Lattice Boltzmann — BGK Collision Operator

D2Q9 LBM: fᵢ(x+eᵢ,t+1) = fᵢ(x,t) − (1/τ)[fᵢ − fᵢᵉq] with obstacles

τ=0.80
The Lattice Boltzmann method (D2Q9 scheme) simulates fluid flow by tracking particle distribution functions on a grid. The BGK collision operator relaxes distributions toward Maxwell-Boltzmann equilibrium with rate 1/τ, recovering the Navier-Stokes equations with kinematic viscosity ν = c_s²(τ−½)Δt.