2D Lid-Driven Cavity Flow

Navier-Stokes vorticity-streamfunction formulation — Re-dependent vortex structure
Vorticity ω
Streamlines ψ
Step: 0
Lid-driven cavity: A unit square filled with viscous fluid, with the top wall (lid) moving at unit velocity. In vorticity-streamfunction form: ∂ω/∂t + u·∇ω = (1/Re)∇²ω and ∇²ψ = −ω, with u=∂ψ/∂y, v=−∂ψ/∂x. At low Re, a single primary vortex fills the cavity. As Re increases, Moffatt corner eddies appear in the bottom corners, and the primary vortex shifts toward the center. Above Re≈1000, the flow becomes unsteady. The Poisson equation for ψ is solved with successive over-relaxation (SOR).