cfd-ns-bkm

# 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 $$ \int_0^T \lVert \omega(\cdot,t) \rVert_{L^\infty}\, dt $$ tracked alongside enstrophy. Computed with a custom **CUDA + cuFFT** kernel on **NVIDIA RTX 5090** (Blackwell, sm_120). > Part of the [bigcompute.science](https://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: | Column | Type | Description | |--------|------|-------------| | `step` | int | Time-step index | | `time` | float | Physical time \\(t\\) | | `max_vorticity` | float | \\(\lVert \omega \rVert_{L^\infty}\\) (max vorticity on the grid) | | `enstrophy` | float | \\(\tfrac{1}{2}\int \lVert \omega \rVert^2 \, dx\\) | | `bkm_cumulative` | float | Running BKM integral \\(\int_0^t \lVert \omega \rVert_{L^\infty}\, ds\\) | Certifying logs are in `logs/`. Run metadata in `metadata.json`. ### Configurations | Config | Grid | \\(\nu\\) | IC | Steps | \\(\Delta t\\) | Final max \\(\lVert \omega \rVert_{L^\infty}\\) | Final BKM | Throughput | |--------|------|---|-----|-------|-----|-----------------|-----------|------------| | `smoke_taylor_green` | \\(256^2\\) | \\(10^{-3}\\) | Taylor–Green | 2000 | 0.01 | 0.157 at \\(t=20\\) | 12.80 | ~1108 steps/s | | `standard_random` | \\(512^2\\) | \\(10^{-4}\\) | Random blob | 5000 | 0.005 | 0.026 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](https://github.com/cahlen/idontknow/blob/main/scripts/experiments/cfd-ns-bkm/ns2d_bkm.cu) ## Related - CFD program hub: [cfd-chaotic-advection experiment](https://bigcompute.science/experiments/cfd-chaotic-advection/) - Experiment page: [cfd-ns-bkm](https://bigcompute.science/experiments/cfd-ns-bkm/) - Finding: [2D NS BKM diagnostic](https://bigcompute.science/findings/cfd-ns-bkm-diagnostic/) — **bronze** / ACCEPT w/ revision (3-model review; consensus = most conservative: 2× silver + 1× bronze) - Phase 3 dataset: [cahlen/cfd-ns3d-bkm](https://huggingface.co/datasets/cahlen/cfd-ns3d-bkm) - Code: [idontknow/scripts/experiments/cfd-ns-bkm](https://github.com/cahlen/idontknow/tree/main/scripts/experiments/cfd-ns-bkm) ## 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.