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--- |
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license: mit |
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task_categories: |
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- image-to-3d |
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tags: |
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- mathematics |
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- partial-differential-equations |
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- computational fluid dynamics |
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- physics |
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- neural operator |
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size_categories: |
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- 1K<n<10K |
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--- |
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# Navier Stokes Dataset of Isotropic Turbulence in a periodic box |
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<!-- Provide a quick summary of the dataset. --> |
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The dataset for tensor-to-tensor or trajectory-to-trajectory neural operators, generated from Navier-Stokes equations |
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to model the isotropic turbulence [1] such that the spectra satisfy the inverse cascade discovered by A.N. Kolmogorov [2]. |
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[1]: McWilliams, J. C. (1984). The emergence of isolated coherent vortices in turbulent flow. *Journal of Fluid Mechanics*, 146, 21-43. |
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[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. |
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## Dataset Details |
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### Dataset Description |
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<!-- Provide a longer summary of what this dataset is. --> |
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The dataset contains several cases of isotropic turbulence modeled by Navier-Stokes equations. The data are generated either |
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by a pseudo-spectral solver with 4th-order Runge-Kutta for the convection term, or a higher order Finite Volume IMEX methods. |
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The different initial conditions have different peak wavenumbers of O(1), and eventually their spectra all converge to the Kolmogorov |
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inverse cascade. |
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- **Curated by:** S. Cao |
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- **Funded by National Science Foundation:** NSF award DMS-2309778 |
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- **License:** MIT license |
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### Dataset Sources [optional] |
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<!-- Provide the basic links for the dataset. --> |
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- **Repository:** [https://github.com/scaomath/torch-cfd](https://github.com/scaomath/torch-cfd) |
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- **Paper:** [More Information Needed] |
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- **Demo:** |
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- [The classical Kolmogorov inverse cascade with a solenoidal forcing and small drag.](https://github.com/scaomath/torch-cfd/blob/main/examples/Kolmogrov2d_rk4_cn_forced_turbulence.ipynb) |
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- [The fast training using the data with a small number of vortices.](https://github.com/scaomath/torch-cfd/blob/main/examples/ex2_SFNO_train_fnodata.ipynb) |
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- [The fast converging to the inverse cascade.](https://github.com/scaomath/torch-cfd/blob/main/examples/ex2_SFNO_5ep_spectra.ipynb) |
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## Dataset Structure |
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<!-- This section provides a description of the dataset fields, and additional information about the dataset structure such as criteria used to create the splits, relationships between data points, etc. --> |
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Each individual chunk of data is pickled in single-file format. |
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## Dataset Creation |
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### TO-DO |
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## Citation |
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<!-- If there is a paper or blog post introducing the dataset, the APA and Bibtex information for that should go in this section. --> |
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```bibtex |
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@article{2024SpectralRefiner, |
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title={Spectral-Refiner: Fine-Tuning of Accurate Spatiotemporal Neural Operator for Turbulent Flows}, |
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author={Shuhao Cao and Francesco Brarda and Ruipeng Li and Yuanzhe Xi}, |
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journal={arXiv preprint arXiv:2405.17211}, |
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year={2024}, |
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primaryClass={cs.LG} |
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} |
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``` |
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