Description
"""
ImplicitFreeSurface(; solver_method=:Default, gravitational_acceleration=g_Earth, solver_settings...)
The implicit free-surface equation is
```math
\\ left [ 𝛁_h ⋅ (H 𝛁_h) - \\ frac{1}{g Δt^2} \\ right ] η^{n+1} = \\ frac{𝛁_h ⋅ 𝐐_⋆}{g Δt} - \\ frac{η^{n}}{g Δt^2} ,
```
where ``η^n`` is the free-surface elevation at the ``n``-th time step, ``H`` is depth, ``g`` is
the gravitational acceleration, ``Δt`` is the time step, ``𝐐_⋆`` is the barotropic volume flux
associated with the predictor velocity field, and ``𝛁_h`` is the horizontal gradient operator.
This equation can be solved in general using the [`PreconditionedConjugateGradientSolver`](@ref).
In the case that ``H`` is constant, we divide through to obtain
```math
\\ left ( ∇^2_h - \\ frac{1}{g H Δt^2} \\ right ) η^{n+1} = \\ frac{1}{g H Δt} \\ left ( 𝛁_h ⋅ 𝐐_⋆ - \\ frac{η^{n}}{Δt} \\ right ) .
```
Thus, for constant ``H`` and on grids with regular spacing in ``x`` and ``y`` directions, the free
surface can be obtained using the `FFTImplicitFreeSurfaceSolver`.
"""
cc: @elise-palethorpe
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