Lattice-Boltzmann Fluid Simulation — Poiseuille Flow

The Lattice-Boltzmann method (D2Q9) models fluid flow by tracking discrete particle distributions on a grid. Each step: collision (BGK relaxation toward Maxwell-Boltzmann equilibrium) + streaming. Poiseuille flow driven by a body force between parallel walls develops a parabolic velocity profile, with Re = ρUL/μ controlling the transition to turbulence.