Parameters
Select a shape and Reynolds number
Then click Run SimulationChorin's Projection Method
The 2D incompressible Navier-Stokes equations are solved on a Cartesian grid using finite differences. Each time step: (1) an intermediate velocity is advanced by advection (2nd-order upwind) and diffusion (central differences), (2) a pressure Poisson equation ∇²p = ∇·u*/Δt is solved to enforce incompressibility, (3) the velocity is corrected to be divergence-free. Time stepping is adaptive based on CFL stability conditions for both advection and diffusion.
Reynolds Number & Flow Regimes
Re < 5: Creeping flow — fully attached, symmetric. No separation.
Re ≈ 5–47: Steady twin vortex wake behind the obstacle.
Re > 47: Onset of Kármán vortex shedding — alternating vortices shed periodically.
Re > 200: Irregular, increasingly turbulent wake. 2D solver over-predicts drag at high Re since 3D span-wise instabilities can't develop.
Vorticity Field (ωz)
Colour shows out-of-plane vorticity: ωz = ∂v/∂x − ∂u/∂y. ■ Red = positive (counterclockwise rotation), ■ Blue = negative (clockwise rotation). The obstacle is shaded grey. Flow enters from the left at uniform velocity U = 1.