Hello deal.ii community,
I've really enjoyed using deal.ii over the past few weeks -- it's very
impressive how complete the software is. I'm in the process of implementing
an ocean equations solver which has a few unusual features:
1. The problem is to be solved over a 3D mesh extruded downwards in
depth from a 2D surface mesh
2. There is a free surface equation which makes use of the original 2D
mesh
3. 3D data is communicated to the 2D surface by integrating finite
element fields vertically over the entire domain in depth (depth-averaged
fields)
4. From a 3D scalar field, I will need to compute another 3D scalar
field representing the original field integrated to depth z (like a
hydrostatic pressure at every point in the domain)
How I was thinking of doing this:
- (1) Mesh the 2D region with gmsh and extrude it using the approach in
step-49; this seems clear
- (2,3) I was considering holding the original 2D mesh in memory and
creating some type of map between the top-level volume elements and the
surface.* Is there a better way I could go about mapping the 3D volume
data and depth-averaged data to the surface mesh?*
- (4) I can re-write the hydrostatic integrals as an ode in depth and
march element-by-element from surface to bottom along each vertical column
using a DG scheme.
- To isolate each vertical column, I could assign a material ID to
each one
- However, I need to extract the value on the bottom of each element
above as a boundary condition to the element below
- I could probably do this with FEFaceValues, *but it's unclear to me
how to "request" values on a top or bottom face* (since element
orientation is general). Is there an ordering I could rely on if I know
it
for a single element?
Any tips would be appreciated!
Best,
Corbin
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