Better validation for LatitudeLongitudeGrid + add test for sum(Azᶜᶜᵃ) ≈ 4πr²

[navidcy]

Closes #3241

[glwagner]

Nice!

Should we implement this test for OrthogonalSphericalShellGrid instead, considering we are going to deprecate LatitutdeLongitudeGrid?

[navidcy]

Nice!

Should we implement this test for OrthogonalSphericalShellGrid instead, considering we are going to deprecate LatitutdeLongitudeGrid?

That's already implemented for OSSG + other similar tests.

Oceananigans.jl/test/test_grids.jl

Lines 934 to 955 in 29a99a0

	Nx, Ny = 10, 8
	grid = OrthogonalSphericalShellGrid(arch, FT, size=(Nx, Ny, 1); z, radius)
	# the sum of area metrics Azᶜᶜᵃ is 1/6-th of the area of the sphere
	@test sum(grid.Azᶜᶜᵃ) ≈ 4π * grid.radius^2 / 6
	# the sum of the distance metrics Δxᶜᶜᵃ and Δyᶜᶜᵃ that correspond to great circles
	# are 1/4-th of the circumference of the sphere's great circle
	#
	# (for odd number of grid points, the central grid points fall on great circles)
	Nx, Ny = 11, 9
	grid = OrthogonalSphericalShellGrid(arch, FT, size=(Nx, Ny, 1); z, radius)
	@test sum(grid.Δxᶜᶜᵃ[:, (Ny+1)÷2]) ≈ 2π * grid.radius / 4
	@test sum(grid.Δyᶜᶜᵃ[(Nx+1)÷2, :]) ≈ 2π * grid.radius / 4
	Nx, Ny = 10, 9
	grid = OrthogonalSphericalShellGrid(arch, FT, size=(Nx, Ny, 1); z, radius)
	@test sum(grid.Δxᶜᶜᵃ[:, (Ny+1)÷2]) ≈ 2π * grid.radius / 4
	Nx, Ny = 11, 8
	grid = OrthogonalSphericalShellGrid(arch, FT, size=(Nx, Ny, 1); z, radius)
	@test sum(grid.Δyᶜᶜᵃ[(Nx+1)÷2, :]) ≈ 2π * grid.radius / 4

[navidcy]

I also improved the validation according to the discussion in #3241.