Grids

Currently only a regular Cartesian grid with constant grid spacings is supported. The spacing can be different for each dimension.

When constructing a RegularCartesianGrid the number of grid points (or size of the grid) and the physical length of each dimension (or length of the grid) must be passed as tuples.

A regular Cartesian grid with $N_x \times N_y \times N_z = 64 \times 32 \times 16$ grid points and a length of $L_x = 200$ meters, $L_y = 100$ meters, and $L_z = 100$ meters is constructed using

using Oceananigans # hide
grid = RegularCartesianGrid(size=(64, 32, 16), length=(200, 100, 100))

Specifying the grid's topology

You can also pass a tuple denoting the grid's topology. Each dimension can be either Periodic, Bounded, or Flat. By default, the RegularCartesianGrid constructor assumes a horizontally periodic grid topology, topology = (Periodic, Periodic, Bounded). To specify a channel model that is periodic in the x-dimension and wall-bounded in the y- and z-dimensions:

using Oceananigans # hide
grid = RegularCartesianGrid(size=(64, 32, 16), length=(200, 100, 100), topology=(Periodic, Bounded, Bounded))

Specifying the domain

To specify a different domain, the x, y, and z keyword arguments can be used instead of length. For example, to use the domain $x \in [-100, 100]$ meters, $y \in [-50, 50]$ meters, and $z \in [0, 100]$ meters

grid = RegularCartesianGrid(size=(64, 32, 16), x=(-100, 100), y=(-50, 50), z=(0, 100))

RegularCartesianGrid{Float64, Periodic, Periodic, Bounded}
                   domain: x ∈ [-103.125, 100.0], y ∈ [-53.125, 50.0], z ∈ [-6.25, 106.25]
                 topology: (Periodic, Periodic, Bounded)
  resolution (Nx, Ny, Nz): (64, 32, 16)
   halo size (Hx, Hy, Hz): (1, 1, 1)
grid spacing (Δx, Δy, Δz): (3.125, 3.125, 6.25)

Two-dimensional grids

Two-dimensional grids can be constructed by setting the number of grid points along the flat dimension to be 1. A two-dimensional grid in the $xz$-plane can be constructed using

using Oceananigans # hide
grid = RegularCartesianGrid(size=(64, 1, 16), length=(200, 1, 100), topology=(Periodic, Flat, Bounded))

In this case the length of the $y$ dimension must be specified but does not matter so we just set it to 1.

2D grids can be used to simulate $xy$, $xz$, and $yz$ planes.

One-dimensional grids

One-dimensional grids can be constructed in a similar manner, most commonly used to set up vertical column models. For example, to set up a 1D model with $N_z$ grid points

using Oceananigans # hide
grid = RegularCartesianGrid(size=(1, 1, 90), length=(1, 1, 1000), topology=(Flat, Flat, Bounded))

The length of the $x$ and $y$ dimensions must be specified but do not matter.