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Mixed velocity-vorticity transport #574

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This PR introduces a new Augmentation object, which allows an equation set to be substituted or augmented for a particular stage. The example I have implemented is the mixed velocity-vorticity transport of this paper

The cool thing about this transport is that it is more accurate than other velocity transport schemes that we use, but @gwimmer also came up with a way of incorporating an SUPG scheme into it. I have been testing this in shallow-water models which take large time steps (such that 0.5 < c < 1.0) and it gives good results. Unfortunately I haven't found anything completely stable for c > 1.0 yet ...

Still to do:

  • unify and simplify approach to subcycling (maybe in a different PR)
  • provide a transport test using the augmentation
  • provide an integration test using my new favourite settings
  • decide on optimal solver parameters
  • test 3D scheme
  • docstrings and tidying

@tommbendall tommbendall added enhancement Pull requests or issues relating to adding a new capability equation Adding or enhancing a new equation labels Nov 18, 2024
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