[Nek5000-users] Adjoint outflow boundary condition

[nek5000-users at lists.mcs.anl.gov]

Hi Andrea,

We can certainly add an inhomogeneity to the natural boundary
condition of the Stokes problem (which I believe is what you
propose below).

I wonder, however, if the notion of adjoints with outflow
boundary condition is even stable, since you have information
coming from a region that is normally an energy sink.  Don't
you have to change the BCs to make this work?   Think of
the convection-diffusion equation with outflow.  What would
be the proper formulation of the adjoint problem?   In the forward
case, the outflow boundary condition yields negative eigenvalues,
corresponding to energy leaving the domain.   In the adjoint,
where the flow is reversed, this would imply positive eigenvalues
and growth of disturbances coming from the outflow boundary.

Of course, I could be completely wrong about this and would
welcome any comments from someone more knowledgeable about
the adjoint problem.   In particular, is there a convection-diffusion
example we could consider as a starting point?


Paul




On Thu, 17 May 2012, nek5000-users at lists.mcs.anl.gov wrote:

> Hi Nek's,
>
>
> I'd like to use the adjoint linear solver. I have a problem concerning the
> outflow condition. The proper boundary condition would be:
>
> (p-(1/Re)grad(u))*n=(U*n)*u
>
> where:  -n is the normal
>            - u is the adjoint velocity vector
>            - U is the base flow  velocity vector
>            - p is the adjoint pressure
>            -Re Reynolds number
>
> How can I apply this condition on the outflow?
>
> Best Regards,
>
> Andrea
>