centered_2nd_nonuniform_cartesian

Family: finite_difference
Grid family: cartesian
Kind: scheme
Accuracy: O(dx^2)
Applies to: d2($u), dim=$x
Rule file: discretizations/finite_difference/centered_2nd_nonuniform_cartesian.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 d2 on the pattern d2($u), dim=$x for grid family cartesian.

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] = 2/(index(dx, $x)·(index(dx, $x) + index(dx, $x + 1)))·index($u, $x + −1) + −2/(index(dx, $x)·index(dx, $x + 1))·index($u, $x)

Source: discretizations/finite_difference/centered_2nd_nonuniform_cartesian.json.