Update limiters
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- Julia
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Description
Our limiters need to be updated in several aspects:
- GPU compatibility (#1493)
- Implement "water borrowing" (discussed in #1386)
For unit tests, I would like to also add some simple analysis. For each limiter, we should document the following cases:
- Low frequency sin wave in the interior domain
- High frequency sin wave (sawtooth) in the interior domain
- Low frequency sin wave on the boundary
- High frequency sin wave (sawtooth) on the boundary
Documenting these four cases across a frequency range really characterizes what the limiter is doing. Adding this to the docs would be helpful, and give us confidence about how the limiters are impacting our simulations.
We could go a step further and let advection or diffusion operate on the perturbation of the limited state (`perturbed_state = (state - limited_state)`), and that would help us get and idea of how we're impacting the phase space, but this is more subjective since different terms can absorb / balance this impact, so it's really more model-dependent.
cc @tapios
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