nn_diffusion_duo

Family: finite_difference
Grid family: unstructured
Kind: scheme
Accuracy: O(h^2) on a quasi-uniform triangular icosahedral mesh
Applies to: laplacian($u), dim=cell
Rule file: discretizations/finite_difference/nn_diffusion_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 laplacian on the pattern laplacian($u), 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 ∈ [0, 2]] ( index(dc_edge, index(edges_on_face, i, k))/(index(dv_edge, index(edges_on_face, i, k))·index(area, i))·(index($u, index(cell_neighbors, i, k)) − index($u, i)) )

Source: discretizations/finite_difference/nn_diffusion_duo.json.