Water swirls into a ring, and that ring flies through the bulk without breaking apart. Such vortex rings, from smoke rings to underwater currents, follow laws that are hard to capture on paper. Usually, the flow is divided into millions of cubic cells, and each one is tracked. The new approach, instead of cubes, releases a cloud of particles into the flow: each particle is a tiny vortex that moves with the water and spins it around itself.

The weak point of this method is small eddies that particles don't see. Their effect is usually added with a separate model that has a constant tuning. Here, the tuning changes on the fly: particles themselves sense how turbulent the flow has become and adjust the correction. It's like adjusting the volume of music by listening to it, not by looking at the notes. Additionally, viscous friction (like honey in water) is smeared over the particles, allowing them to slightly "puff up"—this makes the computation faster.

The method was tested on single vortex rings and on rings chasing each other. Even with a small number of particles, the motion of the rings matched reality: the rings caught up with each other, passed through one another, just like in smoke experiments. But after the flow lost stability and began to churn, the calculation held only thanks to careful "grooming" of the particles. Without that, the vortices fell apart into numerical noise.