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Author	SHA1	Message	Date
Omar SobhandClaude Opus 5	698c844926	solvers: near-wall momentum, Newmark dynamics, QM6, and MMS across elements ... Four parallel work items plus two defects found while integrating them. 561 -> 592 tests, 0 failing, verified stable over repeated runs. ## rtx-cfd: solve the near-wall velocity lines Every u row sits at y = (j+0.5) dy and every v column at x = (i+0.5) dx -- strictly interior. The sweeps froze rows 0 and ny-1 and columns 0 and nx-1 and treated whatever was stored there as a boundary condition, which imposed wall values half a cell inside the domain. They are now unknowns, with the wall entering through the control volume's half-cell conductance (mu dx / (dy/2)), zero convective flux through the wall, and the wall's tangential velocity in the source. That in turn makes continuity enforceable on every cell, with a neighbour coefficient zero only for a genuine boundary face. Extending continuity had been tried before and broke convergence; it works now because the near-wall lines are no longer frozen. Order matters here. Manufactured solutions, which is how any of this is known: n L2 velocity order max |p - p_exact| 16 3.516212e-2 - 9.245576e-2 32 1.953751e-2 0.85 5.225739e-2 64 1.037523e-2 0.91 2.796415e-2 Velocity error is 7.4x smaller at n=16, and the observed order rises from 0.48 toward 1. The pressure error was 0.408 -> 0.624 -> 0.756, *growing* with refinement; it now falls. Divergence on the outer ring of cells goes from 1.0e1 to 2.5e-10. A separate defect found on the way: u_source_term was computed and never called, so the x-momentum equation carried no body force at all while the y-momentum one did. That is exactly the u-versus-v asymmetry the earlier diagnosis had flagged as an unexplained clue. Cavity at 65^2, against Ghia's u_min = -0.2109 at y = 0.4531: -0.1792 at 0.3906 before, -0.1932 at 0.5000 after, in 733 iterations rather than 971. The cavity test now sets FreeSlipWall on all four sides plus the lid through the new set_wall_velocity hook. That is not a weakened benchmark: on a staggered grid the only velocity component living *on* a boundary is the normal one, which is what FreeSlipWall prescribes, and the tangential no-slip arrives through the half-cell wall term with wall velocity zero on the three stationary walls. Prescribing whole u rows and v columns, as before, pins lines half a cell inside the domain and over-determines the cells beside them once every cell has a continuity equation. ## rtx-fea: DynamicAnalysis, previously a stub returning zeros Newmark-beta in acceleration form -- the displacement form divides by beta dt^2, singular at beta = 0 -- with Rayleigh damping, the effective matrix Cholesky-factorised once and reused. Initial acceleration is solved from M a0 = F0 - C v0 - K u0 rather than assumed zero, which would destroy the second-order rate. Verified two ways that cannot both be faked: against the closed-form single-degree-of-freedom response, undamped and damped, with the measured order of accuracy; and against the free-vibration period of the same bar whose modal frequencies are already validated. Time domain and frequency domain come from different code paths. ## rtx-fea: QM6 incompatible modes Wilson's Q6 with Taylor's correction, added alongside compute_stiffness_ matrix rather than replacing it -- the existing method is byte-identical, which matters because the manufactured-solution verification depends on it. Internal modes statically condensed; the incompatible strain block evaluated at the element centre, which is what makes the patch test pass on distorted elements. ## rtx-fea: manufactured solutions across the element library Quad4 order 2.00 Tri3 order 1.98 Quad8 order 3.00 Hex8 order 1.96 (new 3-D solution) Each element asserts its own theoretical rate. ## Two defects found while integrating Reverse Cuthill-McKee node ordering was nondeterministic. All three of its orderings -- seed selection, neighbour ordering, and the trailing sweep -- were decided by HashMap/HashSet iteration order, which std randomises per process. On a rectangular mesh every corner ties at minimum degree, so two calls to displacement_only on the same mesh in the same process returned different DOF indices for the same node, agreeing in only 5 of 20 measured runs. Ties now break by node id. This surfaced as a coin-flip test failure -- 12 in 25 runs -- and would have been dismissed as flaky rather than diagnosed had the integration pass not re-run it. Quadrature: triangle(3) weights summed to 0.25 against a reference area of 0.5, and tetrahedron(3) to 1/36 against a volume of 1/6. Both divided weights that were already tabulated for the reference measure by that measure again, so both rules integrated everything to a fraction of its value -- invisibly, since a scaled quadrature leaves the stiffness matrix symmetric, the mass matrix positive definite and the rigid-body modes exact. New test asserts every rule integrates 1 to its reference measure, across every family and order, plus Gauss-Legendre exactness to degree 2n-1. Co-Authored-By: Claude Opus 5 (1M context) <[email protected]>	2026-08-19 15:39:20 -07:00