Check out the current release ( 3.7 ) of the
Incompressible Flow & Iterative Solver Software (IFISS)
Matlab and Octave toolbox.
This open source software package is associated with the second edition of
Finite Elements and Fast Iterative Solvers
with applications in incompressible fluid dynamics.
The extension to three-dimensions is a recent development.
Check out our highly-regarded (SUMS) textbook on Essential PDEs using Amazon books.
My video tutorials on modelling incompressible flow may also be of interest.