On Wed, Nov 13, 2013 at 12:00 AM, Dave May <[email protected]> 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. >> > >
