Finite_difference
- 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.
- 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.
- upwind_1st
finite_difference
cartesian
scheme
O(dx)
First-order upwind (backward) finite difference for ∂u/∂x on a uniform Cartesian axis.