicit mixed finite element method (Taylor–Hood: [P2]^2 velocity, P1 scalars) on the unit square, implemented in FEniCSx/DOLFINx.

Note: this is the earlier data release (December 2025). It stores pressure as the raw mean-subtracted perturbation and carries no per-sample meta.json. For the newer run with recorded generation parameters and normalized pressure, see Paired_Boussinesq_Compressible_Dataset.

Contents

10,000 sample folders, data0 … data9999 (~57 GB total). Each folder contains:

File	Description
T_bouss.npy, T_comp.npy	Temperature (P1 nodal values)
ux_bouss.npy, uy_bouss.npy	Boussinesq velocity components (P2 nodal values)
ux_comp.npy, uy_comp.npy	Compressible velocity components (P2 nodal values)
p_bouss_pert.npy, p_comp_pert.npy	Pressure, raw mean-subtracted perturbation
rho_comp.npy	Density (compressible solve only)
coords_*.npy	(n, 2) node coordinates matching each field above
paired_fields_2x4.png	2×4 visualization of the Boussinesq/compressible pair

All arrays are float64 and unstructured: they are flat finite-element nodal value arrays, not images. Node counts vary per sample (the mesh resolution is swept across the dataset — roughly 1.5k to 71k temperature nodes), and velocity lives on a richer P2 space than the P1 scalars — so always pair a field with its own coords_*.npy file rather than assuming a common grid.

Loading

import numpy as np

T  = np.load("data0/T_bouss.npy")        # (n,)
xy = np.load("data0/coords_T_bouss.npy") # (n, 2)

# interpolate onto a regular grid for ML use
from scipy.interpolate import griddata
gx, gy = np.meshgrid(np.linspace(0, 1, 64), np.linspace(0, 1, 64))
T_grid = griddata(xy, T, (gx, gy), method="linear")

If you want ready-to-train tensors on a uniform grid instead of raw FE output, use NeuralConvection_2D_TrainTest and NeuralConvection_3D_TrainTest.

Source

Generated with the solver and data-generation pipeline at https://github.com/Nurshat317/NeuralConvection

License

Released under CC BY 4.0. You are free to share and adapt this data, including commercially, provided you give appropriate credit and indicate any changes. The requested form of credit is a citation to the paper below.

Citation

If you use this dataset in your research, please cite:

@article{menglik2026neural,
  title         = {A Neural Surrogate Approach for Simulating Natural Convection Problems},
  author        = {Menglik, Nurshat and Shao, Alex and Hyde, David},
  journal       = {arXiv preprint arXiv:2606.25259},
  year          = {2026},
  eprint        = {2606.25259},
  archivePrefix = {arXiv},
  primaryClass  = {physics.comp-ph},
  url           = {https://arxiv.org/abs/2606.25259}
}

• Paper: arXiv:2606.25259
• Code: github.com/Nurshat317/NeuralConvection