Does anyone know or can provide any examples how fluid flow problem can be formulated and solved in Wolfram Language? Simplest cases of 1D or 2D flows based on Navier-Stokes equations or even their linearized version would be great to see.
This blog is a good start:
It fully solves 2D problem of one moving boundary
and gets nice vertex flows:
There are detailed descriptions of proper equations and numerical discretization. You can generalize to 3D. I would look also in latest V10 functionality to see if anything can be used there to upgrade the methods of the blog - it was written before V10 came out. For instance, take a look at this Stokes Flow example which is a simplification of NS:
The same example is discussed in Solving Partial Differential Equations with Finite Elements tutorial
that goes a bit further and solves for pressure and other quantities: