Team Ai
Datasetpublic

cahlen/cfd-ns-bkm

2D Navier–Stokes BKM Diagnostic Pseudospectral vorticity-form Navier–Stokes on a periodic torus [0,2π)2[0,2\pi)^2[0,2π)2, with the Beale–Kato–Majda (BKM) diagnostic ∫0T∥ω(⋅,t)∥L∞ dt \int_0^T \lVert \omega(\cdot,t) \rVert_{L^\infty}\, dt ∫0T​∥ω(⋅,t)∥L∞​dt tracked alongside enstrophy. Computed with a custom CUDA + cuFFT kernel on NVIDIA RTX 5090 (Blackwell, sm_120). Part of the bigcompute.science CFD conjecture program — GPU infrastructure toward 3D BKM blowup searches. 2D… See the full description on the dataset page: https://huggingface.co/datasets/cahlen/cfd-ns-bkm.

sourceHugging Facemitupdated 4mo agoView on Hugging Face
0likes25downloads
Dataset Card

2D Navier–Stokes BKM Diagnostic

Pseudospectral vorticity-form Navier–Stokes on a periodic torus \\([0,2\pi)^2\\), with the Beale–Kato–Majda (BKM) diagnostic

$$ \int0^T \lVert \omega(\cdot,t) \rVert{L^\infty}\, dt $$

tracked alongside enstrophy. Computed with a custom CUDA + cuFFT kernel on NVIDIA RTX 5090 (Blackwell, sm_120).

Part of the bigcompute.science CFD conjecture program — GPU infrastructure toward 3D BKM blowup searches. 2D incompressible flow is globally regular; these runs are certifying diagnostics, not blowup evidence.

Quick Start

python
from datasets import load_dataset

tg = load_dataset("cahlen/cfd-ns-bkm", "smoke_taylor_green", split="train")
rand = load_dataset("cahlen/cfd-ns-bkm", "standard_random", split="train")
print(tg[-1])  # final Taylor–Green row

What's In This Dataset

Each row is one logged time step from a pseudospectral DNS run:

ColumnTypeDescription
stepintTime-step index
timefloatPhysical time \\(t\\)
max_vorticityfloat\\(\lVert \omega \rVert_{L^\infty}\\) (max vorticity on the grid)
enstrophyfloat\\(\tfrac{1}{2}\int \lVert \omega \rVert^2 \, dx\\)
bkm_cumulativefloatRunning BKM integral \\(\int0^t \lVert \omega \rVert{L^\infty}\, ds\\)

Certifying logs are in logs/. Run metadata in metadata.json.

Configurations

ConfigGrid\\(\nu\\)ICSteps\\(\Delta t\\)Final max \\(\lVert \omega \rVert_{L^\infty}\\)Final BKMThroughput
smoke_taylor_green\\(256^2\\)\\(10^{-3}\\)Taylor–Green20000.010.157 at \\(t=20\\)12.80~1108 steps/s
standard_random\\(512^2\\)\\(10^{-4}\\)Random blob50000.0050.026 at \\(t=25\\)1.77~532 steps/s

Both runs: zero NaN/Inf (exit certificate).

Method (summary)

Vorticity equation:

$$ \partial_t \omega + \mathbf{u}\cdot\nabla\omega = \nu \nabla^2 \omega $$

  • —Streamfunction Poisson solve in Fourier space; 2/3 Orszag dealiasing; RK4; fp64
  • —Random IC: Gaussian-envelope vorticity blob at \\((\pi,\pi)\\) with SplitMix64 amplitudes

Key Results

  • —Taylor–Green: \\(\lVert \omega \rVert_{L^\infty}\\) decays 2.0 → 0.16 by \\(t=20\\); validates spectral accuracy
  • —Random IC at \\(\nu=10^{-4}\\): BKM integral ≈ 1.77 over \\(t=25\\); peak vorticity remains bounded
  • —Infrastructure validated for Phase 3 3D extension

Reproduction

bash
git clone https://github.com/cahlen/idontknow.git
cd idontknow
./scripts/experiments/cfd-ns-bkm/run.sh 256 0.001 2000 0.01 taylor-green
./scripts/experiments/cfd-ns-bkm/run.sh 512 0.0001 5000 0.005 random
python3 scripts/experiments/cfd-ns-bkm/upload_hf.py

CUDA kernel: ns2d_bkm.cu

Related

Citation

bibtex
@misc{humphreys2026cfdnsbkm,
  author = {Humphreys, Cahlen},
  title = {2D Navier–Stokes BKM Diagnostic (GPU Pseudospectral DNS)},
  year = {2026},
  publisher = {Hugging Face},
  howpublished = {\\url{https://huggingface.co/datasets/cahlen/cfd-ns-bkm}}
}

Human–AI collaborative research. Peer-reviewed finding on bigcompute.science. All code and data open for verification.