2D Navier-Stokes: Stream Function-Vorticity

ψ-ω formulation — lid-driven cavity flow
Vorticity ω
— Streamlines ψ
→ Velocity field
100 1.00
40
Stream function-vorticity equations:
∂ω/∂t + (u·∇)ω = ν ∇²ω    ∇²ψ = −ω    u = ∂ψ/∂y, v = −∂ψ/∂x
Lid-driven cavity: top wall moves at speed U, all other walls no-slip. Vortex structure evolves with Re.