🌀 Lattice-Boltzmann Flow — D2Q9 CFD

🌀 What It Demonstrates

This simulator implements the Lattice-Boltzmann Method (LBM) with a D2Q9 lattice — a mesoscopic approach to computational fluid dynamics. Instead of solving the Navier-Stokes equations directly, LBM tracks probability distribution functions of fictitious particles streaming and colliding on a regular lattice. The BGK (Bhatnagar-Gross-Krook) single-relaxation-time collision operator drives the distributions toward a Maxwell-Boltzmann equilibrium. Macroscopic quantities — density ρ and velocity u — emerge naturally from moments of the distribution.

How to Use

• Click and drag on the canvas to draw solid obstacles (bounce-back boundaries).
• Adjust Viscosity — lower viscosity means higher Reynolds number and more turbulent flow.
• Raise the Inlet Velocity to trigger vortex shedding behind obstacles.
• Switch Visualisation mode between velocity magnitude, vorticity (curl of u) and density.
• A circular cylinder is placed by default — watch the Kármán vortex street form.

Did You Know?

The Kármán vortex street is responsible for the "singing" of power lines in the wind, the oscillation of tall chimneys, and even the cloud patterns visible behind islands in satellite imagery. Theodore von Kármán first described the phenomenon mathematically in 1911. In LBM the same pattern emerges spontaneously once the Reynolds number exceeds ~47 — no special boundary conditions needed.