covariant_fv_laplacian_latlon

Family: finite_volume
Grid family: latlon
Kind: scheme
Accuracy: O(h^2)
Applies to: laplacian($u)
Rule file: discretizations/finite_volume/covariant_fv_laplacian_latlon.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 laplacian on the pattern laplacian($u) for grid family latlon.

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):

index(g_xx, lat, lon)/(dlon·dlon)·(index($u, lat, lon + 1) + −2·index($u, lat, lon)) + index(g_yy, lat, lon)/(dlat·dlat)·(index($u, lat + 1, lon) + −2·index($u, lat, lon))

Source: discretizations/finite_volume/covariant_fv_laplacian_latlon.json.