D2Q9 LBM simulates viscous fluid flow in a square cavity with a moving top lid. Recirculating vortex structure emerges at various Reynolds numbers.
D2Q9 Lattice Boltzmann Method with BGK collision: fᵢ(x+eᵢ,t+1) = fᵢ(x,t) − (1/τ)[fᵢ−fᵢᵉᵠ]. Relaxation time τ = 3ν + 0.5, Re = U·L/ν. No-slip walls via bounce-back. Moving lid via modified bounce-back. At low Re, a single primary vortex forms; at higher Re, secondary corner vortices develop.