How it works

The fluid lives on a coarse grid (each cell tracks a velocity and a dye density). Every frame the solver runs the same three moves, then the result is upscaled with smoothing so the low-resolution grid reads as soft, organic flow.

• Diffusion lets velocity and dye bleed into neighbouring cells, solved with a few Gauss-Seidel relaxation passes (the "solver iterations" knob).
• Advection moves each quantity along the velocity field by tracing backwards in time and sampling where it came from. This backward, semi-Lagrangian step is what makes the method stable, at the cost of some numerical smearing.
• Projection subtracts off the divergent part of the velocity so the fluid stays incompressible, which is where the swirls and vortices come from.

Because the backward advection step trades some accuracy for stability, this is not a physically exact fluid. But it captures the essentials, the swirls, vortices, and buoyant plumes, while staying cheap enough to run every single frame in your browser.

Based on Jos Stam's Real-Time Fluid Dynamics for Games.