Navier-Stokes Equations: Governs viscous, incompressible fluid flow through momentum and continuity:
1. Semi-Lagrangian Advection: Particles back-trace velocities through space to stably transport dye and momentum.
2. Jacobi Pressure Poisson Solver: Enforces zero divergence by iteratively computing pressure fields p via ∇²p = ∇·u.
3. Vorticity Confinement: Amplifies turbulent eddies and micro-vortices otherwise damped by numerical dissipation.