Swap plane Poisson solver with slab Poisson solver in GK IWL simulations & 2x LBO energy conservation

[manauref]

This goes with PR 93 of gkylcas

Problem

Currently the IWL simulations are using the Poisson solver on planes (fem_poisson_deflated). This has been shown to break energy conservation. One reason we have continued to do that is that:
a) We didn't have the ability to bias the limiter corner in the slab Poisson solver (fem_poisson_perp).
b) We didn't have a working workflow that used the slab Poisson solver and twist-shift BCs (TS BCs).

Here we address both of these points, and deprecate the use of fem_poisson_deflated in favor of fem_poisson_perp.

Solution

Biasing

We implemented the ability to bias the limiter corner in fem_poisson_perp. Some info is in the DR #898 .

Unlike biasing in fem_poisson, where can bias whole planes in the solver, in fem_poisson_perp we bias lines. That's at the moment we just need to bias the lines at (x,z)=(x_LCFS,z_min) and (x,z)=(x_LCFS,z_max).

Tests with biasing were added to the fem_poisson_perp unit test.

Workflow with TS BCs

We implemented a new set of steps to make sure the potential is twist-shift periodic with this new slab solver. These are:

1. Smooth the charge density, without BCs (fem_parproj).
2. Solve the perpendicular Poisson problem (fem_poisson_perp).
3. In the core, apply TS BC to phi at the lower z-boundary, and a ghost-from-skin-surf BC at the upper z-boundary.
4. Smooth phi, with Dirichlet BCs that take the Dirichlet value from the ghost in the core, and witih Dirichlet BCs that take the Dirichlet value from the skin in the SOL.

Commentary on alternatives

• Regarding step 1: It's unclear whether BCs are needed here, or what they should be. In SOL simulations we don't apply BCs, and that's the option that makes the operator self-adjoint and preserves energy. Perhaps indirectly using TS BCs as done in steps 3-4 would be worthwhile, but doesn't seem necessary so far.
• Note that steps 3-4 only apply TS BC at the lower boundary. This is as it's done in main now. We tried, both in main and in this branch, but applying TS BC only at the upper boundary or in combination with the lower, does not work.

Additional perks

We noticed that the LBO collision operator was not conserving energy in 2x. We fixed that in this branch.

This fix is not the final one, though. Through more testing I found scenarios (large gradients + normNu) in which the LBO still doesn't conserve energy. I think we need to compute nu-weighted moments to truly conserve energy, which we may pursue in another branch.

Tests

This branch is valgrind and compute-sanitizer clean.

Regression tests

Regression tests run, but they are expected to yield slightly different solutions since we are using a different algorithm now.

rt_gk_d3d_iwl_2x2v_p1

rt_gk_tcv_iwl_adapt_source_2x2v_p1

rt_gk_d3d_iwl_3x2v_p1

rt_gk_tcv_iwl_adapt_source_3x2v_p1

Production simulation

We ran a TCV case provided by @Antoinehoff in both main and this branch. Here are some snapshots.