A GPU-accelerated pseudo-spectral solver for probing classical blow-up scenarios in 3D incompressible Navier-Stokes equations.

The BKM Engine implements a high-fidelity numerical framework for investigating potential finite-time singularities in 3D incompressible fluid flows. Key features include:

• GPU Acceleration: Full CUDA support via CuPy for grids up to 512³
• Beale-Kato-Majda Monitoring: Continuous tracking of BKM integral I(t)
• Vorticity-Strain Alignment: Real-time geometric diagnostics
• Adaptive Timestepping: CFL-based control with diagnostic guards
• Machine-Precision Incompressibility: Spectral projection maintaining ∇·u < 10⁻¹⁴
• Comprehensive Test Suite: Five canonical benchmarks with standardized data export

An early draft can be found in the repository here: https://github.com/JDCurry/bkm-engine/blob/main/BKM_Engine___Unpublished_Draft.pdf

Computational tests are complete, and we are currently compiling results and figures as of August 31, 2025.

• Python 3.8+
• CUDA-capable GPU (optional but recommended)
• 16GB+ RAM for 256³ simulations
• 32GB+ GPU memory for 512³ simulations

git clone https://github.com/JDCurry/bkm-engine.git
cd bkm-engine
pip install -r requirements.txt
python setup.py install