Implement alternating division schemes between adjacent hexahedra and wedges

[connoramoreno]

Modifies the source mesh workflow to alternate the scheme by which hexahedra and wedges are split into tetrahedra. The alternating schemes ensure that the faces of adjacent tetrahedra, but not belonging to the same hexahedron or wedge, match one another. This avoids gaps and overlaps between adjacent non-planar hexahedron and wedge faces. This alignment is ensured for adjacent wedge-wedge, wedge-hexahedron, and hexahedron-hexahedron pairs. Code changes are as follows:

• Introduces alternate_scheme, toroidal_alt_scheme, and cfs_alt_scheme boolean parameters to control whether an alternate division scheme should be used for a given element
• Introduces an alternate division scheme, in the form of MOAB canonical indices defining the tetrahedral division of a given element, for both hexahedra and wedges

The alternate splitting schemes are illustrated below. Plots will follow to demonstrate expected behavior of total volume and total source strength as a function of mesh discretization.

(a)
(b)

Figure 1. Alternate schemes for adjacent hexahedra. (a) Original and (b) alternate.

(a)
(b)

Figure 2. Alternate schemes for adjacent wedges. (a) Original and (b) alternate.

Closes #168

[gonuke]

Thanks for the quick fix @connoramoreno

[connoramoreno]

Below are plots demonstrating that total source strength (in the form of fusion power, calculated for four periods even though only one period of the source mesh is modeled) and total mesh volume scale as expected with mesh discretization.

Expected behavior:

• For increasing CFS discretization, total source strength converges to some value and total volume remains constant
• For changing poloidal discretization, total source strength changes are small and trend similarly to those for total volume. Total volume converges to some value.
• For changing toroidal discretization, total source strength changes are small and trend similarly to those for total volume. Total volume converges to some value.

(a)
(b)
Figure 1. Behavior of total source strength and volume as a function of CFS discretization. Numbers of poloidal and toroidal grid points are kept constant at 121 each. (a) Total source strength. Total relative change is 3.15%. (b) Total mesh volume. Total relative change is 0%.

(a)
(b)
Figure 2. Behavior of total source strength and volume as a function of poloidal discretization. Numbers of CFS and toroidal grid points are kept constant at 16 and 121, respectively. (a) Total source strength. Total relative change is 0.39%. (b) Total mesh volume. Total relative change is 0.41%.

(a)
(b)
Figure 3. Behavior of total source strength and volume as a function of toroidal discretization. Numbers of CFS and poloidal grid points are kept constant at 16 and 121, respectively. (a) Total source strength. Total relative change is 0.40%. (b) Total mesh volume. Total relative change is 0.23%.

[connoramoreno]

I have another PR lined up once this is merged that will allow users to input their own grids, rather than us enforce uniformly spaced grids. I'd like to include checks on inputs (such as warnings for when grid sizes are not even) in that subsequent PR, since it touches a lot of that part of the code.

[gonuke]

do we need to keep these different alternative scheme variables? For me it's hard to follow. If we require even numbers of poloidal voxels, I think there may be a cleaner way to do it.

[gonuke]

Can we just determine the meshing scheme from whether s_idx + theta_idx + phi_idx is even or odd?

For the very first wedge of the first toroidal plane it's 0+0+0 =0 even. Then it alternates until we get to the last wedge which must be odd if we have an even number of poloidal voxels. Then the first hex on the next cfs layer is 1+0+0 =1 odd and alternates... and so on.

The first wedge on the next toroidal slice is 0+1+0 =1 odd - which is what we need it to be... and so on.

So within each hex generation method you can have

alternate_scheme = (s_idx + phi_idx + theta_idx) % 2

[gonuke]

Could then have canonical ordering indexed in a list with index 0 and 1 and directly use the one you want indexed by the alternate scheme variable.