This simulation solves the Navier-Stokes equations for incompressible fluids in a GPU fragment shader. I implemented no-slip boundary conditions at the borders to keep the fluid contained within the bounds of the screen. To increase performance, I solved for the velocity vector field of the fluid at a lower resolution than I used to compute the visualization of fluid flow; I used bilinear interpolation to smooth out artifacts caused by this speedup. I've also added 160,000 Lagrangian particles on top of the simulation - these particles are rendered using threejs, but their positions are computed on the GPU.

To learn more about the math involved, check out the following sources:

Real-time ink simulation using a grid-particle method - mixing Eulerian and Lagrangian techniques for fluids.

Fast Fluid Dynamics Simulation on the GPU - a very well written tutorial about programming the Navier-Stokes equations on a GPU. Though not WebGL specific, it was still very useful.

Fluid Simulation (with WebGL demo) - this article has some nice, interactive graphics that helped me debug my code.

Stable Fluids - a paper about stable numerical methods for evaluating Navier-Stokes on a discrete grid.

By Amanda Ghassaei, code on Github.