# How are boundary consitions implemented correctly in time dependent hydrodynamics?

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?

• As an astrophysicist, I can't help at all with boundary conditions or incompressible flows. However I do know that moving-mesh methods were originally developed in order to deal with (time-dependent) boundary conditions, specifically the flow of (incompressible) fluid in elastic blood vessels. Since moving meshes are many times more complicated than fixed grids, I take this to be a sign that there weren't easy alternatives.
– user10851
May 27, 2016 at 20:36
• In Navier-Stokes, just set v = 0 at the boundaries. May 28, 2016 at 2:30
• @ChesterMiller Did you read the linked post? I know that no-slip means $\mathbf{v}=0$ at the boundaries. I would like to understand how this can be a consistent boundary condition. May 28, 2016 at 13:05