Re: [Libmesh-users] Periodic boundary conditions

[Roy S. <roy...@ic...>]

On Thu, 8 Apr 2010, David Knezevic wrote:

>> Oh, and even if adaptivity is working, you'll definitely need the
>> coarse mesh to match up.  Otherwise there's no way to enforce
>> periodic continuity without "locking" destroying your accuracy.
>
> Thanks for the info Roy. We're not doing adaptivity, we just generated a mesh 
> (using gmsh) for a periodic channel flow, but the mesh generator doesn't 
> necessarily match up inflow and outflow nodes so it sounds like that is a 
> problem?

Definitely.  Imagine a grid of piecewise linears or bilinears,
intended to be periodic from left to right, and offset the nodes on
the right side down by just a little bit.  For strict C0 continuity,
then, the slope on the left bottom element must match the slopes on
the two right bottom elements.  But the slope on the
second-from-bottom element on the right must match the
second-from-bottom on the left, etc., and by the time you're done your
"piecewise bilinear" mesh has been constrained to a single linear
along that entire edge.  Disaster.

Your only hope in that case is to enforce periodicity weakly: use a DG
term or mortar method or some such on those boundaries, remembering
that you'd have to add the appropriate terms to the send_list &
sparsity pattern by hand.  It would probably be easier to fix up the
mesh generator output.

Copying this to libmesh-users; I haven't documented the
PeriodicBoundary usage well enough, and it would be nice if people
Googling it found *something*...
---
Roy