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

[Dave May]

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.



> 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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