{"id": "extruded_3d", "title": "Three-dimensional consistency", "description": "The inviscid NACA 0012 case is solved in 2-D and on a spanwise-periodic extrusion of the same section into curved hexahedra. A correct 3-D implementation \u2014 metrics in conservative-curl form, neighbour coupling across hexahedral faces, the Newton\u2013Krylov solver with p-multigrid, force integration and the discrete adjoint \u2014 must reproduce the 2-D outputs and derivatives per unit span, with no spanwise flow. A structured extrusion only contains faces whose two sides use the same local axes, so this study cannot detect an error in the face-orientation tables; those are exercised by the imported-mesh study and by unit tests on randomly re-oriented meshes.", "passed": true, "checks": [{"name": "both solves converged", "value": true, "expected": "true", "passed": true}, {"name": "cl: |3-D \u2212 2-D| / |2-D|", "value": 3.454914907747166e-13, "expected": "< 1e-08", "passed": true}, {"name": "cd: |3-D \u2212 2-D| / |2-D|", "value": 1.6398675656918697e-13, "expected": "< 1e-08", "passed": true}, {"name": "cm: |3-D \u2212 2-D| / |2-D|", "value": 4.176168459980821e-12, "expected": "< 1e-08", "passed": true}, {"name": "dcl_dalpha: |3-D \u2212 2-D| / |2-D|", "value": 1.018619774369077e-11, "expected": "< 1e-06", "passed": true}, {"name": "dcl_dmach: |3-D \u2212 2-D| / |2-D|", "value": 4.415413194623616e-09, "expected": "< 1e-06", "passed": true}, {"name": "spanwise momentum (max |\u03c1w|)", "value": 7.345847477253279e-14, "expected": "< 1e-10", "passed": true}, {"name": "spanwise variation of the state", "value": 6.048807098174497e-14, "expected": "< 1e-10", "passed": true}], "charts": [], "tables": [{"id": "comparison", "title": "2-D solution versus 3-D extrusion", "columns": ["quantity", "2-D", "3-D (per unit span)", "relative difference"], "rows": [["cl", 0.2684845681710782, 0.2684845681709854, 3.454914907747166e-13], ["cd", 0.0055854144229587, 0.005585414422959616, 1.6398675656918697e-13], ["cm", -0.001794988370895173, -0.0017949883708876769, 4.176168459980821e-12], ["dcl_dalpha", 7.518154448674204, 7.518154448750785, 1.018619774369077e-11], ["dcl_dmach", 0.18670898148988202, 0.18670898231427932, 4.415413194623616e-09]]}, {"id": "sizes", "title": "Problem sizes", "columns": ["case", "dim", "elements", "DOF", "Newton steps"], "rows": [["2-D", 2, 64, 2304, 15], ["3-D extruded", 3, 192, 25920, 24]]}], "provenance": {"version": "0.4.0", "commit": "39979fcf902ad6116eb550b881b4278d4599c8e2", "dirty": false, "describe": "39979fcf90", "device": {"platform": "gpu", "device": "cuda:0", "device_kind": "NVIDIA GeForce RTX 3060 Ti", "jax": "0.11.2", "x64": true}, "timestamp": "2026-11-12T11:03:54-0500"}, "wall_time": 300.8, "level": "quick"}