Check out the current release 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.