4 Commits

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Author	SHA1	Message	Date
Omar SobhandClaude Fable 5	796cf173e6	rtx-cfd: second-order convection by deferred-correction TVD; MMS order 1.84, cavity closes on Ghia ... First-order upwind's O(h) numerical viscosity was the measured limit on the whole discretisation: MMS order ~0.9 at Re = 20 against 2.05 in the Stokes limit. This adds a ConvectionScheme parameter to SimPLE — Upwind (default, behaviour unchanged), TvdVanAlbada, TvdVanLeer — implemented by deferred correction: the upwind operator stays implicit, so a_p = sum(a_nb) and diagonal dominance survive unconditionally, and the limited high-order-minus-upwind flux difference enters the source explicitly at the current iterate. At a fixed point the two agree, so the converged answer is the TVD discretisation. Faces whose far-upwind node lies outside the domain fall back to pure upwind; wall faces pass no mass, so no correction enters. Measured by the manufactured solution (van Albada, 16 -> 32 -> 64): L2 velocity 1.325e-3 4.406e-4 1.232e-4 orders 1.59, 1.84 (upwind) 3.516e-2 1.954e-2 1.038e-2 orders 0.85, 0.91 The error is 27x to 84x below upwind's at equal resolution, the order climbs toward 2 (the shortfall is limiter clipping plus the boundary fallback, both of which shrink with h), the pressure error falls at the same rate, and continuity still holds to solver tolerance in every cell. On the Re = 100 lid-driven cavity at 65^2 the centreline minimum moves from -0.1932 (upwind) to -0.2036 against Ghia's -0.2109 — 59% of the remaining gap closed at equal resolution, converged in 790 iterations — and the vortex position moves from 0.5000 to 0.4844 toward Ghia's 0.4531. Both new cavity bounds exclude the upwind values, so falling back to first order fails them. 284 tests, 0 failing. Co-Authored-By: Claude Fable 5 <[email protected]>	2026-08-19 19:16:48 -07:00
Omar SobhandClaude Opus 5	1a740e0b2c	rtx-cfd: the wall treatment is second order, not first — correct the record ... The manufactured-solution test carried a hypothesis for why the observed order sits below 1: that `(u_P - u_wall)/(dy/2)` approximates the wall gradient at y = dy/4 rather than at the wall, making the near-wall rows first order. Measuring in the Stokes limit refutes it. With convection negligible every remaining operator is second order, so the observed rate there reports the wall treatment directly: rho = 1.000 (Re = 20.00) 3.52e-2 1.95e-2 1.04e-2 orders 0.85 0.91 rho = 0.001 (Re = 0.02) 2.21e-3 5.35e-4 1.28e-4 orders 2.05 2.06 2.05 and 2.06. The half-cell wall term is second-order accurate and the Stokes discretisation reaches its nominal rate. The shortfall at Re = 20 is first-order upwind and nothing else, which is what a first-order convection scheme is supposed to give. Comment corrected rather than left standing: a plausible explanation that happens to be wrong is worse than none, because it sends the next person to fix something that is not broken. Co-Authored-By: Claude Opus 5 (1M context) <[email protected]>	2026-08-19 17:42:14 -07:00
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
Omar SobhandClaude Opus 5	b5814a304f	rtx-cfd: manufactured solution finds the diffusion conductances were 1/h too ... large Applies MMS to the SIMPLE solver. It found a major discretisation error on the first run, which is the point of the method. The diffusion conductances read `mu / dx` and `mu / dy`. Finite volume requires `Gamma * A / delta` — the face area over the distance between the nodes it separates — so they should be `mu * dy / dx` and `mu * dx / dy`. The face area was missing entirely, making viscosity too large by a factor of `1/h`: sixty-five times on a 65x65 mesh. Every other term in the equation was already a force (`dp * dy` for pressure, `rho u dy` for the convective flux), so the mismatch was confined to diffusion. The consequence was that the solver ran at an effective Reynolds number far below the one requested. Before the fix the manufactured-solution error did not reduce under refinement at all — observed order about -0.05, because the spurious viscosity grows with the mesh. After it, the error falls monotonically. This also explains an apparent regression that is really a correction. The cavity vortex position moved from y = 0.484 to y = 0.391 against Ghia's 0.4531, which reads as worse agreement. It is not: a strongly over-diffusive cavity approaches Stokes flow, whose vortex sits near mid-height, so the old number was closer to the reference than the scheme deserved. Correcting the viscosity exposed the discretisation's own error. The test now states that disagreement plainly rather than asserting a band around the reference. What MMS reports now, and it is not yet good enough: n = 16 L2 velocity error = 2.586104e-1 order - n = 32 L2 velocity error = 1.797373e-1 order 0.52 n = 64 L2 velocity error = 1.277188e-1 order 0.49 First-order upwind should give 1. It gives about 0.5, and the u component is markedly further from exact than v on the same mesh. Both say there is at least one more defect in the discretisation or its boundary treatment, and the asymmetry between the two momentum equations is the clue. The test asserts only monotone error reduction — what is established — and records the shortfall, because asserting a rate the solver does not achieve would either redden the suite or invite someone to weaken it later. This changes the plan: raising the observed order to 1 is now a precondition for the second-order convection work rather than a consequence of it. There is no value in adding a higher-order scheme to a discretisation that has not demonstrated first order. Supporting changes: - `SimpleSolver::set_momentum_source` applies a volumetric body force, which is what lets a manufactured solution be imposed at all. - Divergence is now detected by growth, not only by NaN. The 8x8 case at Reynolds 10^6 reached 1e149 before anything caught it, because `is_finite` stays true right up until it does not. - `test_simple_solver_workflow` specified water properties on a unit domain, which is Reynolds 10^6 on ten cells: no steady laminar solution exists and the solver diverges on it, correctly. It passed only while the excess diffusion stabilised it. Now set to Reynolds 100. 561 tests across the three crates, 0 failing. Co-Authored-By: Claude Opus 5 (1M context) <[email protected]>	2026-08-19 12:25:52 -07:00