laplacian_operators.jl

#####
##### Horizontal Laplacians
#####

@inline function ∇²hᶜᶜᶜ(i, j, k, grid, c)
    return 1/Vᶜᶜᶜ(i, j, k, grid) * (δxᶜᵃᵃ(i, j, k, grid, Ax_∂xᶠᶜᶜ, c) +
                                    δyᵃᶜᵃ(i, j, k, grid, Ay_∂yᶜᶠᶜ, c))
end

@inline function ∇²hᶠᶜᶜ(i, j, k, grid, u)
    return 1/Vᶠᶜᶜ(i, j, k, grid) * (δxᶠᵃᵃ(i, j, k, grid, Ax_∂xᶜᶜᶜ, u) +
                                    δyᵃᶜᵃ(i, j, k, grid, Ay_∂yᶠᶠᶜ, u))
end

@inline function ∇²hᶜᶠᶜ(i, j, k, grid, v)
    return 1/Vᶜᶠᶜ(i, j, k, grid) * (δxᶜᵃᵃ(i, j, k, grid, Ax_∂xᶠᶠᶜ, v) +
                                    δyᵃᶠᵃ(i, j, k, grid, Ay_∂yᶜᶜᶜ, v))
end

@inline function ∇²hᶜᶜᶠ(i, j, k, grid, w)
    return 1/Vᶜᶠᶜ(i, j, k, grid) * (δxᶜᵃᵃ(i, j, k, grid, Ax_∂xᶠᶠᶜ, v) +
                                    δyᵃᶠᵃ(i, j, k, grid, Ay_∂yᶜᶜᶜ, v))
end

"""
    ∇²ᶜᶜᶜ(i, j, k, grid, c)

Calculate the Laplacian of ``c`` via

```julia
1/V * [δxᶜᵃᵃ(Ax * ∂xᶠᵃᵃ(c)) + δyᵃᶜᵃ(Ay * ∂yᵃᶠᵃ(c)) + δzᵃᵃᶜ(Az * ∂zᵃᵃᶠ(c))]
```

which ends up at the location `ccc`.
"""
@inline function ∇²ᶜᶜᶜ(i, j, k, grid, c)
    return 1/Vᶜᶜᶜ(i, j, k, grid) * (δxᶜᵃᵃ(i, j, k, grid, Ax_∂xᶠᶜᶜ, c) +
                                    δyᵃᶜᵃ(i, j, k, grid, Ay_∂yᶜᶠᶜ, c) +
                                    δzᵃᵃᶜ(i, j, k, grid, Az_∂zᶜᶜᶠ, c))
end

@inline function ∇²ᶠᶜᶜ(i, j, k, grid, u)
    return 1/Vᶠᶜᶜ(i, j, k, grid) * (δxᶠᵃᵃ(i, j, k, grid, Ax_∂xᶜᶜᶜ, u) +
                                    δyᵃᶜᵃ(i, j, k, grid, Ay_∂yᶠᶠᶜ, u) +
                                    δzᵃᵃᶜ(i, j, k, grid, Az_∂zᶠᶜᶠ, u))
end

@inline function ∇²ᶜᶠᶜ(i, j, k, grid, v)
    return 1/Vᶜᶠᶜ(i, j, k, grid) * (δxᶜᵃᵃ(i, j, k, grid, Ax_∂xᶠᶠᶜ, v) +
                                    δyᵃᶠᵃ(i, j, k, grid, Ay_∂yᶜᶜᶜ, v) +
                                    δzᵃᵃᶜ(i, j, k, grid, Az_∂zᶜᶠᶠ, v))
end

@inline function ∇²ᶜᶜᶠ(i, j, k, grid, w)
    return 1/Vᶜᶜᶠ(i, j, k, grid) * (δxᶜᵃᵃ(i, j, k, grid, Ax_∂xᶠᶜᶠ, w) +
                                    δyᵃᶜᵃ(i, j, k, grid, Ay_∂yᶜᶠᶠ, w) +
                                    δzᵃᵃᶠ(i, j, k, grid, Az_∂zᶜᶜᶜ, w))
end