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

[Shangxin Liu]

Hi Wolfgang and Timo,

This question is about the application of a dealii function in ASPECT. I'm
not sure whether it can give what I need or I should find other solutions.

I notice that in the current ASPECT's postprocessors, the variable gradient
(velocity, temperature, etc) is commonly evaluated at the quadrature points
on the boundary face of each boundary cell (FEFaceValues<dim>). I'm now
interested in recomputing variable gradients at the quadrature points in
each boundary cell's volume (FEValues<dim>). The rewriting of the code is
pretty straightforward except that I'm stuck at one issue.

In the current "boundary face" calculation, the outward normal can be
easily grabbed by "fe_face_values.normal_vector(q)". However, in the
"boundary cell volume" calculation, the quadrature points are inside a
boundary cell's volume instead of on the face, in this case grabbing the
outward normal of each quadrature point seems no longer convenient.

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 ith
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?)

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?

Best,
Shangxin
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