Spaces

A Space represents a discretized function space over some domain. Currently two main discretizations are supported: Spectral Element Discretization (both Continuous Galerkin and Discontinuous Galerkin types) and a staggered Finite Difference Discretization. Combination of these two in the horizontal/vertical directions, respectively, is what we call a hybrid space.

Sketch of a 2DX hybrid discretization:

3D hybrid discretization in a Cartesian domain

ClimaCore.Spaces — Module

Meshes

domain
topology
coordinates
metric terms (inverse partial derivatives)
quadrature rules and weights

References / notes

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ClimaCore.Spaces.Δz_data — Function

Δz_data(space::AbstractSpace)

A DataLayout containing the Δz on a given space space.

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Finite Difference Spaces

ClimaCore.jl supports staggered Finite Difference discretizations. Finite Differences discretize an interval domain by approximating the function by a value at either the center of each element (also referred to as cell) (CenterFiniteDifferenceSpace), or the interfaces (faces in 3D, edges in 2D or points in 1D) between elements (FaceFiniteDifferenceSpace).

ClimaCore.Spaces.FiniteDifferenceSpace — Type

FiniteDifferenceSpace(
    grid::Grids.FiniteDifferenceGrid,
    staggering::Staggering
)

A 1D finite-difference space, that lives on either:

cell centers (where staggering is Grids.CellCenter) or
cell faces (where staggering is Grids.CellFace)

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Users should construct either the center or face space from the mesh, then construct the other space from the original one: this internally reuses the same data structures, and avoids allocating additional memory.

Spectral Element Spaces

ClimaCore.Spaces.SpectralElementSpace1D — Type

SpectralElementSpace1D(grid::SpectralElementGrid1D)
SpectralElementSpace1D(
    topology::Topologies.IntervalTopology,
    quadrature_style::Quadratures.QuadratureStyle;
    kwargs...
)

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ClimaCore.Spaces.SpectralElementSpace2D — Type

SpectralElementSpace2D(grid::SpectralElementGrid1D)
SpectralElementSpace2D(
    topology::Topologies.Topology2D,
    quadrature_style::Quadratures.QuadratureStyle;
    kwargs...,
)

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ClimaCore.Spaces.SpectralElementSpaceSlab — Type

SpectralElementSpaceSlab <: AbstractSpace

A view into a SpectralElementSpace2D for a single slab.

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ClimaCore.Spaces.node_horizontal_length_scale — Function

Spaces.node_horizontal_length_scale(space::AbstractSpectralElementSpace)

The approximate length scale of the distance between nodes. This is defined as the length scale of the mesh (see Meshes.element_horizontal_length_scale), divided by the number of unique quadrature points along each dimension.

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Extruded Finite Difference Spaces

ClimaCore.Spaces.ExtrudedFiniteDifferenceSpace — Type

ExtrudedFiniteDifferenceSpace(grid, staggering)

ExtrudedFiniteDifferenceSpace(
    horizontal_space::AbstractSpace,
    vertical_space::FiniteDifferenceSpace,
    hypsography::Grids.HypsographyAdaption = Grids.Flat();
    deep::Bool = false,
)

An extruded finite-difference space, where the extruded direction is staggered, containing grid information at either

cell centers (where staggering is Grids.CellCenter) or
cell faces (where staggering is Grids.CellFace)

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Utilities

ClimaCore.Spaces.area — Function

Spaces.area(space::Spaces.AbstractSpace)

The length/area/volume of space. This is computed as the sum of the quadrature weights $W_i$ multiplied by the Jacobian determinants $J_i$:

\[\sum_i W_i J_i \approx \int_\Omega \, d \Omega\]

If space is distributed, this uses a ClimaComms.allreduce operation.

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ClimaCore.Spaces.local_area — Function

Spaces.local_area(space::Spaces.AbstractSpace)

The length/area/volume of space local to the current context. See Spaces.area

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