Hi @ChrisRackauckas,
I appreciate if you can skim through this quick overview on FVM for the equations: http://caminos.udc.es/info/asignaturas/201/Finite%20Volumes%20IMWE.pdf
What I have currently for space discretizattion is a backward difference in space that propagates the fluxes properly in the direction of the velocity field (it is called the upwind scheme) given that the time step is small enough (satisfies the CLF condition described in the document).
I think my implementation is working fine, but I would like to be able to switch from one PDE to another quickly in the future and play with different solvers, in other words, enjoy the goodies of DifferentialEquations.jl 