FVM in 1-D spherical coordinates
 

I'm trying to obtain discretised equations in 1-D using FVM. It seems to me that there are two ways of doing it,

1) Firstly for the general momentum equation written in vector form (including divergence operators) I apply FVM (i.e. integrate over a control-volume and apply Gauss's theorem). I then write the resulting equation in 1-D spherical coordinates.

2) I write the momentum equation in 1-D spherical coordinates and I have extra geometric source terms compared with the Cartesian case. I then apply FVM (integrate over the volume). This is actually more like finite difference method.

I find the difference between the two discretisation is the extra geometric source terms. I'm not sure which method is more correct but I thought that in 1-D both FVM and finite-difference should yeild the same discretisation. Could anyone suggest which method is best?

Thanks.