Cubed-sphere

Grid family
cubed_sphere
Kind
grid
Source
src/grids/cubed_sphere.jl
Tags
#grid #block-structured #spherical #cubed-sphere #gnomonic

Description

A cubed-sphere mesh tiles the sphere with six logically rectangular panels — one per face of an inscribed cube — projected outward by a gnomonic projection. Each panel carries an in-panel (ξ, η) curvilinear coordinate system on [-1, 1]², discretized into Nc × Nc cells with uniform isotropic spacing h = π/(2 Nc).

The metric tensor is non-diagonal: g^{ξξ}, g^{ηη}, g^{ξη} are all non-zero and depend on position within the panel. Cross-panel adjacency is resolved by the panel-connectivity table (src/grids/panel_connectivity.jl); discretization rules reference only in-panel offsets and rely on the accessor to fill cross-panel ghosts and rotate vector components on panel boundaries.

Visualization

Cubed-sphere C6 mesh
Gnomonic cubed-sphere with `Nc = 6` (216 cells across 6 panels). Each panel is colored differently. The non-uniform pixel density visible at panel corners reflects the well-known gnomonic distortion.

Trait coverage

Subtype of AbstractCubedSphereGrid (which is itself a curvilinear grid). Implements the bulk-array contract panel-by-panel; metric_g, metric_ginv, metric_jacobian, and metric_dgij_dxk are required by the covariant_laplacian_cubed_sphere rule.

Canonical fixtures

  • discretizations/grids/cubed_sphere/c24.esm — Nc=24
  • discretizations/grids/cubed_sphere/c48.esm — Nc=48
  • discretizations/grids/cubed_sphere/c96.esm — Nc=96

See also