Finite_difference
- centered_2nd_deriv_nonuniform_vertical
finite_difference
vertical
scheme
O(dz_k^2)
Auto-generated catalog entry for the centered_2nd_deriv_nonuniform_vertical rule (finite_difference, grid family vertical). The discrete operator is pretty-printed directly from the rule's replacement AST.
- centered_2nd_deriv_uniform
finite_difference
cartesian
scheme
O(dx^2)
Auto-generated catalog entry for the centered_2nd_deriv_uniform rule (finite_difference, grid family cartesian). The discrete operator is pretty-printed directly from the rule's replacement AST.
- centered_2nd_deriv_uniform_vertical
finite_difference
vertical
scheme
O(dz^2)
Auto-generated catalog entry for the centered_2nd_deriv_uniform_vertical rule (finite_difference, grid family vertical). The discrete operator is pretty-printed directly from the rule's replacement AST.
- centered_2nd_nonuniform_cartesian
finite_difference
cartesian
scheme
O(dx^2)
Auto-generated catalog entry for the centered_2nd_nonuniform_cartesian rule (finite_difference, grid family cartesian). The discrete operator is pretty-printed directly from the rule's replacement AST.
- centered_2nd_nonuniform_vertical
finite_difference
vertical
scheme
O(dz_k^2)
Auto-generated catalog entry for the centered_2nd_nonuniform_vertical rule (finite_difference, grid family vertical). The discrete operator is pretty-printed directly from the rule's replacement AST.
- centered_2nd_uniform
finite_difference
cartesian
scheme
O(dx²)
Two-point centered second-order finite difference for ∂u/∂x on a uniform Cartesian axis, expressed as a closed §4.2 arrayop lowering.
- 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.
- centered_4th_deriv_uniform
finite_difference
cartesian
scheme
O(dx^4)
Auto-generated catalog entry for the centered_4th_deriv_uniform rule (finite_difference, grid family cartesian). The discrete operator is pretty-printed directly from the rule's replacement AST.
- centered_4th_uniform
finite_difference
cartesian
scheme
O(dx^4)
Auto-generated catalog entry for the centered_4th_uniform rule (finite_difference, grid family cartesian). The discrete operator is pretty-printed directly from the rule's replacement AST.
- centered_4th_uniform_latlon
finite_difference
latlon
scheme
O(h^4)
Auto-generated catalog entry for the centered_4th_uniform_latlon rule (finite_difference, grid family latlon). The discrete operator is pretty-printed directly from the rule's replacement AST.
- centered_4th_uniform_vertical
finite_difference
vertical
scheme
O(h^4)
Auto-generated catalog entry for the centered_4th_uniform_vertical rule (finite_difference, grid family vertical). The discrete operator is pretty-printed directly from the rule's replacement AST.
- centered_6th_deriv_uniform
finite_difference
cartesian
scheme
O(dx^6)
Auto-generated catalog entry for the centered_6th_deriv_uniform rule (finite_difference, grid family cartesian). The discrete operator is pretty-printed directly from the rule's replacement AST.
- centered_6th_uniform
finite_difference
cartesian
scheme
O(dx^6)
Auto-generated catalog entry for the centered_6th_uniform rule (finite_difference, grid family cartesian). The discrete operator is pretty-printed directly from the rule's replacement AST.
- centered_6th_uniform_latlon
finite_difference
latlon
scheme
O(h^6)
Auto-generated catalog entry for the centered_6th_uniform_latlon rule (finite_difference, grid family latlon). The discrete operator is pretty-printed directly from the rule's replacement AST.
- centered_6th_uniform_vertical
finite_difference
vertical
scheme
O(h^6)
Auto-generated catalog entry for the centered_6th_uniform_vertical rule (finite_difference, grid family vertical). The discrete operator is pretty-printed directly from the rule's replacement AST.
- centered_8th_deriv_uniform
finite_difference
cartesian
scheme
O(dx^8)
Auto-generated catalog entry for the centered_8th_deriv_uniform rule (finite_difference, grid family cartesian). The discrete operator is pretty-printed directly from the rule's replacement AST.
- centered_8th_uniform
finite_difference
cartesian
scheme
O(dx^8)
Auto-generated catalog entry for the centered_8th_uniform rule (finite_difference, grid family cartesian). The discrete operator is pretty-printed directly from the rule's replacement AST.
- centered_8th_uniform_latlon
finite_difference
latlon
scheme
O(h^8)
Auto-generated catalog entry for the centered_8th_uniform_latlon rule (finite_difference, grid family latlon). The discrete operator is pretty-printed directly from the rule's replacement AST.
- centered_8th_uniform_vertical
finite_difference
vertical
scheme
O(h^8)
Auto-generated catalog entry for the centered_8th_uniform_vertical rule (finite_difference, grid family vertical). The discrete operator is pretty-printed directly from the rule's replacement AST.
- godunov_norm_1st_uniform_cartesian_2d
finite_difference
cartesian
scheme
O(dx)
Auto-generated catalog entry for the godunov_norm_1st_uniform_cartesian_2d rule (finite_difference, grid family cartesian). The discrete operator is pretty-printed directly from the rule's replacement AST.
- laplacian_2nd_uniform_cartesian
finite_difference
cartesian
scheme
O(dx^2)
Auto-generated catalog entry for the laplacian_2nd_uniform_cartesian rule (finite_difference, grid family cartesian). The discrete operator is pretty-printed directly from the rule's replacement AST.
- mixed_deriv_2nd_nonuniform
finite_difference
cartesian
scheme
O(dx_i*dy_j)
Auto-generated catalog entry for the mixed_deriv_2nd_nonuniform rule (finite_difference, grid family cartesian). The discrete operator is pretty-printed directly from the rule's replacement AST.
- mixed_deriv_2nd_uniform
finite_difference
cartesian
scheme
O(dx^2)
Auto-generated catalog entry for the mixed_deriv_2nd_uniform rule (finite_difference, grid family cartesian). The discrete operator is pretty-printed directly from the rule's replacement AST.
- nn_diffusion_duo
finite_difference
unstructured
scheme
O(h^2) on a quasi-uniform triangular icosahedral mesh
Auto-generated catalog entry for the nn_diffusion_duo rule (finite_difference, grid family unstructured). The discrete operator is pretty-printed directly from the rule's replacement AST.
- 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.
- nonlinear_laplacian_nonuniform
finite_difference
cartesian
scheme
O(dx_i^2)
Auto-generated catalog entry for the nonlinear_laplacian_nonuniform rule (finite_difference, grid family cartesian). The discrete operator is pretty-printed directly from the rule's replacement AST.
- nonlinear_laplacian_uniform
finite_difference
cartesian
scheme
O(dx^2)
Auto-generated catalog entry for the nonlinear_laplacian_uniform rule (finite_difference, grid family cartesian). The discrete operator is pretty-printed directly from the rule's replacement AST.
- periodic_bc
finite_difference
cartesian
boundary_condition
exact (index rewrite)
Periodic boundary handling as a downstream index-rewrite rule: wraps an out-of-range stencil access index(u, i − offset) to index(u, mod(i − offset + Nx, Nx)) on axes declared periodic by the domain.
- spherical_laplacian_nonuniform
finite_difference
cartesian
scheme
O(dr_i^2)
Auto-generated catalog entry for the spherical_laplacian_nonuniform rule (finite_difference, grid family cartesian). The discrete operator is pretty-printed directly from the rule's replacement AST.
- spherical_laplacian_uniform
finite_difference
cartesian
scheme
O(dr^2)
Auto-generated catalog entry for the spherical_laplacian_uniform rule (finite_difference, grid family cartesian). The discrete operator is pretty-printed directly from the rule's replacement AST.
- staggered_1st_uniform_cc_to_face
finite_difference
arakawa
scheme
O(h^2) (two-point centered difference at the half-offset face)
Auto-generated catalog entry for the staggered_1st_uniform_cc_to_face rule (finite_difference, grid family arakawa). The discrete operator is pretty-printed directly from the rule's replacement AST.
- staggered_1st_uniform_face_to_cc
finite_difference
arakawa
scheme
O(h^2) (two-point centered difference at the half-offset cell center)
Auto-generated catalog entry for the staggered_1st_uniform_face_to_cc rule (finite_difference, grid family arakawa). The discrete operator is pretty-printed directly from the rule's replacement AST.
- upwind_1st
finite_difference
cartesian
scheme
O(dx)
First-order upwind (backward) finite difference for ∂u/∂x on a uniform Cartesian axis.
- upwind_1st_latlon
finite_difference
latlon
scheme
O(h)
Auto-generated catalog entry for the upwind_1st_latlon rule (finite_difference, grid family latlon). The discrete operator is pretty-printed directly from the rule's replacement AST.
- upwind_1st_nonuniform
finite_difference
cartesian
scheme
O(dx_i)
Auto-generated catalog entry for the upwind_1st_nonuniform rule (finite_difference, grid family cartesian). The discrete operator is pretty-printed directly from the rule's replacement AST.
- upwind_1st_vertical
finite_difference
vertical
scheme
O(h)
Auto-generated catalog entry for the upwind_1st_vertical rule (finite_difference, grid family vertical). The discrete operator is pretty-printed directly from the rule's replacement AST.
- weno5_grad
finite_difference
cartesian
scheme
O(dx^5)
Auto-generated catalog entry for the weno5_grad rule (finite_difference, grid family cartesian). The discrete operator is pretty-printed directly from the rule's replacement AST.