Test for incompressibility in hydrostatic and non-hydrostatic models

[navidcy]

This follows from the discussions after the bug fix in #1932.

cc: @kburns, @sandreza, @francispoulin

[glwagner]

We test that NonhydrostaticModel maintains incompressibility on both fully regular and vertically-stretched grids:

Oceananigans.jl/test/test_time_stepping.jl

Lines 311 to 341 in e929631

	@testset "Incompressibility" begin
	for FT in float_types, arch in archs
	Nx, Ny, Nz = 32, 32, 32
	regular_grid = RegularRectilinearGrid(FT, size=(Nx, Ny, Nz), x=(0, 1), y=(0, 1), z=(-1, 1))
	S = 1.3 # Stretching factor
	hyperbolically_spaced_nodes(k) = tanh(S * (2 * (k - 1) / Nz - 1)) / tanh(S)
	hyperbolic_vs_grid = VerticallyStretchedRectilinearGrid(FT,
	architecture = arch,
	size = (Nx, Ny, Nz),
	x = (0, 1),
	y = (0, 1),
	z_faces = hyperbolically_spaced_nodes)
	regular_vs_grid = VerticallyStretchedRectilinearGrid(FT,
	architecture = arch,
	size = (Nx, Ny, Nz),
	x = (0, 1),
	y = (0, 1),
	z_faces = collect(range(0, stop=1, length=Nz+1)))
	for grid in (regular_grid, hyperbolic_vs_grid, regular_vs_grid)
	@info " Testing incompressibility [$FT, $(typeof(grid).name.wrapper)]..."
	for Nt in [1, 10, 100], timestepper in timesteppers
	@test incompressible_in_time(arch, grid, Nt, timestepper)
	end
	end
	end
	end

We don't have tests for the hydrostatic model however.

A similar but possibly slightly simpler test might test that compute_w_from_continuity! correctly calculates a vertical velocity field given some horizontally divergent horizontal velocity field.

[francispoulin]

Since like a good idea

[glwagner]

So, we do have tests for incompressibilty