[petsc-users] solving stokes-like equation in 3D staggered grid in irregular domain with petscsection

[Bishesh Khanal]

On Wed, Nov 13, 2013 at 12:00 AM, Dave May <dave.mayhem23 at gmail.com> wrote:

> Since your using staggered grids, the physical boundary of your domain
> will be approximate by a "stair-case" type of boundary. (Correct me if this
> is not what you were thinking to do) Thus, imposing traction boundary
> conditions on the stair-case boundary should be no more complex than it was
> in your standard cube domain with staggered grids. The only exception is
> that you have to implement, in a cell-wise manner, the imposition of the
> traction condition. The functionality should already exist in your original
> cube staggered grid implementation, but possible the implementation of this
> boundary condition was done "wall-wise" rather than cell-wise.
>
> Thanks Dave. I have not implemented traction condition on the cuboid (A U
B) walls till now because for the cuboid walls it's a Dirichlet condition.
Traction condition would be needed only if I want to solve for the
irregularly shaped domain A. I have to solve for many different cases,
where the shape of A will keep on changing. (The input for the domain is a
3D binary mask). So it's hard for me to see the generic method to take care
of the each boundary cell for the traction condition, but I take your word
on its possibility and would discuss it further here if I go in that
direction of solving the system for just the domain A. As for now, I would
like to solve for both A and B domains in the way Jed suggested. There are
few other reasons for this coming from my other image processing pipelines.


>
>
> > 3. I'm trying to put both domains in a single matrix to avoid the
>> > difficulty I would have if I want to consider only the domain A. In this
>> > case I would need a traction free boundary condition on the irregular
>> > boundary of domain A, and it seems a bit too challenging for me to
>> > incorporate it with the staggered grid. If there is an idea to implement
>> > this and if you think this could be more suitable than the approach in 2
>> > above, I would like to learn about that too!
>>
>> Complexity of implementing boundary conditions on staggered grids is one
>> reason some people turn to other discretization technology, such as
>> finite elements.
>>
>
>
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