AxisymmetricGrid2D

AxisymmetricGrid2D(x::AbstractMatrix{T}, y::AbstractMatrix{T},  nhalo::Int,  snap_to_axis::Bool,  rotational_axis::Symbol;  T=Float64, backend=CPU())

Create an axisymmetric 2d grid with x and y coordinates, with the symmetry axis rotational_axis = :x or rotational_axis = :y. Enforce coordinates to stay on the axis via snap_to_axis=True. The input coordinates do not include halo / ghost data since the geometry is undefined in these regions. The nhalo argument defines the number of halo cells along each dimension.

CurvilinearGrid1D

Fields

• x: Node function, e.g. x -> f(ξ)
• ∂x∂ξ: Derivative of x wrt ξ; ∂x∂ξ(ξ)
• nhalo: Number of halo cells for all dims
• nnodes: Number of nodes/vertices
• limits: Cell loop limits based on halo cells

CurvilinearGrid1D(x::Function, (n_ξ,), nhalo)

Create a CurvilinearGrid1D with a function x(ξ) and nhalo halo cells. n_ξ is the total number of nodes/vertices (not including halo).

CurvilinearGrid2D

CurvilinearGrid2D(x::AbstractArray{T,2}, y::AbstractArray{T,2}, nhalo::Int, discretization_scheme=:MEG6; backend=CPU()) where {T}

Create a 2d grid with x and y coordinates. The input coordinates do not include halo / ghost data since the geometry is undefined in these regions. The nhalo argument defines the number of halo cells along each dimension.

CurvilinearGrid3D

Fields

• x: Node function; e.g., x(i,j,k)
• y: Node function; e.g., y(i,j,k)
• z: Node function; e.g., z(i,j,k)
• jacobian_matrix_func: Function to compute the jacobian matrix, e.g., J(i,j,k)
• conserv_metric_func: Function to compute the conservative metrics
• nhalo: Number of halo cells for all dims
• nnodes: Number of nodes/vertices
• limits: Cell loop limits based on halo cells

CurvilinearGrid3D(

x::AbstractArray{T,3}, y::AbstractArray{T,3}, z::AbstractArray{T,3}, nhalo::Int, discretization_scheme=:MEG6; backend=CPU(), ) where {T}

RThetaGrid((r0, θ0), (r1, θ1), (ni_cells, nj_cells), nhalo, snap_to_axis, rotational_axis, backend=CPU(), T=Float64)

Create an equally spaced axisymmetric polar grid based on r and θ. The axis of rotation is set by rotational_axis as :x or :y

AxisymmetricRThetaGrid(r, θ, nhalo, snap_to_axis, rotational_axis::Symbol, backend=CPU())

Create polar grid based on vectors of r and θ coordinates. The axis of rotation is set by rotational_axis as :x or :y

RThetaGrid((r0, θ0), (r1, θ1), (ni_cells, nj_cells), nhalo::Int, backend=CPU(), T=Float64)

Create an equally spaced polar grid based on r and θ

RThetaGrid(r, θ, nhalo::Int, backend=CPU())

Create polar grid based on vectors of r and θ coordinates

Get the size of the grid for cell-based arrays

Get the size of the grid for cell-based arrays when the halo cells are included

Get the position of the centroid for the given cell index. NOTE: these indices are consistent with halo cells included. This means that if your grid has 2 halo cells, the position of the first non-halo centroid is index at coord(mesh, 3). The CurvilinearGrid only keeps track of the number of halo cells for each dimension, whereas the grid functions have no knowledge halos. Therefore, the coord function applies a shift to the index for you.

Get the radial centroid coordinate of a axisymmetric mesh

Get the position/coordinate at a given index. NOTE: these indices are consistent with halo cells included. This means that if your grid has 2 halo cells, the position of the first non-halo vertex is index at coord(mesh, 3). The CurvilinearGrid only keeps track of the number of halo cells for each dimension, whereas the grid functions have no knowledge halos. Therefore, the coord function applies a shift to the index for you.

Get the Jacobian of the forward transformation (ξ,η,ζ) → (x,y,z).

jacobian(mesh::CurvilinearGrid2D, idx)

The cell-centroid Jacobian (determinant of the Jacobian matrix)

Get the Jacobian matrix of the forward transformation (ξ,η,ζ) → (x,y,z).

jacobian_matrix(mesh::CurvilinearGrid2D, idx)

The cell-centroid Jacobian matrix (the forward transformation: ∂x/∂ξ, ∂y/∂ξ, ... ). Use inv(jacobian_matrix(mesh, idx)) to get the inverse transformation (∂ξ/∂x, ∂ξ/∂y, ...)

Get the radial node coordinate of a axisymmetric mesh

Update metrics after grid coordinates change

Update metrics after grid coordinates change

Update metrics after grid coordinates change

Update metrics after grid coordinates change

Functions used to work on CartesianIndex and CartesianIndices to make looping and stencil creation easy for arbitary dimensions and axes

Go down by n on a given axis of a CartesianIndex

Expand the CartesianIndices ranges by n on axis

Expand the CartesianIndices ranges by n on all axes

Expand the CartesianIndices starting index by -n on all axes

Expand the CartesianIndices ending index by +n on all axes

Take a given CartesianIndices and extract only the lower boundary indices at an offset of n along a given axis.

Example

julia> domain = CartesianIndices((1:10, 4:8))
CartesianIndices((1:10, 4:8))

julia> lower_boundary_indices(domain, 2, 0) # select the first index on axis 2
CartesianIndices((1:10, 4:4))

Get indices of of ±n for an arbitary axis. For a 2d index, and and offset on the j axis, this would be [i,j-n:j+n]. This makes it simple to generate arbitrary stencils on arbitrary axes.

Arguments

• I::CartesianIndex{N}
• axis::Int: which axis to provide the ±n to
• n::Int: how much to offset on a given axis

Example

julia> I = CartesianIndex((4,5))
CartesianIndex(4, 5)

julia> plus_minus(I, 2, 2)
CartesianIndices((4:4, 3:7))

Go up by n on a given axis of a CartesianIndex

Take a given CartesianIndices and extract only the upper boundary indices at an offset of n along a given axis.

Example

julia> domain = CartesianIndices((1:10, 4:8))
CartesianIndices((1:10, 4:8))

julia> upper_boundary_indices(domain, 2, 1)
CartesianIndices((1:10, 8:8))

Apply a delta function to the cartesian index on a specified axis. For example, δ(3, CartesianIndex(1,2,3)) will give CartesianIndex(0,0,1).

Functions used to work on CartesianIndex and CartesianIndices to make looping and stencil creation easy for arbitary dimensions and axes

Go down by n on a given axis of a CartesianIndex

Expand the CartesianIndices ranges by n on axis

Expand the CartesianIndices ranges by n on all axes

Expand the CartesianIndices starting index by -n on all axes

Expand the CartesianIndices ending index by +n on all axes

Take a given CartesianIndices and extract only the lower boundary indices at an offset of n along a given axis.

Example

julia> domain = CartesianIndices((1:10, 4:8))
CartesianIndices((1:10, 4:8))

julia> lower_boundary_indices(domain, 2, 0) # select the first index on axis 2
CartesianIndices((1:10, 4:4))

Get indices of of ±n for an arbitary axis. For a 2d index, and and offset on the j axis, this would be [i,j-n:j+n]. This makes it simple to generate arbitrary stencils on arbitrary axes.

Arguments

• I::CartesianIndex{N}
• axis::Int: which axis to provide the ±n to
• n::Int: how much to offset on a given axis

Example

julia> I = CartesianIndex((4,5))
CartesianIndex(4, 5)

julia> plus_minus(I, 2, 2)
CartesianIndices((4:4, 3:7))

Go up by n on a given axis of a CartesianIndex

Take a given CartesianIndices and extract only the upper boundary indices at an offset of n along a given axis.

Example

julia> domain = CartesianIndices((1:10, 4:8))
CartesianIndices((1:10, 4:8))

julia> upper_boundary_indices(domain, 2, 1)
CartesianIndices((1:10, 8:8))

Apply a delta function to the cartesian index on a specified axis. For example, δ(3, CartesianIndex(1,2,3)) will give CartesianIndex(0,0,1).

Write the mesh to .VTK format