gradient field in 3D

I have also posted this question in comp.graphics.algorithms, but i thourght
this forum might be better

Im trying to implement  3D edition of Jos Stam's "Real-Time fluid
dynamics for games" 2D example.

In this paper it is described that mass conservation can be achieved by
using the Hodge decomposition. Something about saying that "every velocity
field is the sum of a mass conserving field and a gradient field".

Anyways I need to find that gradient field so I can substract it from my
velocity field and thereby conserve mass. (when I conserve mass, I should
get the fluid like vortices.)

It is further mentioned that the computing gradient field is equivalent to
computing a height field. At least in 2D.

But how do I approach the problem in 3D?

I can imagine how to approach the problem in 2D. Just find the slope along
the 2 axis. But in 3d???