2D Lattice-Boltzmann Flow: D2Q9 Vortex Street

It is a computational fluid dynamics technique that evolves particle distribution functions on a regular grid instead of solving the Navier-Stokes equations directly. Particles stream to neighbouring cells and then collide, relaxing toward a local equilibrium; averaging the distributions recovers density and velocity.

D2Q9 names the lattice geometry: two dimensions (D2) with nine discrete velocity directions (Q9) — a rest state, four axis-aligned moves and four diagonal moves, weighted 4/9, 1/9 and 1/36 respectively. It is the standard lattice for two-dimensional LBM.

Both run the identical D2Q9 streaming-and-collision algorithm on a 2D grid. The 3D page uploads the resulting field to a WebGL texture and draws it on a Three.js quad; this page paints the same kind of field directly onto a 2D canvas with putImageData — a genuinely different rendering pipeline, not a different physics model.

Behind a bluff body, flow becomes unstable above a critical Reynolds number and small disturbances grow into alternating shed vortices. The discrete LBM dynamics already contain the required nonlinearity, so the pattern emerges without any extra forcing once viscosity is low enough.

Viscosity sets the BGK relaxation time via τ = 3ν + 0.5, which controls how quickly distributions return to equilibrium. Lower viscosity raises the Reynolds number and produces more vortex shedding; higher viscosity damps the flow toward smooth, laminar streamlines.