# Stable Fluids (Jos Stam)

**Track:** Simulation & Complexity — Advanced Creative Coding — proposed (50)
**Framework / surface:** GLSL
**Level:** Insane
**Prerequisites:** Feedback / Ping-Pong Buffers, Verlet Integration & Constraints

**In one line:** Semi-Lagrangian advection, diffusion, projection — real-time Navier–Stokes.

## Theory, aesthetics & inspiration

Jos Stam's "Stable Fluids," presented at SIGGRAPH 1999, made real-time fluid simulation tractable by solving the Navier–Stokes equations in a way that never blows up. Its key move is semi-Lagrangian advection: rather than push quantities forward, trace each grid cell backward along the velocity field and sample where it came from, an unconditionally stable step. A diffusion stage and a projection stage — enforcing incompressibility via a Helmholtz–Hodge decomposition — complete the loop. Stam's later "Real-Time Fluid Dynamics for Games" distilled it for practitioners. The visual result is the genuine article: ink blooming, smoke curling, velocity advecting dye into swirling, self-similar filaments.