scaomath/navier-stokes-dataset

Navier Stokes Dataset of Isotropic Turbulence in a periodic box

The dataset for tensor-to-tensor or trajectory-to-trajectory neural operators, generated from Navier-Stokes equations to model the isotropic turbulence [1] such that the spectra satisfy the inverse cascade discovered by A.N. Kolmogorov [2].

[1]: McWilliams, J. C. (1984). The emergence of isolated coherent vortices in turbulent flow. Journal of Fluid Mechanics, 146, 21-43. [2]: Kolmogorov, A. N. (1941). The local structure of turbulence in incompressible viscous fluid for very large Reynolds Numbers. Dokl. Akad. Nauk SSSR, 30, 301.

Dataset Details

Dataset Description

The dataset contains several cases of isotropic turbulence modeled by Navier-Stokes equations. The data are generated either by a pseudo-spectral solver with 4th-order Runge-Kutta for the convection term, or a higher order Finite Volume IMEX methods. The different initial conditions have different peak wavenumbers of O(1), and eventually their spectra all converge to the Kolmogorov inverse cascade.

• Curated by: S. Cao
• Funded by National Science Foundation: NSF award DMS-2309778
• License: MIT license

Dataset Sources [optional]

• Repository: https://github.com/scaomath/torch-cfd
• Paper: [More Information Needed]
• Demo:
  • The classical Kolmogorov inverse cascade with a solenoidal forcing and small drag.
  • The fast training using the data with a small number of vortices.
  • The fast converging to the inverse cascade.

Dataset Structure

Each individual chunk of data is pickled in single-file format.

Dataset Creation

TO-DO

Citation

@article{2024SpectralRefiner,
  title={Spectral-Refiner: Fine-Tuning of Accurate Spatiotemporal Neural Operator for Turbulent Flows},
  author={Shuhao Cao and Francesco Brarda and Ruipeng Li and Yuanzhe Xi},
  journal={arXiv preprint arXiv:2405.17211},
  year={2024},
  primaryClass={cs.LG}
}