Hi Wolfgang,
thanks for the reply. I'm working on Immersed Boundary Method and flagella
swimming, and, more specifically, I'm trying to model a unit square domain,
which is infinitely replicated in two dimensions, governed by the
incompressible time-dependent stokes equations for low Reynolds number. For
this reason I need periodic boundary conditions for velocity in both
directions, but also for pressure. Therefore, for my unit square domain, I
need to have *pure* periodicity, i.e.,
\bold{u}_left = \bold{u}_left and p_left = p_right
\bold{u}_bottom = \bold{u}_top and p_bottom = p_top
Does that make sense to you?
My main problem with that is that when I'm trying to use the Block
Preconditioner for the time-dependent Stokes (without convection), i.e.
when I need to form the {\tilde{S}}^{-1} \approx [B^T (diag M)^{-1}
B]^{-1} + \Delta{t}(\nu)M_p^{-1}, I have problems to invert the B^T (diag
M)^{-1} B - it says not invertible. Any ideas?
Best,
Magda
On Tuesday, January 15, 2019 at 6:22:12 PM UTC-5, Wolfgang Bangerth wrote:
>
> On 1/15/19 10:02 AM, [email protected] <javascript:> wrote:
> > thank you for replying. I have looked thoroughly step 45 but it's not of
> much
> > help for my case. I actually want to impose periodic boundary conditions
> for
> > both velocities and pressure (I need to have a representative periodic
> cell).
>
> Is this really what you want to do? Can you elaborate on your setup?
>
> I'm asking this because generally, mathematically speaking, you can only
> impose the *stress* at the boundary, not the pressure alone. Second, if
> you
> think for example about an infinite pipe and you cut a piece out, then at
> the
> left and right end of that pipe segment, you can enforce that the velocity
> is
> periodic -- but the pressure will *not* be periodic, as there will be a
> pressure drop along the pipe which counters the friction forces.
>
> Best
> W.
>
> --
> ------------------------------------------------------------------------
> Wolfgang Bangerth email: [email protected]
> <javascript:>
> www: http://www.math.colostate.edu/~bangerth/
>
>
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