Corbin,
a month late, but maybe still useful: For your particular situation, where you
replicate a mesh in depth direction multiple times, it might also be
worthwhile thinking of this as "just a 2d problem" where at each node, you
just define as many variables as there are depth slices. In other words, you
work with just one 2d mesh but many variables via an FESystem object. This
makes a lot of operations much simpler where you're having to walk along
individual mesh lines from surface to ocean bottom or back up: These are in
essence all just equations defined at individual node points on the 2d mesh.
Best
W.
On 1/1/21 10:53 AM, Corbin Foucart wrote:
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.
o To isolate each vertical column, I could assign a material ID to each
one
o However, I need to extract the value on the bottom of each element
above as a boundary condition to the element below
o 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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