The regular person that I show new experimental equations to is not here, or contactable, I wanted to tell someone, so I decided, the world wide web would have to do.
So, the problem is: how to find vortices (read whirlpools) in particle-based fluid simulations. There is a way to format vorticity confinement that involves tracking and introducing by means of a Eulerian grid. I don't like Eulerian grids, so I needed a way to do this without a background mesh.
In smoothed particle hydrodynamics, values around a particle are found by means of kernel functions. I now need a kernel function that can characterize the vorticity around a particle AKA, how much the particles around is are spiraling around it. The real question is: How tangential are the velocities of each particles neighbors relative to that particle.
It's the bell shaped curve. For particle velocities that are 90 degrees away from the direction that would point to the particle that we're looking at, the value would be at the top of the bell. But, for particle velocities that are either moving toward or away from the particle, the value would be low. You could also use this to measure divergence.
So, here's my equation for vorticity:
So, maybe that'll work, maybe it won't, we'll see.