I have a velocity field `V`

on an annulus. It might look like this:

If you propagate a particle with this velocity field, it is quickly transpored to one of the two border components of the annulus (e.g. hole in the middle or the outer circle).

I also have a quantity `ρ(t)`

that gets transported accoring to a simple transport equation:

`dρ/dt = -div(V*ρ)`

What I am interested in is the following: Given an initial distribution `ρ_0`

how much will end up in each border component for `t → ∞`

?

Can this be solved with `fenics`

?