advection_mpas_velocity_first

Family: finite_volume
Grid family: unstructured
Kind: scheme
Accuracy: O(h) L-inf median on a quasi-uniform Voronoi mesh (see advection_mpas)
Applies to: div({'op': '*', 'args': ['$u', '$q']}), dim=cell
Rule file: discretizations/finite_volume/advection_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 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, index(n_edges_on_cell, i)]] ( index(edge_sign_on_cell, i, k)·index(dv_edge, index(edges_on_cell, i, k))/index(area_cell, i)·index($u, index(edges_on_cell, i, k))·(index($q, index(cells_on_edge, index(edges_on_cell, i, k), 1)) + index($q, index(cells_on_edge, index(edges_on_cell, i, k), 2)))/2 )

Source: discretizations/finite_volume/advection_mpas.json.