Incompressible Wake and the Projection Method

Chorin's projection method made visible: the incompressible Navier-Stokes equations $\partial_t\vec u+(\vec u\cdot\nabla)\vec u=-\nabla p+\nu\nabla^2\vec u$ with the constraint $\nabla\cdot\vec u=0$, solved on a MAC staggered grid (semi-Lagrangian advection, implicit diffusion, an SOR pressure-Poisson projection, the gate-tested shared engine). Flow past a bluff body, coloured by speed $|\vec u|$ over the dark field: the uniform stream, the bright acceleration over the shoulders of the body, the dark wake deficit, and the discrete shed cores. The headline is the live $\max|\nabla\cdot\vec u|$ readout: the pressure solve drives it small every step, so the flow stays incompressible. Sweep the Reynolds number $Re=UD/\nu$ from a glassy creep, through a steady recirculating bubble, to a genuine periodic von Karman vortex street. (The live path switches on the engine's BFECC low-dissipation advection and Steinhoff vorticity confinement, both default-off so the offline invariants are unaffected: these cut the semi-Lagrangian numerical viscosity so the effective $Re$ tracks the nominal one and the wake genuinely sheds. The shed period gives an approximate Strouhal number; the precise $St(Re)$ stays a documented finer-grid quantity.)