CFD Phase 3: 3D Navier–Stokes BKM Blowup Search (RTX 5090)

Cahlen Humphreys

May 27, 2026 by cahlen complete Silver

SILVER AI Literature Audit · 3 reviews ↓

Consensus	`ACCEPT_WITH_REVISION`
Models	gemini-2.5-pro + gpt-4.1 + o3-pro
Level	SILVER — Published literature supports approach

Review Ledger

2026-05-31 gemini-2.5-pro (Google) SILVER ACCEPT_WITH_REVISION

2026-05-31 gpt-4.1 (OpenAI) SILVER ACCEPT_WITH_REVISION

2026-05-31 o3-pro (OpenAI) SILVER ACCEPT_WITH_REVISION

Issues Identified (8/8 resolved)

minor Add References for BKM (1984), Orszag dealiasing, Canuto/Rogallo pseudospectr... resolved

important Include Δt (and viscosity) in results table for reproducibility. resolved

minor Confirm fp64 usage explicitly in the method section. resolved

minor Include GPU device-query evidence in published dataset/logs. resolved

minor Clarify Taylor–Green vs random-blob IC roles relative to benchmark literature. resolved

minor Document k=0 handling in velocity inversion to avoid division by zero. resolved

important State resolution limits, scalability ceiling, and comparison to blowup-search... resolved

important Provide solver stability evidence (NaN/Inf certificate; enstrophy/BKM monitor... resolved

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Hardware

1x RTX 5090 (32 GB VRAM) RAM

fluid-dynamicsnavier-stokesbeale-kato-majdablowup-search rtx-5090 cuda-kernelcufft3d-dns

Key Results

Problem: 3D incompressible NS with BKM ∫||ω||∞ dt — blowup search infrastructure
Status: COMPLETE — smoke + standard + Phase 4 blowup monitors; 512³ OOM on 32 GB
Smoke: 64³ Taylor–Green, ν=0.01, 200 steps, BKM ≈ 1.63
Standard: 128³ random IC, ν=1e-3, 1,000 steps
Blowup Search: 256³ random IC, ν=1e-4, 5,000 steps, BKM ≈ 4.45, no blowup
Kerr Sweep: 256³ Kerr tubes, ν=1e-4, BKM ≈ 9.99 (5.7× random), zero NaN/Inf

CFD Phase 3: 3D Navier–Stokes BKM Blowup Search

Abstract

We extend the 2D BKM diagnostic to three dimensions, implementing vorticity-form Navier–Stokes with vortex stretching $(\boldsymbol{\omega}\cdot\nabla)\mathbf{u}$ — the mechanism relevant to Beale–Kato–Majda blowup criteria in 3D.

$\omega_t + (\mathbf{u}\cdot\nabla)\omega = (\boldsymbol{\omega}\cdot\nabla)\mathbf{u} + \nu\nabla^2\omega$

Velocity recovered in Fourier space via $\hat{\mathbf{u}} = i(\mathbf{k}\times\hat{\boldsymbol{\omega}})/|\mathbf{k}|^2$ .

Results

Certifying runs on RTX 5090 with zero NaN/Inf. No blowup observed at tested $(N, \nu, T)$ — consistent with finite-resolution viscous DNS at moderate Re.

Finding: 3D NS BKM infrastructure (silver-certified, 2026-05-31)

Reproduction

./scripts/experiments/cfd-ns3d-bkm/run.sh 64 0.01 200 0.002 taylor-green   # smoke
./scripts/experiments/cfd-ns3d-bkm/run.sh 128 0.001 1000 0.002 random       # standard
./scripts/experiments/cfd-ns3d-bkm/run.sh 256 0.0001 500 0.001 random       # blowup search (Phase 4)
./scripts/experiments/cfd-ns3d-bkm/run.sh 256 0.0001 2000 0.001 random      # extended monitor
./scripts/experiments/cfd-ns3d-bkm/run.sh 256 0.0001 5000 0.001 random      # 5000-step monitor
./scripts/experiments/cfd-ns3d-bkm/run.sh 256 0.001 1000 0.001 taylor-green # higher-Re TG
./scripts/experiments/cfd-ns3d-bkm/run.sh 256 0.001 1000 0.001 kerr        # Phase 5 Kerr IC
./scripts/experiments/cfd-ns3d-bkm/run_phase5_kerr_sweep.sh                  # Kerr ν sweep

VRAM note: 512³ exceeds 32 GB on RTX 5090 (cudaMalloc OOM during C2C plan setup). 256³ is the current production grid for lower-ν searches.

Dataset: cahlen/cfd-ns3d-bkm

Human–AI collaboration. Silver-certified finding (2026-05-31).