I posted this question more than one year ago and got an answer recently. This answer looks good to me, but indicates that something is wrong in my original approach to the problem.
Can someone tell me what is going wrong there? If I insist on naively computing the time evolution of an incompressible fluid in a constrained space (see the original post for the details),
$$\mathbf{v}(t+dt) = \mathbf{v}(t) + dt \cdot \text{Navier-Stokes}(t) \, . $$
How do I implement the no-slip boundary conditions?
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