Cubedsphere

Cubed-sphere refers to a family of spherical grid constructions used in numerical simulation and geometric discretization. The basic idea maps the six faces of a circumscribed cube onto the surface of the sphere, producing a mesh of six quadrilateral panels that cover the globe without the polar singularities inherent to latitude–longitude grids. Variants differ by the projection used (e.g., gnomonic, equiangular, or equidistant), which affects cell shape, spacing, and metric terms.

The cubed-sphere was developed to provide a more uniform distribution of grid cell areas and to facilitate high-performance computing. Each panel can be treated as a logically rectangular mesh, allowing reuse of solvers and data structures from Cartesian codes and straightforward domain decomposition for parallel computation. The gnomonic variant is valued for making great circles straight lines on panel coordinates, which simplifies advection and wave propagation schemes.

Practical advantages include reduced grid clustering near the poles, improved numerical stability for global models, and compatibility with a range of discretization methods (finite-volume, finite-element, spectral-element, and others). Challenges include handling discontinuities and metric mismatches at panel boundaries, designing conservative and accurate inter-panel communication, and controlling numerical anisotropy introduced by panel geometry.

Cubed-sphere grids are widely used in atmospheric, oceanic, and planetary modeling where global coverage, scalability, and relatively uniform resolution are important. They continue to evolve with adaptive refinement, hybrid discretizations, and improved inter-panel numerical treatments.