godunov_norm_1st_uniform_cartesian_2d

Family: finite_difference
Grid family: cartesian
Kind: scheme
Accuracy: O(dx)
Applies to: sqrt({'op': '+', 'args': [{'op': '^', 'args': [{'op': 'grad', 'args': ['$u'], 'dim': '$x'}, 2.0]}, {'op': '^', 'args': [{'op': 'grad', 'args': ['$u'], 'dim': '$y'}, 2.0]}]})
Rule file: discretizations/finite_difference/godunov_norm_1st_uniform_cartesian_2d.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 sqrt on the pattern sqrt({'op': '+', 'args': [{'op': '^', 'args': [{'op': 'grad', 'args': ['$u'], 'dim': '$x'}, 2.0]}, {'op': '^', 'args': [{'op': 'grad', 'args': ['$u'], 'dim': '$y'}, 2.0]}]}) for grid family cartesian.

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):

√max(((index($u, $x, $y) − index($u, $x + −1, $y))/dx), 0)² + min(((index($u, $x + 1, $y) − index($u, $x, $y))/dx), 0)² + max(((index($u, $x, $y) − index($u, $x, $y + −1))/dx), 0)² + min(((index($u, $x, $y + 1) − index($u, $x, $y))/dx), 0)²

Source: discretizations/finite_difference/godunov_norm_1st_uniform_cartesian_2d.json.