{"id": "free_stream", "title": "Free-stream preservation on curved meshes", "description": "A uniform flow must remain an exact steady state on arbitrarily curved elements. This requires discrete metric identities: cross-product metrics in 2-D and the conservative-curl form in 3-D. Meshes are smoothly warped periodic boxes (6 % amplitude); the table reports the largest weak residual of the uniform state and the closure of each element's discrete surface (geometric conservation law).", "passed": true, "checks": [{"name": "max |Rw| of uniform flow and GCL defect", "value": 2.909118989456355e-15, "expected": "< 1e-11", "passed": true}], "charts": [], "tables": [{"id": "residuals", "title": "Uniform-flow residual on warped meshes", "columns": ["dim", "elements", "p", "geometry degree", "viscous", "min J / max J", "max |Rw|", "surface closure"], "rows": [["2-D", "6x5", 3, 4, false, 0.45104694416115027, 1.3492293702041834e-15, 3.0531133177191805e-16], ["2-D", "6x5", 3, 4, true, 0.45104694416115027, 1.3367892724119473e-15, 3.0531133177191805e-16], ["2-D", "4x4", 5, 4, false, 0.4535560221510909, 2.856048730848215e-15, 4.996003610813204e-16], ["2-D", "4x4", 5, 4, true, 0.4535560221510909, 2.909118989456355e-15, 4.996003610813204e-16], ["3-D", "3x3x3", 2, 2, false, 0.276158830865354, 2.631639762074445e-16, 3.469446951953614e-17], ["3-D", "3x3x3", 2, 2, true, 0.276158830865354, 2.631639762074445e-16, 3.469446951953614e-17], ["3-D", "3x3x3", 3, 3, false, 0.4170885457998705, 3.252606517456514e-16, 6.982261990806649e-17], ["3-D", "3x3x3", 3, 3, true, 0.4170885457998705, 3.2823045731398904e-16, 6.982261990806649e-17]]}], "provenance": {"version": "0.4.0", "commit": "39979fcf902ad6116eb550b881b4278d4599c8e2", "dirty": false, "describe": "39979fcf90", "device": {"platform": "cpu", "device": "cpu:0", "device_kind": "cpu", "jax": "0.11.2", "x64": true}, "timestamp": "2026-11-12T10:22:33-0500"}, "wall_time": 18.67, "level": "quick"}