Grids

We currently support only RegularCartesianGrids with constant grid spacings. The spacing can be different for each dimension.

A RegularCartesianGrid is constructed by specifying the size of the grid (a Tuple specifying the number of grid points in each direction) and either the extent (a Tuple specifying the physical extent of the grid in each direction), or 2-Tuples x, y, and z (for a 3D grid) that defines the the end points in each direction.

A regular Cartesian grid with $N_x \times N_y \times N_z = 32 \times 64 \times 256$ grid points and an extent of $L_x = 128$ meters, $L_y = 256$ meters, and $L_z = 512$ meters is constructed using

julia> grid = RegularCartesianGrid(size=(32, 64, 256), extent=(128, 256, 512))
RegularCartesianGrid{Float64, Periodic, Periodic, Bounded}
                   domain: x ∈ [0.0, 128.0], y ∈ [0.0, 256.0], z ∈ [-512.0, 0.0]
                 topology: (Periodic, Periodic, Bounded)
  resolution (Nx, Ny, Nz): (32, 64, 256)
   halo size (Hx, Hy, Hz): (1, 1, 1)
grid spacing (Δx, Δy, Δz): (4.0, 4.0, 2.0)

Default domain

When using the extent keyword, the domain is $x \in [0, L_x]$, $y \in [0, L_y]$, and $z \in [-L_z, 0]$ –- a sensible choice for oceanographic applications.

Specifying the grid's topology

Another crucial keyword is a 3-Tuple that specifies the grid's topology. In each direction the grid may be Periodic, Bounded, or Flat. Flat dimensions are used to specify two-dimensional and one-dimensional domains. By default, the RegularCartesianGrid constructor assumes the grid topology is horizontally-periodic and bounded in the vertical, such that topology = (Periodic, Periodic, Bounded).

A "channel" model that is periodic in the x-direction and wall-bounded in the y- and z-dimensions is build with,

julia> grid = RegularCartesianGrid(topology=(Periodic, Bounded, Bounded), size=(64, 64, 32), extent=(1e4, 1e4, 1e3))
RegularCartesianGrid{Float64, Periodic, Bounded, Bounded}
                   domain: x ∈ [0.0, 10000.0], y ∈ [0.0, 10000.0], z ∈ [-1000.0, 0.0]
                 topology: (Periodic, Bounded, Bounded)
  resolution (Nx, Ny, Nz): (64, 64, 32)
   halo size (Hx, Hy, Hz): (1, 1, 1)
grid spacing (Δx, Δy, Δz): (156.25, 156.25, 31.25)

To specify a two-dimensional, horizontally-periodic model, write

julia> grid = RegularCartesianGrid(topology=(Periodic, Periodic, Flat), size=(64, 64), extent=(1e4, 1e4))
RegularCartesianGrid{Float64, Periodic, Periodic, Flat}
                   domain: x ∈ [0.0, 10000.0], y ∈ [0.0, 10000.0], z ∈ [0.0, 0.0]
                 topology: (Periodic, Periodic, Flat)
  resolution (Nx, Ny, Nz): (64, 64, 1)
   halo size (Hx, Hy, Hz): (1, 1, 0)
grid spacing (Δx, Δy, Δz): (156.25, 156.25, 0.0)

Grid spacing in Flat directions is 0. Notice that two-dimensional domains accept 2-Tuples for size and extent. To specify a one-dimensional "column" model that varies only in $z$, write

julia> grid = RegularCartesianGrid(topology=(Flat, Flat, Bounded), size=128, extent=256)
RegularCartesianGrid{Float64, Flat, Flat, Bounded}
                   domain: x ∈ [0.0, 0.0], y ∈ [0.0, 0.0], z ∈ [-256.0, 0.0]
                 topology: (Flat, Flat, Bounded)
  resolution (Nx, Ny, Nz): (1, 1, 128)
   halo size (Hx, Hy, Hz): (0, 0, 1)
grid spacing (Δx, Δy, Δz): (0.0, 0.0, 2.0)

For one-dimensional domains, size and extent may either be scalars or 1-Tuples.

Specifying domain end points

To specify a domain with a different origin than the default, the x, y, and z keyword arguments must be used. For example, a grid with $x \in [-100, 100]$ meters, $y \in [0, 12.5]$ meters, and $z \in [0, \pi]$ meters is constructed via

julia> grid = RegularCartesianGrid(size=(32, 16, 256), x=(-100, 100), y=(0, 12.5), z=(-π, π))
RegularCartesianGrid{Float64, Periodic, Periodic, Bounded}
                   domain: x ∈ [-100.0, 100.0], y ∈ [0.0, 12.5], z ∈ [-3.141592653589793, 3.141592653589793]
                 topology: (Periodic, Periodic, Bounded)
  resolution (Nx, Ny, Nz): (32, 16, 256)
   halo size (Hx, Hy, Hz): (1, 1, 1)
grid spacing (Δx, Δy, Δz): (6.25, 0.78125, 0.02454369260617026)

For two- and one-dimensional domains, Flat dimensions may be omitted, or provided as a scalar:

julia> grid = RegularCartesianGrid(size=(32, 32), x=(-100, 100), y=(0, 200), z=-1000, topology=(Periodic, Periodic, Flat))
RegularCartesianGrid{Float64, Periodic, Periodic, Flat}
                   domain: x ∈ [-100.0, 100.0], y ∈ [0.0, 200.0], z ∈ [-1000.0, -1000.0]
                 topology: (Periodic, Periodic, Flat)
  resolution (Nx, Ny, Nz): (32, 32, 1)
   halo size (Hx, Hy, Hz): (1, 1, 0)
grid spacing (Δx, Δy, Δz): (6.25, 6.25, 0.0)