[aspect-devel] How to grab the outward normal vectors at the quadrature points in boundary cell's volume?

[Wolfgang Bangerth]

> I found the related instruction in the online dealii manual about the normal 
> vector. It says (I just copy it here for the convenience):
> 
> "For a face, return the outward normal vector to the cell at the |i|th 
> quadrature point.
> 
> For a cell of codimension one, return the normal vector. There are of course 
> two normal directions to a manifold in that case, and this function returns 
> the "up" direction as induced by the numbering of the vertices. "
> 
> I'm a little confused on the normal vector of the cell and got a couple of 
> questions:
> 
> 1. What does "a cell of codimension one" mean? What kind of cell should it be? 
> (Does it work in ASPECT's cell like that in 3D box, 3D chunk, 3D spherical 
> shell, etc?)

"codimension one" means that you have a 2d cell in a 3d space. This happens 
if, for example, you want to solve PDEs on surfaces (think for modeling an 
erosion process on the two-dimensional surface of the 3d earth). This is not 
applicable in your case.


> 2. Is the normal vector evaluated at the quadrature points inside the boundary 
> cell's volume what the calculation needs, i.e., the outward normal direction?
> 
> 3. If not, any other suggestion on how to work around this issue?

The problem you need to think about is what you want this normal vector to be. 
Think about what the normal vector should be at a quadrature point inside the 
cell if this is a cell with a face along a curved boundary? And what is 
supposed to have if you are on a cell that has *two* faces at the boundary.

I don't know the answer to this question, but it is not about how to 
*implement* this. You first have to ask yourself *how* the normal vector is 
*supposed to be defined*.

Best
  W.


-- 
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Wolfgang Bangerth          email:                 bangerth at colostate.edu
                            www: http://www.math.colostate.edu/~bangerth/