I have been trying to do a fluid simulator using vector fields, just toying around with ideas not trying to follow something already invented and smart like SPH or the likes. I have got seriously stuck now when trying to self advect velocity fields, that is make a velocity field move itself ( evolve maybe) i have googled the matter and found many promising guides (link) and tutorials but they all seem to expect that i would be familiar with math i am not familiar with. I'm not asking for some magic easy solution, what i would like is for someone to tell me what the mathematical principles are that i would need to understand prior to trying this. i understand vector fields and operations on the on a rudimentary level (curl,div,grad) but self advection eludes me.
any answers or links to helpfull articles would be much appreciated