advection_duo

Family: finite_volume
Grid family: unstructured
Kind: scheme
Accuracy: O(h) on a quasi-uniform icosahedral triangular mesh
Applies to: div({'op': '*', 'args': ['$U', '$q']}), dim=cell
Rule file: discretizations/finite_volume/advection_duo.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 div on the pattern div({'op': '*', 'args': ['$U', '$q']}), dim=cell 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 = Σ[k ∈ [1, 3]] ( index(edge_sign_on_face, i, k)·index(dc_edge, index(edges_on_face, i, k))/index(tri_area, i)·index($U, index(edges_on_face, i, k))·0.5·(index($q, i) + index($q, index(cell_neighbors, i, k))) )

Source: discretizations/finite_volume/advection_duo.json.