Oil over water
 

What method can I use to solve a problem of oil flowing over water in a two dimensional domain? The source would be from the middle of the domain at a single point.

Note that I mean how do I solve for the masses of oil at points at different times. I only ask this because when I read through a few textbooks on the finite volume method they kept using temperature examples and I don't know how to use it to find densities at control volumes.