API

ClimaCore.DataLayouts

Notation:

• i,j are horizontal node indices within an element
• k is the vertical node index within an element
• f is the field index (1 if field is scalar, >1 if it is a vector field)
• v is the vertical element index in a stack
• h is the element stack index

Data layout is specified by the order in which they appear, e.g. IJKFVH indexes the underlying array as [i,j,k,f,v,h]

DataF{S, A} <: Data0D{S}

Backing DataLayout for 0D point data.

IF{S, Ni, A} <: DataSlab1D{S, Ni}

Backing DataLayout for 1D spectral element slab data.

Nodal element data (I) are contiguous for each S datatype struct field (F) for a single element slab.

A DataSlab1D view can be returned from other Data1D objects by calling slab(data, idx...).

IJF{S, Nij, A} <: DataSlab2D{S, Nij}

Backing DataLayout for 2D spectral element slab data.

Nodal element data (I,J) are contiguous for each S datatype struct field (F) for a single element slab.

A DataSlab2D view can be returned from other Data2D objects by calling slab(data, idx...).

VF{S, A} <: DataColumn{S}

Backing DataLayout for 1D FV column data.

Column level data (V) are contiguous for each S datatype struct field (F).

A DataColumn view can be returned from other Data1DX, Data2DX objects by calling column(data, idx...).

IFH{S, Ni, A} <: Data1D{S, Ni}

Backing DataLayout for 1D spectral element slabs.

Element nodal point (I) data is contiguous for each datatype S struct field (F), for each 1D mesh element (H).

IJFH{S, Nij, A} <: Data2D{S, Nij}

Backing DataLayout for 2D spectral element slabs.

Element nodal point (I,J) data is contiguous for each datatype S struct field (F), for each 2D mesh element slab (H).

VIFH{S, Ni, A} <: Data1DX{S, Ni}

Backing DataLayout for 1D spectral element slab + extruded 1D FV column data.

Column levels (V) are contiguous for every element nodal point (I) for each datatype S struct field (F), for each 1D mesh element slab (H).

VIJFH{S, Nij, A} <: Data2DX{S, Nij}

Backing DataLayout for 2D spectral element slab + extruded 1D FV column data.

Column levels (V) are contiguous for every element nodal point (I, J) for each S datatype struct field (F), for each 2D mesh element slab (H).

AbstractPoint

Represents a point in space.

The following types are supported:

• XPoint(x)
• YPoint(y)
• ZPoint(z)
• XYPoint(x, y)
• XZPoint(x, z)
• XYZPoint(x, y, z)
• LatLongPoint(lat, long)
• LatLongZPoint(lat, long, z)
• Cartesian1Point(x1)
• Cartesian2Point(x2)
• Cartesian3Point(x3)
• Cartesian12Point(x1, x2)
• Cartesian13Point(x1, x3)
• Cartesian123Point(x1, x2, x3)

float_type(T)

Return the floating point type backing T: T can either be an object or a type.

AbstractDomain

A domain represents a region of space.

IntervalDomain(coord⁻, coord⁺; periodic=true)
IntervalDomain(coord⁻, coord⁺; boundary_names::Tuple{Symbol,Symbol})

Construct a IntervalDomain, the closed interval is given by coord⁻, coord⁺ coordinate arguments.

Either a periodic or boundary_names keyword argument is required.

RectangleDomain(x1::ClosedInterval, x2::ClosedInterval;
    x1boundary::Tuple{Symbol,Symbol},
    x2boundary::Tuple{Symbol,Symbol},
    x1periodic = false,
    x2periodic = false,
)

Construct a RectangularDomain in the horizontal. If a given x1 or x2 boundary is not periodic, then x1boundary or x2boundary boundary name keyword arguments must be supplied.

SphereDomain(radius)

A domain representing the surface of a sphere with radius radius.

boundary_names(obj::Union{AbstractDomain, AbstractMesh, AbstractTopology})

A tuple or vector of unique boundary names of a spatial domain.

AbstractMesh{dim}

A Mesh is an object which represents how we discretize a domain into elements.

It should be lightweight (i.e. exists on all MPI ranks), e.g for meshes stored in a file, it would contain the filename.

Face and vertex numbering

In 1D, faces and vertices are the same, and both are numbered [1,2].

In 2D, a face is a line segment between to vertices, and both are numbered [1,2,3,4], in a counter-clockwise direction.

 v4        f3        v3
   o-----------------o
   |                 |	    face    vertices
   |                 |	      f1 =>  v1 v2
f4 |                 | f2     f2 =>  v2 v3
   |                 |	      f3 =>  v3 v4
   |                 |        f4 =>  v4 v1
   |                 |
   o-----------------o
  v1       f1        v2

Interface

A subtype of AbstractMesh should define the following methods:

• domain(mesh)
• elements(mesh)
• is_boundary_face(mesh, elem, face)
• boundary_face_name(mesh, elem, face)
• opposing_face(mesh, elem, face)
• coordinates(mesh, elem, vert)
• containing_element (optional)

The following types/methods are provided by AbstractMesh:

• SharedVertices(mesh, elem, vert)
• face_connectivity_matrix(mesh[,elemorder])
• vertex_connectivity_matrix(mesh[,elemorder])

IntervalMesh <: AbstractMesh

A 1D mesh on an IntervalDomain.

Constuctors

IntervalMesh(domain::IntervalDomain, faces::AbstractVector)

Construct a 1D mesh with face locations at faces.

IntervalMesh(domain::IntervalDomain[, stretching=Uniform()]; nelems=)

Constuct a 1D mesh on domain with nelems elements, using stretching. Possible values of stretching are:

• Uniform()
• ExponentialStretching(H)
• GeneralizedExponentialStretching(dz_surface, dz_top)

RectilinearMesh <: AbstractMesh2D

Constructors

RectilinearMesh(domain::RectangleDomain, n1, n2)

Construct a RectilinearMesh of equally-spaced n1 by n2 elements on domain.

RectilinearMesh(intervalmesh1::IntervalMesh1, intervalmesh2::IntervalMesh2)

Construct the product mesh of intervalmesh1 and intervalmesh2.

AbstractCubedSphere <: AbstractMesh2D

This is an abstract type of cubed-sphere meshes on SphereDomains. A cubed-sphere mesh has 6 panels, laid out as follows:

                                          :   Panel 1   :
                            +-------------+-------------+
                            |     +x1     |     +x1     |
                            |             |             |
                            |    Panel    |    Panel    |
                            |+x3   5   -x3|-x2   6   +x2|
                            |     -x2     |     -x3     |
                            |             |             |
                            |     -x1     |     -x1     |
              +-------------+-------------+-------------+
              |     -x2     |     -x2     |
              |             |             |
              |    Panel    |    Panel    |
              |+x1   3   -x1|+x3   4   -x3|
              |     +x3     |     -x1     |
              |             |             |
              |     +x2     |     +x2     |
+-------------+-------------+-------------+
|     +x3     |     +x3     |
|             |             |
|    Panel    |    Panel    |
|-x2   1   +x2|+x1   2   -x1|
|     +x1     |     +x2     |
|             |             |
|     -x3     |     -x3     |
+-------------+-------------+
:   Panel 6   :

This is the same panel ordering used by the S2 Geometry library (though we use 1-based instead of 0-based numering).

Elements are indexed by a CartesianIndex{3} object, where the components are:

• horizontal element index (left to right) within each panel.
• vertical element index (bottom to top) within each panel.
• panel number

Subtypes should have the following fields:

• domain: a SphereDomain
• ne: number of elements across each panel

External links

• S2Geometry library
• MIT GCM exch2

EquiangularCubedSphere <: AbstractCubedSphere

An equiangular gnomonic mesh proposed by C. Ronchi, R. Iacono, P. S. Paolucci (1996). Uses the element indexing convention of AbstractCubedSphere.

Constructors

EquiangularCubedSphere(
    domain::Domains.SphereDomain,
    ne::Integer,
    localelementmap=NormalizedBilinearMap()
    )

Constuct an EquiangularCubedSphere on domain with ne elements across each panel.

EquidistantCubedSphere <: AbstractCubedSphere

An equidistant gnomonic mesh outlined in M. Rančić, R. J. Purser, F. Mesinger (1996) and Ramachandran D Nair, Stephen J Thomas, Richard D Loft (2005). Uses the element indexing convention of AbstractCubedSphere.

Constructors

EquidistantCubedSphere(domain::Domains.SphereDomain, ne::Integer)

Constuct an EquidistantCubedSphere on domain with ne elements across each panel.

ConformalCubedSphere <: AbstractCubedSphere

A conformal mesh outlined in M. Rančić, R. J. Purser, F. Mesinger (1996). Uses the element indexing convention of AbstractCubedSphere.

Constructors

ConformalCubedSphere(domain::Domains.SphereDomain, ne::Integer)

Constuct a ConformalCubedSphere on domain with ne elements across each panel.

LocalElementMap

An abstract type of mappings from the reference element to a physical domain.

IntrinsicMap()

This LocalElementMap uses the intrinsic mapping of the cubed sphere to map the reference element to the physical domain.

NormalizedBilinearMap()

The LocalElementMap for meshes on spherical domains of O. Guba, M. A. Taylor, P. A. Ullrich, J. R. Overfelt, M. N. Levy (2014). It uses bilinear interpolation between the Cartesian coordinates of the element vertices, then normalizes the result to lie on the sphere.

Uniform()

Use uniformly-sized elements.

ExponentialStretching(H)

Apply exponential stretching to the domain when constructing elements. H is the scale height (a typical atmospheric scale height H ≈ 7.5km).

For an interval $[z_0,z_1]$, this makes the elements uniformally spaced in $\zeta$, where

\[\zeta = \frac{1 - e^{-\eta/h}}{1-e^{-1/h}},\]

where $\eta = \frac{z - z_0}{z_1-z_0}$, and $h = \frac{H}{z_1-z_0}$ is the non-dimensional scale height.

domain(topology)

Returns the domain of the topology from the underlying mesh

Meshes.domain(mesh::AbstractMesh)

The Domains.AbstractDomain on which the mesh is defined.

Meshes.elements(mesh::AbstractMesh)

An iterator over the elements of a mesh. Elements of a mesh can be of any type.

nelements(mesh::AbstractMesh)

The number of elements in the mesh.

Meshes.is_boundary_face(mesh::AbstractMesh, elem, face::Int)::Bool

Determine whether face face of element elem is on the boundary of mesh.

elem should be an element of elements(mesh).

Meshes.boundary_face_name(mesh::AbstractMesh, elem, face::Int)::Union{Symbol,Nothing}

The name of the boundary facing face of element elem, or nothing if it is not on the boundary.

opelem, opface, reversed = Meshes.opposing_face(mesh::AbstractMesh, elem, face::Int)

The element and face (opelem, opface) that oppose face face of element elem.

Meshes.coordinates(mesh, elem, vert::Int)
Meshes.coordinates(mesh, elem, ξ::SVector)

Return the physical coordinates of a point in an element elem of mesh. The position of the point can either be a vertex number vert or the coordinates ξ in the reference element.

elem = Meshes.containing_element(mesh::AbstractMesh, coord)

The element elem in mesh containing the coordinate coord. If the coordinate falls on the boundary between two or more elements, an arbitrary element is chosen.

ξ = Meshes.reference_coordinates(mesh::AbstractMesh, elem, coord)

An SVector of coordinates in the reference element such that

Meshes.coordinates(mesh, elem, ξ) == coord

This can be used for interpolation to a specific point.

Meshes.SharedVertices(mesh, elem, vert)

An iterator over (element, vertex) pairs that are shared with (elem,vert).

M = Meshes.face_connectivity_matrix(mesh, elemorder = elements(mesh))

Construct a Bool-valued SparseCSCMatrix containing the face connections of mesh. Elements are indexed according to elemorder.

Note that M[i,i] == true only if two distinct faces of element i are connected.

M = Meshes.vertex_connectivity_matrix(mesh, elemorder = elements(mesh))

Construct a Bool-valued SparseCSCMatrix containing the vertex connections of mesh. Elements are indexed according to elemorder.

Note that M[i,i] == true only if two distinct vertices of element i are connected.

Meshes.linearindices(elemorder)

Given a data structure elemorder[i] = elem that orders elements, construct the inverse map from orderindex = linearindices(elemorder) such that orderindex[elem] = i.

This will try to use the most efficient structure available.

AbstractTopology

Subtypes of AbstractHorizontalTopology define connectiveness of a mesh in the horizontal domain.

Interfaces

• nelems
• domain
• mesh
• nlocalelems
• nneighbors
• nsendelems
• nghostelems
• localelemindex
• vertex_coordinates
• opposing_face
• face_node_index
• interior_faces
• ghost_faces
• vertex_node_index
• vertices
• local_neighboring_elements
• ghost_neighboring_elements
• local_vertices
• ghost_vertices
• neighbors
• boundary_tags
• boundary_tag
• boundary_faces

IntervalTopology(mesh::IntervalMesh)

A sequential topology on an Meshes.IntervalMesh.

Topology2D(mesh::AbstractMesh2D, elemorder=Mesh.elements(mesh))

This is a generic non-distributed topology for 2D meshes. elemorder is a vector or other linear ordering of the Mesh.elements(mesh).

spacefillingcurve(mesh::Meshes.AbstractCubedSphere)

Generate element ordering, elemorder, based on a space filling curve for a CubedSphere mesh.

spacefillingcurve(mesh::Meshes.RectilinearMesh)

Generate element ordering, elemorder, based on a space filling curve for a Rectilinear mesh.

mesh(topology)

Returns the mesh underlying the topology

nlocalelems(topology)

The number of local elements in topology.

(c1,c2,c3,c4) = vertex_coordinates(topology, elem)

The coordinates of the 4 vertices of element elem.

(opelem, opface, reversed) = opposing_face(topology, elem, face)

The opposing face of face number face of element elem in topology.

• opelem is the opposing element number, 0 for a boundary, negative for a ghost element
• opface is the opposite face number, or boundary face number if a boundary
• reversed indicates whether the opposing face has the opposite orientation.

interior_faces(topology::AbstractTopology)

An iterator over the interior faces of topology. Each element of the iterator is a 5-tuple the form

(elem1, face1, elem2, face2, reversed)

where elemX, faceX are the element and face numbers, and reversed indicates whether they have opposing orientations.

boundary_tags(topology)

A Tuple or NamedTuple of the boundary tags of the topology. A boundary tag is an integer that uniquely identifies a boundary.

boundary_tag(topology, name::Symbol)

The boundary tag of the topology for boundary name name. A boundary tag is an integer that uniquely identifies a boundary.

boundary_faces(topology, boundarytag)

An iterator over the faces of topology which face the boundary with tag boundarytag. Each element of the iterator is an (elem, face) pair.

local_neighboring_elements(topology::AbstractTopology, lidx::Integer)

An iterator of the local element indices (lidx) of the local elements which are neighbors of the local element lidx in topology (excluding lidx itself).

ghost_neighboring_elements(topology::AbstractTopology, ridx::Integer)

An iterator of the receive buffer indices (ridx) of the ghost elements which are neighbors of the local element lidx in topology.

Meshes

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

References / notes

• ceed
• QA

QuadratureStyle

Quadrature style supertype. See sub-types:

• GLL
• GL
• Uniform

GLL{Nq}()

Gauss-Legendre-Lobatto quadrature using Nq quadrature points.

GL{Nq}()

Gauss-Legendre quadrature using Nq quadrature points.

Uniform{Nq}()

Uniformly-spaced quadrature.

degrees_of_freedom(QuadratureStyle) -> Int

Returns the degreesoffreedom of the QuadratureStyle concrete type

polynomial_degree(QuadratureStyle) -> Int

Returns the polynomial degree of the QuadratureStyle concrete type

points, weights = quadrature_points(::Type{FT}, quadrature_style)

The points and weights of the quadrature rule in floating point type FT.

barycentric_weights(x::SVector{Nq}) where {Nq}

The barycentric weights associated with the array of point locations x:

\[w_j = \frac{1}{\prod_{k \ne j} (x_i - x_j)}\]

See Jean-Paul Berrut, Lloyd N Trefethen (2004), equation 3.2.

interpolation_matrix(x::SVector, r::SVector{Nq})

The matrix which interpolates the Lagrange polynomial of degree Nq-1 through the points r, to points x. The matrix coefficients are computed using the Barycentric formula of Jean-Paul Berrut, Lloyd N Trefethen (2004), section 4:

\[I_{ij} = \begin{cases} 1 & \text{if } x_i = r_j, \\ 0 & \text{if } x_i = r_k \text{ for } k \ne j, \\ \frac{\displaystyle \frac{w_j}{x_i - r_j}}{\displaystyle \sum_k \frac{w_k}{x_i - r_k}} & \text{otherwise,} \end{cases}\]

where $w_j$ are the barycentric weights, see barycentric_weights.

differentiation_matrix(r::SVector{Nq, T}) where {Nq, T}

The spectral differentiation matrix for the Lagrange polynomial of degree Nq-1 interpolating at points r.

The matrix coefficients are computed using the Jean-Paul Berrut, Lloyd N Trefethen (2004), section 9.3:

\[D_{ij} = \begin{cases} \displaystyle \frac{w_j}{w_i (x_i - x_j)} &\text{ if } i \ne j \\ -\sum_{k \ne j} D_{kj} &\text{ if } i = j \end{cases}\]

where $w_j$ are the barycentric weights, see barycentric_weights.

differentiation_matrix(FT, quadstyle::QuadratureStyle)

The spectral differentiation matrix at the quadrature points of quadstyle, using floating point types FT.

V = orthonormal_poly(points, quad)

V_{ij} contains the j-1th Legendre polynomial evaluated at points[i]. i.e. it is the mapping from the modal to the nodal representation.

dss_transform(arg, local_geometry, weight, I...)

Transfrom arg[I...] to a basis for direct stiffness summation (DSS). Transformations only apply to vector quantities.

• local_geometry[I...] is the relevant LocalGeometry object. If it is nothing, then no transformation is performed
• weight[I...] is the relevant DSS weights. If weight is nothing, then the result is simply summation.

See Spaces.weighted_dss!.

dss_untransform(T, targ, local_geometry, I...)

Transform targ[I...] back to a value of type T after performing direct stiffness summation (DSS).

See Spaces.weighted_dss!.

dss_interior_faces!(topology, data [, local_geometry_data=nothing, local_weights=nothing])

Perform DSS on the local interior faces of the topology.

If local_geometry is nothing, no transformations are applied to vectors. If local_weights is nothing, no weighting is applied (i.e. colocated values are summed).

Part of Spaces.weighted_dss!.

dss_local_vertices!(topology, data[, local_geometry_data=nothing, local_weights=nothing])

Perform DSS on the local vertices of the topology.

Part of Spaces.weighted_dss!.

dss_ghost_faces!(topology, data, ghost_data,
    local_geometry_data=nothing, ghost_geometry_data=nothing,
    local_weights=nothing ghost_weights=nothing;
    update_ghost=false)

Perform DSS on the ghost faces of the topology. ghost_data should contain the ghost element data.

Part of Spaces.weighted_dss!.

dss_ghost_vertices!(topology, data, ghost_data,
    local_geometry_data=nothing, ghost_geometry_data=nothing,
    local_weights=nothing ghost_weights=nothing;
    update_ghost=false)

Perform DSS on the ghost faces of the topology. ghost_data should contain the ghost element data.

Part of Spaces.weighted_dss!.

RecursiveApply

This module contains operators to recurse over nested Tuples or NamedTuples.

To extend to another type T, define RecursiveApply.rmap(fn, args::T...)

tuplemap(fn::Function, tup)

A map impl for mapping function fn a tuple argument tup

Currently just calls Base.map behind the scenes but is left stubbed out for potential specialization in the future.

tuplemap(fn::Function, tup1, tup2)

A map impl for mapping function fn over tup1, tup2 tuple arguments.

Currently just calls Base.map behind the scenes but is left stubbed out for potential specialization in the future.

Field(values, space)

A set of values defined at each point of a space.

coordinate_field(space::AbstractSpace)

Construct a Field of the coordinates of the space.

local_geometry_field(space::AbstractSpace)

Construct a Field of the LocalGeometry of the space.

zeros(space::AbstractSpace)

Construct a field on space that is zero everywhere.

ones(space::AbstractSpace)

Construct a field on space that is one everywhere.

sum([f=identity,]v::Field)

Approximate integration of v or f.(v) over the domain. In an AbstractSpectralElementSpace, an integral over the entire space is computed by summation over the elements of the integrand multiplied by the Jacobian determinants and the quadrature weights at each node within an element. Hence, sum is computed by summation of the field values multiplied by the Jacobian determinants and quadrature weights:

\[\sum_i f(v_i) W_i J_i \approx \int_\Omega f(v) \, d \Omega\]

where $v_i$ is the value at each node, and $f$ is the identity function if not specified.

mean([f=identity, ]v::Field)

The mean value of field or f.(field) over the domain, weighted by area. Similar to sum, in an AbstractSpectralElementSpace, this is computed by summation of the field values multiplied by the Jacobian determinants and quadrature weights:

\[\frac{\sum_i f(v_i) W_i J_i}{\sum_i W_i J_i} \approx \frac{\int_\Omega f(v) \, d \Omega}{\int_\Omega \, d \Omega}\]

where $v_i$ is the Field value at each node, and $f$ is the identity function if not specified.

norm(v::Field, p=2; normalize=true)

The approximate $L^p$ norm of v, where $L^p$ represents the space of measurable functions for which the p-th power of the absolute value is Lebesgue integrable, that is:

\[\| v \|_p = \left( \int_\Omega |v|^p d \Omega \right)^{1/p}\]

where $|v|$ is defined to be the absolute value if $v$ is a scalar-valued Field, or the 2-norm if it is a vector-valued Field or composite Field (see LinearAlgebra.norm). Similar to sum and mean, in an AbstractSpectralElementSpace, this is computed by summation of the field values multiplied by the Jacobian determinants and quadrature weights. If normalize=true (the default), then internally the discrete norm is divided by the sum of the Jacobian determinants and quadrature weights:

\[\left(\frac{\sum_i |v_i|^p W_i J_i}{\sum_i W_i J_i}\right)^{1/p} \approx \left(\frac{\int_\Omega |v|^p \, d \Omega}{\int_\Omega \, d \Omega}\right)^{1/p}\]

If p=Inf, then the norm is the maximum of the absolute values

\[\max_i |v_i| \approx \sup_{\Omega} |v|\]

Consequently all norms should have the same units for all $p$ (being the same as calling norm on a single value).

If normalize=false, then the denominator term is omitted, and so the result will be the norm as described above multiplied by the length/area/volume of $\Omega$ to the power of $1/p$.

set!(f::Function, field::Field, args = ())

Apply function f to populate values in field field. f must have a function signature with signature f(::LocalGeometry[, args...]). Additional arguments may be passed to f with args.

ColumnIndex(ij,h)

An index into a column of a field. This can be used as an argument to getindex of a Field, to return a field on that column.

Example

colidx = ColumnIndex((1,1),1)
field[colidx]

Fields.bycolumn(fn, space)

Call fn(colidx) to every ColumnIndex colidx of space. This can be used to apply multiple column-wise operations in a single pass, making use of multiple threads.

Example

∇ = GradientF2C()
div = DivergenceC2F()

bycolumn(axes(f)) do colidx
    @. ∇f[colidx] = ∇(f[colidx])
    @. df[colidx] = div(∇f[colidx])
end

QuasiMonotoneLimiter

This limiter is inspired by the one presented in Guba et al Oksana Guba, Mark Taylor, Amik St-Cyr (2014). In the reference paper, it is denoted by OP1, and is outlined in eqs. (37)-(40). Quasimonotone here is meant to be monotone with respect to the spectral element nodal values. This limiter involves solving a constrained optimization problem (a weighted least square problem up to a fixed tolerance) that is completely local to each element.

As in HOMME, the implementation idea here is the following: we need to find a grid field which is closest to the initial field (in terms of weighted sum), but satisfies the min/max constraints. So, first we find values that do not satisfy constraints and bring these values to a closest constraint. This way we introduce some change in the tracer mass, which we then redistribute so that the l2 error is smallest. This redistribution might violate constraints; thus, we do a few iterations (until abs(Δtracer_mass) <= rtol * tracer_mass).

• ρq: tracer density Field, where q denotes tracer concentration per unit mass. This can be a scalar field, or a struct-valued field.
• ρ: fluid density Field (scalar).

Constructor

limiter = QuasiMonotoneLimiter(ρq::Field; rtol = eps(eltype(parent(ρq))))

Creates a limiter instance for the field ρq with relative tolerance rtol.

Usage

Call compute_bounds! on the input fields:

compute_bounds!(limiter, ρq, ρ)

Then call apply_limiter! on the output fields:

apply_limiter!(ρq, ρ, limiter)

compute_bounds!(limiter::QuasiMonotoneLimiter, ρq::Field, ρ::Field)

Compute the desired bounds for the tracer concentration per unit mass q, based on the tracer density, ρq, and density, ρ, fields.

This is computed by

1. compute_element_bounds!
2. starts the ghost exchange (if distributed)
3. compute_neighbor_bounds_local!
4. completes the ghost exchange (if distributed)
5. compute_neighbor_bounds_ghost! (if distributed)

apply_limiter!(ρq, ρ, limiter::QuasiMonotoneLimiter)

Apply the limiter on the tracer density ρq, using the computed desired bounds on the concentration q and density ρ as an optimal weight. This iterates over each element, calling apply_limit_slab!. If the limiter fails to converge for any element, a warning is issued.

compute_element_bounds!(limiter::QuasiMonotoneLimiter, ρq, ρ)

Given two fields ρq and ρ, computes the min and max of q in each element, storing it in limiter.q_bounds.

Part of compute_bounds!.

compute_neighbor_bounds_local!(limiter::QuasiMonotoneLimiter, topology)

Update the field limiter.q_bounds_nbr based on limiter.q_bounds in the local neighbors.

Part of compute_bounds!.

compute_neighbor_bounds_ghost!(limiter::QuasiMonotoneLimiter, topology)

Update the field limiter.q_bounds_nbr based on limiter.q_bounds in the ghost neighbors. This should be called after the ghost exchange has completed.

Part of compute_bounds!.

apply_limit_slab!(slab_ρq, slab_ρ, slab_WJ, slab_q_bounds, rtol)

Apply the computed bounds of the tracer concentration (slab_q_bounds) in the limiter to slab_ρq, given the total mass slab_ρ, metric terms slab_WJ, and relative tolerance rtol. Return whether the tolerance condition could be satisfied.

HDF5Writer(filename::AbstractString[, context::ClimaComms.AbstractCommsContext])

An AbstractWriter for writing to HDF5-formatted files using the ClimaCore storage conventions. An internal cache is used to avoid writing duplicate domains, meshes, topologies and spaces to the file. Use HDF5Reader to load the data from the file.

The optional context can be used for writing distributed fields: in this case, the MPICommsContext used passed as an argument: this must match the context used for distributing the Field.

Interface

write!

Usage

writer = InputOutput.HDF5Writer(filename)
InputOutput.write!(writer, Y, "Y")
close(writer)

write!(writer::AbstractWriter, obj[, preferredname])

Write the object obj using writer. An optional preferredname can be provided, otherwise defaultname will be used to generate a name. The name of the object will be returned.

A cache of domains, meshes, topologies and spaces is kept: if one of these objects has already been written, then the file will not be modified: instead the name under which the object was first written will be returned. Note that Fields and FieldVectors are not cached, and so can be written multiple times.

write!(filename, fvpair)

Write 'FieldVector' data, specified by a pair fieldvectorname => fieldvector, to HDF5 file 'filename'.

HDF5Reader(filename::AbstractString[, context::ClimaComms.AbstractCommsContext])

An AbstractReader for reading from HDF5 files created by HDF5Writer. The reader object contains an internal cache of domains, meshes, topologies and spaces that are read so that duplicate objects are not created.

The optional context can be used for reading distributed fields: in this case, the MPICommsContext used passed as an argument: resulting Fields will be distributed using this context. As with HDF5Writer, this requires a HDF5 library with MPI support.

Interface

• read_domain
• read_mesh
• read_topology
• read_space
• read_field

Usage

reader = InputOutput.HDF5Reader(filename)
Y = read_field(reader, "Y")
Y.c |> propertynames
Y.f |> propertynames
ρ_field = read_field(reader, "Y.c.ρ")
w_field = read_field(reader, "Y.f.w")
close(reader)

To explore the contents of the reader, use either

julia> reader |> propertynames

e.g, to explore the components of the space,

julia> reader.space_cache
Dict{Any, Any} with 3 entries:
  "center_extruded_finite_difference_space" => CenterExtrudedFiniteDifferenceSpace:…
  "horizontal_space"                        => SpectralElementSpace2D:…
  "face_extruded_finite_difference_space"   => FaceExtrudedFiniteDifferenceSpace:…

Once "unpacked" as shown above, ClimaCorePlots or ClimaCoreMakie can be used to visualise fields. ClimaCoreTempestRemap supports interpolation onto user-specified grids if necessary.

read_domain(reader::AbstractReader, name)

Reads a domain named name from reader. Domain objects are cached in the reader to avoid creating duplicate objects.

read_mesh(reader::AbstractReader, name)

Reads a mesh named name from reader, or from the reader cache if it has already been read.

read_topology(reader::AbstractReader, name)

Reads a topology named name from reader, or from the reader cache if it has already been read.

read_space(reader::AbstractReader, name)

Reads a space named name from reader, or from the reader cache if it has already been read.

read_field(reader, name)

Reads a Field or FieldVector named name from reader. Fields are not cached, so that reading the same field multiple times will create multiple distinct objects.