EarthSciDiscretizations
Catalog of declarative discretization rules and grid families used by ESD.
EarthSciDiscretizations catalog
This site is auto-generated from the rule files under
discretizations/ and the
grid family sources under
src/grids/.
Each grid family page describes the topology of a supported grid (connectivity, coordinates, metric tensor) and shows a visualization of a typical configuration. Each rule page renders the stencil pattern and coefficient diagram, plus a convergence plot for rules whose Layer-B fixtures are currently producing.
- Grid families →
- Discretization rules →
- Tutorials → — contributor walkthroughs, starting with adding a new rule.
- Rule × grid matrix → — what dispatches where, with observed convergence orders and visible holes in fixture coverage.
- Browse by family (
finite_difference,finite_volume, …) - Browse by grid family
The source of truth is the rule file (JSON) and the grid trait
implementation (Julia). Drop a new rule under discretizations/<family>/
and CI regenerates this catalog.
- Add a new discretization rule
End-to-end contributor walkthrough: declare a rule JSON, ship canonical + convergence fixtures, register with the walker, and render the catalog page. Worked example: centered_2nd_uniform on a Cartesian axis.
- Arakawa staggered grid
arakawa
grid
Staggered grid wrapping a base curvilinear grid — A / B / C / D variants — with per-stagger location keys.
- Cartesian
cartesian
grid
Logically rectangular Cartesian mesh with optional non-uniform spacing per axis (1D / 2D / 3D).
- centered_2nd_uniform
finite_difference
cartesian
scheme
O(dx²)
Two-point centered second-order finite difference for ∂u/∂x on a uniform Cartesian axis.
- centered_2nd_uniform_latlon
finite_difference
latlon
scheme
O(h²)
Centered second-order finite difference on a regular lat-lon grid, with the standard cos λ metric on the longitudinal stencil.
- centered_2nd_uniform_vertical
finite_difference
vertical
scheme
O(h²)
Two-point centered second-order finite difference for ∂u/∂k on a uniformly-spaced vertical axis.
- covariant_laplacian_cubed_sphere
finite_difference
cubed_sphere
scheme
O(h²)
9-point covariant Laplacian on the gnomonic cubed sphere — orthogonal + cross-metric corrections from the inverse metric tensor.
- Cubed-sphere
cubed_sphere
grid
Six gnomonic panels covering the sphere; in-panel curvilinear (ξ, η) coordinates with cross-panel ghost stitching.
- divergence_arakawa_c
finite_volume
arakawa
scheme
O(h²)
Two-point centered finite-volume divergence on a C-grid — F_x at face_x, F_y at face_y, divergence emitted at cell_center.
- Duo (geodesic triangular)
duo
grid
Geodesic triangular mesh on the sphere; recursively subdivided icosahedron.
- flux_limiter_minmod
limiter
cartesian
limiter
O(dx²) in smooth monotone regions; O(dx) at extrema
Minmod TVD flux limiter (Roe 1986) — the most diffusive of the symmetric second-order TVD limiters.
- flux_limiter_superbee
limiter
cartesian
limiter
O(dx²) in smooth monotone regions; compressive near discontinuities
Superbee TVD flux limiter (Roe 1986) — sits on the upper edge of the second-order TVD region.
- Lat-Lon
latlon
grid
Regular spherical lat-lon mesh with metric corrections for the spherical surface.
- MPAS
mpas
grid
Quasi-uniform Voronoi mesh on the sphere with icosahedral dual (12 pentagons + hexagons).
- nn_diffusion_mpas
finite_difference
mpas
scheme
O(h²) on quasi-uniform Voronoi
Nearest-neighbor diffusion on an MPAS Voronoi mesh, summed over edges_on_cell with dv_edge / (dc_edge · area_cell) coefficients.
- ppm_reconstruction
finite_volume
cartesian
scheme
O(dx³)
Piecewise-parabolic method (Colella & Woodward 1984) — 4th-order edge values + a parabola per cell, no limiter.
- upwind_1st
finite_difference
cartesian
scheme
O(dx)
First-order upwind (backward) finite difference for ∂u/∂x on a uniform Cartesian axis.
- Vertical
vertical
grid
1D vertical column with arbitrary level spacing — pressure / sigma / hybrid coordinates.
- weno5_advection
finite_volume
cartesian
scheme
O(dx⁵)
Jiang–Shu 5th-order WENO reconstruction — three sub-stencils, smoothness indicators, nonlinear weights.
- weno5_advection_2d
finite_volume
cartesian
scheme
O(h⁵) per axis
Dimension-by-dimension Jiang–Shu WENO5 reconstruction on a 2D structured uniform Cartesian grid.