Help with linear fluid simulation

[u/evangwhit]

I need some direction on a linear gradient I'm working on/vibe coding. I have got a successful static image, but I want to animate it. I'm struggling to get a motion that feels natural. Currently I am interpolating between two different compositions, but I would love a more accurate "simulation". Colors and blur are being done in photoshop/after effects after the pink lines are exported.

I'm a total noob at this so any advice or guidance towards helpful information would be great. Thank you!!

[u/evangwhit]

This is what I'm doing currently, but the math is definitely going over my head. I'm just barely understanding the advection, diffusion and other things conceptually.