staggered_1st_uniform_face_to_cc

Family: finite_difference
Grid family: arakawa
Kind: scheme
Accuracy: O(h^2) (two-point centered difference at the half-offset cell center)
Applies to: grad($u)
Rule file: discretizations/finite_difference/staggered_1st_uniform.json

This page is auto-generated from the rule's JSON by tools/render_doc_plots.py. The discrete operator below is pretty-printed directly from the rule's replacement AST using EarthSciSerialization (earthsci_toolkit). Rules with a hand-authored page carry richer prose plus stencil and convergence diagrams; see the curated entries linked from the rule index.

Pattern

Matches the §4.2 operator grad on the pattern grad($u) for grid family arakawa.

Discrete operator

Pretty-printed from the rule’s replacement AST ($-prefixed names are pattern variables bound by applies_to; grid metrics such as dx/dz are resolved by the grid):

out[$x] = −1/h·index($u, $x) + 1/h·index($u, $x + 1)

Source: discretizations/finite_difference/staggered_1st_uniform.json.