2D Turbulence Simulation (SciPy / CuPy)

Source code: https://github.com/mannetroll/cupystorm

A Direct Numerical Simulation (DNS) code for 2D homogeneous incompressible turbulence

It supports:

• SciPy / NumPy for CPU runs
• CuPy (optional) for GPU acceleration on CUDA devices (e.g. RTX 3090)

one-liner CPU/SciPy

$ curl -LsSf https://astral.sh/uv/install.sh | sh
$ uv cache clean mannetroll-cupystorm
$ uv run --python 3.13 --with "mannetroll-cupystorm==0.1.2" turbulence

one-liner GPU/CuPy

$ uv run --python 3.13 --with "mannetroll-cupystorm[cuda]==0.1.2" turbulence

DNS solver

The solver includes:

• PAO-style random-field initialization
• 3/2 de-aliasing in spectral space
• Crank–Nicolson time integration
• CFL-based adaptive time stepping (Δt updated from the current flow state)

cupystorm GUI (PySide6)

Run an cupystorm window that:

• Displays the flow field as a live image (fast Indexed8 palette rendering)
• Lets you switch displayed variable:
  • U, V (velocity components)
  • K (kinetic energy)
  • Ω (vorticity)
  • φ (stream function)
• Lets you switch colormap (several built-in palettes)
• Lets you change simulation parameters on the fly:
  • Grid size N
  • Reynolds number Re
  • Initial spectrum peak K0
  • CFL number CFL
  • Max steps / auto-reset limit
  • GUI update interval (how often to refresh the display)
• Includes force/initialization modes:
  • Navier-Stokes: PAO spectrum init
  • High-k + Ekman/Rayleigh: High-k spectral forcing + Ekman/Rayleigh large-scale drag
  • Rain: random “kick” forcing events
  • Circle: a forcing point moves on a circular trajectory (continuous forcing)
  • Mouse: apply forcing by click/drag in the image

Keyboard shortcuts

Single-key shortcuts (application-wide) for fast control:

• V: cycle variable
• C: cycle colormap
• N: cycle grid size
• R: cycle Reynolds number
• K: cycle K0
• L: cycle CFL
• S: cycle max steps
• U: cycle update interval

Saving / exporting

From the GUI you can:

• Save the current frame as a PNG image
• Dump full-resolution fields to a folder as PGM images:
  • u-velocity, v-velocity, kinetic energy, vorticity

Display scaling

To keep the GUI responsive for large grids, the displayed image is automatically upscaled/downscaled depending on N. The window is resized accordingly when you change N.

Installation

Using uv

From the project root:

uv sync
uv run turbulence

High-k spectral forcing + Ekman/Rayleigh large-scale drag

The flow remains fully turbulent after 1,000,000 iterations (256 x 256) CuPy

Rain (256 x 256) SciPy

Circle (256 x 256) SciPy

Mouse (256 x 256) SciPy

Full CLI

$ python -m cupystorm.turbo_simulator N Re K0 STEPS CFL BACKEND [MODE]

Where:

• N — grid size
• Re — Reynolds number
• K0 — peak wavenumber of the energy spectrum
• STEPS — number of time steps
• CFL — target CFL number
• BACKEND — "cpu", "gpu", or "auto"
• MODE — "pao" | "highh" | "rain" | "circle" | "mouse"

Examples:

# CPU run (SciPy with 4 workers)
$ python -m cupystorm.turbo_simulator 256 10000 10 1001 0.75 cpu

# Auto-select backend (GPU if CuPy + CUDA are available)
$ python -m cupystorm.turbo_simulator 256 10000 10 1001 0.75 auto

Enabling GPU with CuPy (CUDA 13)

On a CUDA machine (e.g. RTX 5090):

Download: https://developer.nvidia.com/cuda-downloads

1. Check that the driver/CUDA are available:

   $ nvidia-smi
   

2. Install CuPy into the uv environment:

   $ uv sync --extra cuda
   $ uv run turbulence
   

3. Verify that CuPy sees the GPU:

   $ uv run python -c "import cupy as cp; x = cp.arange(5); print(x, x.device)"
   

4. Run in GPU mode:

   $ uv run python -m cupystorm.turbo_simulator 256 10000 10 1001 0.75 gpu
   

Or let the backend auto-detect:

   $ uv run python -m cupystorm.turbo_simulator 256 10000 10 1001 0.75 auto

The DNS with CuPy (7776 x 7776) Navier-Stokes

Profiling

cProfile (CPU)

$ python -m cProfile -o turbo_simulator.prof -m cupystorm.turbo_simulator    

Inspect the results:

$ python -m pstats turbo_simulator.prof
# inside pstats:
turbo_simulator.prof% sort time
turbo_simulator.prof% stats 20

GUI profiling with SnakeViz

Install SnakeViz:

$ uv pip install snakeviz

Visualize the profile:

$ snakeviz turbo_simulator.prof

Memory & CPU profiling with Scalene (GUI)

Install Scalene:

$ uv pip install "scalene==1.5.55"

Run with a GUI report:

$ scalene -m cupystorm.turbo_simulator 256 10000 10 201 0.75 cpu

Memory & CPU profiling with Scalene (CLI only)

For a terminal-only summary:

$ scalene --cli --cpu -m cupystorm.turbo_simulator 256 10000 10 201 0.75 cpu

License

Copyright © 2026 Mannetroll