ccm/navier-stokes-singularity-simulation

Native Navier–Stokes simulation voxels

Lossless exports of velocity and manufactured forcing from Oliver's completed AMReX / incflo experiment. The source has 280 saved states from exact rest through t = 0.995, including an exactly quiescent interval through t = 0.55. An explicitly labeled prototype may contain fewer states; each release's manifest.json is authoritative about its coverage.

Layout and access

Each content-addressed releases/<manifest-hash-prefix>/ directory contains manifest.json, source-best.json, and fields.zarr. The manifest lists actual times, source plotfile names, component order, level geometry, and per-frame, per-level SHA-256 hashes of uncompressed values. Publication never overwrites another release. Pin both the dataset commit and release prefix when citing, downloading, or analyzing the fields.

fields.zarr/level_0 through level_4 have axes (t, x, y, z, component). Every level occupies a 64 × 64 × 64 rectangular native patch. Components are u_x, u_y, u_z, f_x, f_y, f_z, stored as little-endian float64 in nondimensional model units. Origins are cell-boundary coordinates; cell centers are origin + (index + 0.5) * spacing.

The full periodic domain is [−1,1]³. The base spacing is 2/64; four fixed inner cubes have half-widths 0.5, 0.25, 0.125, and 0.0625, with spacing halved at each level. Thus 1024³-equivalent spacing applies only to the innermost core. There are 1,310,720 stored cells and 1,179,648 active composite cells per state. Covered coarse cells are retained for fidelity to the native files. Exclude them from composite integrals and select the finest containing cell for slices.

Zarr v3 uses lossless Blosc Zstd/bitshuffle compression, 8³-cell chunks split into velocity and force triplets, and one shard per level per saved state. The entire uncompressed field payload is 16.40625 GiB. No dense 1024³ regridding, float32 conversion, spatial smoothing, or temporal interpolation is performed. Pressure, ghost cells, and solver checkpoints are not included.

Use Zarr 3.3 and huggingface_hub / fsspec to open hf://datasets/ccm/navier-stokes-singularity-simulation@<commit>/releases/<hash>/fields.zarr. The interactive Space provides a three-plane viewer without requiring a whole-history download.

Validation and limitations

Each exported level is read back and compared exactly with its native float64 values. Checks also require finite fields, exact rest, source timestamps, active-grid peak speed, full-domain volume, and endpoint kinetic energy. Independent C++ slice comparisons test all three axes, and synthetic nested-grid tests check axis order, boundary selection, and refinement precedence.

These are archive and visualization integrity checks, not accuracy bounds. The experiment uses a finite, localized, three-pulse manufactured-force surrogate inspired by the analytical construction. It does not implement that construction's exact infinite hierarchy or certify a Navier–Stokes singularity. The coarser outer grid can remain under-resolved; resampling cannot repair it.

Provenance and reuse

Created by Chris McComb's independent numerical project, not affiliated with OpenAI. Run settings, upstream solver revisions, archive hashes, and diagnostics are retained in each release's source-best.json.

• —Simulation source
• —Numerical record
• —Method and limitations

Released under the project's MIT license. Cite this dataset's repository, immutable commit, release prefix, and source run ID so the exact fields remain identifiable.

Current verified release

280 states, complete history; t = 0.0 to 0.995.

• —Dataset commit: 25266bfc068a729fb169833521eeddfde9c943e9
• —Release: releases/9be10c40938a9d02