💨 Lattice-Boltzmann — Fluid Simulation on a Grid
Real-time 2D fluid dynamics — Kármán vortex streets, drag, and pipe flow from microscopic collisions
Presets
Display
Parameters
Flow Stats
Physics
f_i → f_i + (f_i^eq − f_i)/τ
τ = 3ν + 0.5
Re = U·L/ν
Kármán: Re ≈ 40–200
About the Lattice-Boltzmann Method
Microscopic to Macroscopic
Unlike traditional Navier-Stokes solvers, LBM simulates fluid as a grid of particles streaming and colliding. Each cell holds 9 distribution functions f_i representing particle populations moving in each of the D2Q9 directions. After collision (relaxation toward equilibrium) and streaming (shifting f_i to neighbouring cells), macroscopic density ρ = Σf_i and velocity u = Σf_i·c_i/ρ emerge naturally.
Kármán Vortex Street
At Reynolds numbers between 40 and a few hundred, flow past a cylinder becomes unstable. Vortices shed alternately from either side of the obstacle, forming a regular pattern known as the Kármán vortex street. The shedding frequency f, cylinder diameter D, and flow speed U are related by the Strouhal number St = f·D/U ≈ 0.21 at Re=100. This phenomenon shook the Tacoma Narrows Bridge to destruction in 1940.
Reynolds Number
The Reynolds number Re = U·L/ν (inertial / viscous forces) determines flow character: Re < 5 gives smooth creeping flow with symmetric recirculation; Re ~ 40–200 produces the periodic Kármán vortex street; Re > 1000 leads to turbulent, chaotic wakes. In the LBM, viscosity links to the relaxation time τ = 3ν + 0.5, and stability requires τ > 0.5.