gradient_mpas

Family: finite_volume
Grid family: unstructured
Kind: scheme
Accuracy: O(h^2) on a quasi-uniform Voronoi mesh
Applies to: grad($phi), dim=edge
Rule file: discretizations/finite_volume/gradient_mpas.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($phi), dim=edge for grid family unstructured.

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 = (index($phi, index(cells_on_edge, i, 2)) − index($phi, index(cells_on_edge, i, 1)))/index(dc_edge, i)

Source: discretizations/finite_volume/gradient_mpas.json.