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 an extent of $L_x = 200$ meters, $L_y = 100$ meters, and $L_z = 100$ meters is constructed using

julia> grid = RegularCartesianGrid(size=(64, 32, 16), extent=(200, 100, 100))
RegularCartesianGrid{Float64, Periodic, Periodic, Bounded}
                   domain: x ∈ [0.0, 200.0], y ∈ [0.0, 100.0], z ∈ [-100.0, 0.0]
                 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)

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:

julia> grid = RegularCartesianGrid(topology=(Periodic, Bounded, Bounded),
                            size=(64, 32, 16), extent=(200, 100, 100))
RegularCartesianGrid{Float64, Periodic, Bounded, Bounded}
                   domain: x ∈ [0.0, 200.0], y ∈ [0.0, 100.0], z ∈ [-100.0, 0.0]
                 topology: (Periodic, Bounded, 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)

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, $y \in [0, 12.5]$ meters, and $z \in [0, \pi]$ meters

julia> grid = RegularCartesianGrid(size=(64, 32, 16), 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): (64, 32, 16)
   halo size (Hx, Hy, Hz): (1, 1, 1)
grid spacing (Δx, Δy, Δz): (3.125, 0.390625, 0.39269908169872414)

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

julia> grid = RegularCartesianGrid(topology=(Periodic, Flat, Bounded),
                            size=(64, 1, 16), extent=(200, 1, 100))
RegularCartesianGrid{Float64, Periodic, Flat, Bounded}
                   domain: x ∈ [0.0, 200.0], y ∈ [0.0, 1.0], z ∈ [-100.0, 0.0]
                 topology: (Periodic, Flat, Bounded)
  resolution (Nx, Ny, Nz): (64, 1, 16)
   halo size (Hx, Hy, Hz): (1, 1, 1)
grid spacing (Δx, Δy, Δz): (3.125, 1.0, 6.25)

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

julia> grid = RegularCartesianGrid(topology=(Flat, Flat, Bounded),
                            size=(1, 1, 90), extent=(1, 1, 1000))
RegularCartesianGrid{Float64, Flat, Flat, Bounded}
                   domain: x ∈ [0.0, 1.0], y ∈ [0.0, 1.0], z ∈ [-1000.0, -2.471452993948034e-14]
                 topology: (Flat, Flat, Bounded)
  resolution (Nx, Ny, Nz): (1, 1, 90)
   halo size (Hx, Hy, Hz): (1, 1, 1)
grid spacing (Δx, Δy, Δz): (1.0, 1.0, 11.11111111111111)

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