Problem with Dirichlet boundary

1

Hi everyone,

I’ve been working with time-dependent Stokes equation. Here is a snapshot of velocity on one of the first time-steps before reaching the steady state:

stokes
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To me it looks good. When it comes to boundary conditions, there is parabolic inflow (time independent for the simplest case), do-nothing on the outflow and zero Dirichlet boundary condition everywhere else.

I want to do some post processing and among other things I looked at v_n - v_{n - 1}, where v_n is the discrete velocity at the n-th time-step. And it looks strange:

subtract
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Because the inflow is time independent everywhere except the outflow I have zero on the boundary as it should be. But still I have this strange effect close to the boundary. Only the Neumann part looks fine.
Does anyone have an idea where it comes from and how can I get rid of it?

2

I think I know. With every time-step the solution more and more approaches a parabolic profile. And values closer to the center of the channel get bigger and values closer to the boundary get smaller. So that’s why I get these spikes near the boundary. I thought it has something to do with how I implement the Dirichlet boundary conditions when it fact it might be actually correct. Sorry for bothering you.