//! Turek–Hron FSI2: the self-excited flapping flag — rung C2 of the ladder
//! (omni-cortex `docs/turek_hron_geometry_decision.md`).
//!
//! Re = 100 channel flow (`U = 1`) past the rigid cylinder with the elastic
//! flag at density ratio `rho_s / rho_f = 10`: the flow destabilises the
//! flag into a large-amplitude limit cycle. Reference (FEATFLOW level 4,
//! dt = 0.0005): `ux(A) = −14.85 ± 12.70 mm [3.86 Hz]`,
//! `uy(A) = 1.30 ± 81.6 mm [1.93 Hz]`, drag `215.06 ± 77.65`,
//! lift `0.61 ± 237.8`.
//!
//! # The march
//!
//! Unlike FSI1's steady fixed point, FSI2 marches in time: per TIME STEP
//! the fluid step and the flag's nonlinear-Newmark step are subiterated
//! until the end-of-step interface displacement converges — the coupled
//! piston benchmark's structure, with the real 2-D solvers. The fluid
//! step is re-runnable inside a subiteration through
//! [`EmbeddedPisoSolver::snapshot`]/`restore` plus a [`FlowField`] clone;
//! the flag step is re-runnable because [`NonlinearDynamicStepper::step`]
//! commits nothing. The moving polygon carries the flag's actual interface
//! velocity — finite-differenced end-of-step positions over `dt`,
//! interpolated along the nearest edge (`polygon_interface_velocity`) —
//! replacing the zero-velocity closure FSI1's steady case allowed. The
//! fluid keeps TVD convection (shedding physics; limiter chatter is
//! harmless in time marching) and the multigrid projection.
//!
//! The geometry, load sampling (spike clamp + optional surface
//! smoothing), fluid configuration and the march itself live in
//! `fsi2_harness/` (shared with FSI3); the interface-noise-floor probe
//! `fsi2_interface_noise.rs` measures the same machinery's pass-to-pass
//! continuity.
//!
//! # Phases (the validation ladder inside FSI2)
//!
//! 1. **Rigid flag** to `t_release`: the ramped inflow over the fixed
//!    geometry must land near the CFD2 steady state this solver already
//!    measured (surface drag 121.4 / 123.3 at ny = 62 / 82 vs its CFD2
//!    runs' ~121 / 122.6) — the harness's fluid configuration is checked
//!    against a known number before anything couples.
//! 2. **Release**: the flag starts at rest under the sampled fluid load
//!    (consistent initial acceleration), and the coupled march runs to
//!    `t_end`.
//!
//! # What the 2026-08-21 study measured at the loose default (t = 30 s)
//!
//! **At the loosely-coupled default (8 fluid substeps per coupled step,
//! per-step Aitken, ~1 subiteration) the coupled system self-excites but
//! lands in a wake-forced cycle at 3.729 / 3.728 Hz with uy(A) ± 17.3 mm
//! at BOTH ny = 62 and ny = 82 — grid-converged, protocol-independent.
//! This is NOT the benchmark's cycle** (1.93 Hz, ± 81.6 mm). The
//! identification is clean: the flag's vacuum mode 2 is 1.9245 Hz (modal
//! analysis, 35x2 Quad8) — the reference cycle IS mode-2 resonance —
//! while 3.73 Hz matches no structural mode (mode 3 is 5.26 Hz); the
//! measured state is the heavy flag's off-resonance forced response at
//! the wake's own shedding frequency, and its ux mean (−0.8 mm) matches
//! the foreshortening scaling (amp/81.6)^2 x (−14.85).
//!
//! Why mode 2 does not win at the default coupling: the motion-load
//! staggered phase lag (~omega dt_c) starves the resonant channel. The
//! tenth session's attempt at tighter coupling (subcycle 2 at the SAME
//! 2e-4 tolerance) blew up — the accepted interface scatter feeds the
//! no-slip closure a wall-velocity noise of tol / dt_c, 30% of the mean
//! inflow there — and was read as an impassable interface noise floor.
//!
//! # What the eleventh session (2026-08-21) measured: the mode-2 cycle
//!
//! The noise probe (`fsi2_interface_noise.rs`) showed the floor was a
//! tolerance mis-budgeting: the real step map converges to ~1e-9 at
//! subcycle 2. With the `IqnIls` coupler and the tolerance budgeted
//! from that measurement (`RTX_FSI2_COUPLER=iqn RTX_FSI2_SUBCYCLE=2
//! RTX_FSI2_TOL=1.5e-5`), the march self-excites through resonant
//! growth (2.34 → 2.23 Hz, drifting toward mode 2) into **the
//! benchmark's mode-2 flapping cycle: uy = 3.7 ± 57.6 mm at 2.227 Hz
//! at ny = 62 (t_end = 16), 1.99 ± 57.1 mm at 2.236 Hz at ny = 82
//! (t_end = 20) — grid-converged to 0.9% / 0.4% — and stable over a
//! 24 s record (3.68 ± 55.9 mm at 2.224 Hz over [27, 30] s)**. The
//! ladder localizes mode selection in dt_c: subcycle 4 opens the
//! resonant channel for ~4 s (2.5 Hz) before the wake recaptures it
//! (3.67 Hz, ±15.5 mm); subcycle 1 reaches 1.955 Hz / ±73 mm mid-growth
//! (89% of the reference amplitude at essentially its frequency), so
//! the remaining gap to the reference is coupling lag, not grid. Cost:
//! 1.4 (subcycle 2) to 2.8 (subcycle 1) subiterations per step.
//!
//! Coupler failure modes met on the way, each measured and handled
//! (`rtx_fsi::coupling` docs): stale secant history overshooting during
//! rapid amplitude growth (history reset + one retry from the
//! predictor), an ill-conditioned secant step sweeping a candidate
//! interface to the domain wall (trust-region cap at 50x the
//! residual), and a rare violent step near peak motion stalling an
//! order below its own increment (accepted, counted, bounded).
//!
//! Robustness findings from the tenth session, both measured: rare wild
//! tractions from near-degenerate reconstructions (19 samples in 2.4
//! million) killed a t = 25.8 s march through the flag's Newton until
//! the spike CLAMP (20x the sample median, direction kept — clamping,
//! not dropping: a hard drop makes the coupling pass discontinuous and
//! the subiteration bounces at the step scale) and a 60-iteration Newton
//! budget; with both, the same march runs to t = 30 clean.
//!
//! Machinery invariants asserted every run: load-transfer conservation
//! (partition of unity) at 1e-10 (measured 8e-12 over 9,263 steps),
//! coupled convergence bookkeeping, finite fields. The committed default
//! (t_end = 7) pins the deterministic release response; study horizons
//! pin the measured attractor of each configuration (the wake state at
//! t_end >= 25 under the default; the mode-2 cycle at t_end >= 16 under
//! IQN / subcycle 2) so any material change is loud. Full trajectories:
//! the session scratchpad study logs.
//!
//! Environment knobs: `RTX_FSI2_NY` (fluid resolution, default 62),
//! `RTX_FSI2_T_RELEASE` (default 6 s), `RTX_FSI2_T_END` (default 7 s —
//! the committed onset segment; studies run 16–30), `RTX_FSI2_SUBCYCLE`
//! (fluid substeps per coupled step, default 8), `RTX_FSI2_TOL` /
//! `RTX_FSI2_RTOL` (interface tolerance floor and its
//! relative-to-increment part), `RTX_FSI2_MAXSUB` (subiteration budget,
//! default 12), `RTX_FSI2_FLAG_NX` (flag mesh, default 35),
//! `RTX_FSI2_SMOOTH` (traction smoothing radius in multiples of the cell
//! size, default 0 = off), `RTX_FSI2_COUPLER` (`aitken` default, or `iqn`
//! for IQN-ILS with `RTX_FSI2_REUSE` steps of secant history, default 2),
//! `RTX_FSI2_CSV` (trajectory dump path).

mod fsi2_harness;

use fsi2_harness::FSI2;
use fsi2_harness::march::{MarchConfig, run_march};

// FEATFLOW level-4, dt 0.0005 reference values.
const REF_UY_MEAN: f64 = 1.30e-3;
const REF_UY_AMP: f64 = 81.6e-3;
const REF_UY_FREQ: f64 = 1.93;
const REF_UX_MEAN: f64 = -14.85e-3;
const REF_UX_AMP: f64 = 12.70e-3;
const REF_DRAG_MEAN: f64 = 215.06;
const REF_LIFT_AMP: f64 = 237.8;

#[test]
fn fsi2_flapping_flag() {
    // The tenth-session defaults. The tolerance floor is the measured
    // interface noise floor of THIS configuration (loose coupling at
    // subcycle 8): the floor rides with the loads and with dt_c, and a
    // tighter coupling budgets its own (see the module docs and the
    // noise probe).
    let config = MarchConfig::from_env(
        "FSI2",
        MarchConfig {
            ny: 62,
            flag_nx: 35,
            t_release: 6.0,
            t_end: 7.0,
            subcycle: 8,
            tol_floor: 2e-4,
            rtol: 1e-2,
            stall_accept: 5.0,
            mask_hysteresis: 0.0,
            max_subiterations: 12,
            coupler: "aitken".into(),
            reuse: 2,
            smooth_in_h: 0.0,
            csv_path: None,
            snap_path: None,
            snap_every: 10,
            initial_relaxation: 0.5,
            trace_steps: 0,
            trace_from: usize::MAX,
            coupling_rescue: false,
            poisson_f32: false,
            coarse_episode: 0,
            inc_trace: None,
            increment_factor: 0.0,
            speed_fraction: 0.0,
            c1_interface: false,
            predictor: "structure".into(),
            quiescent_release: false,
            ffld_dir: None,
        },
    );
    let MarchConfig {
        ny,
        flag_nx,
        t_release,
        t_end,
        subcycle,
        smooth_in_h,
        ..
    } = config;
    let case = fsi2_harness::case_from_env("FSI2", FSI2);
    let result = run_march(case, &config);
    let w = result.window(3.0);

    println!(
        "  loads over the window: drag {:.2} ± {:.2} (ref {REF_DRAG_MEAN} ± 77.65), \
         lift {:.2} ± {:.2} (ref 0.61 ± {REF_LIFT_AMP})",
        w.drag_mid, w.drag_amp, w.lift_mid, w.lift_amp
    );
    println!(
        "  FSI2 (fluid ny = {ny}, flag {flag_nx}x2 Quad8, dt = {:.2e}, {}): coupled {} \
         steps in {:.0} s wall total; {:.1} subit/step (max {}); {} stalled steps, {} \
         history-reset retries (worst residual {:.2e}); worst conservation {:.2e}; \
         skipped samples {} (of which {} spike-clamped); Newton rescues {:?}; coupling \
         rescues {} (+{} failed ladders)\n  \
         measured over [{:.1}, {t_end:.1}] s: \
         uy(A) = {:.4} ± {:.4} mm (ref {:.2} ± {:.1}), ux(A) = {:.4} ± {:.4} mm (ref {:.2} ± \
         {:.2}), f = {} Hz (ref {REF_UY_FREQ}); onset amp {:.3e} -> {:.3e} m",
        result.dt,
        config.coupler,
        result.coupled_steps,
        result.elapsed,
        result.mean_subiterations,
        result.max_subiterations,
        result.stalled_steps,
        result.retried_steps,
        result.worst_stall,
        result.worst_conservation,
        result.skipped,
        result.spiked,
        result.newton_rescues,
        result.coupling_rescues,
        result.coupling_rescue_failures,
        w.t_start,
        w.uy_mid * 1e3,
        w.uy_amp * 1e3,
        REF_UY_MEAN * 1e3,
        REF_UY_AMP * 1e3,
        w.ux_mid * 1e3,
        w.ux_amp * 1e3,
        REF_UX_MEAN * 1e3,
        REF_UX_AMP * 1e3,
        w.frequency.map_or("n/a".to_string(), |f| format!("{f:.3}")),
        w.amp_early,
        w.amp_late,
    );

    // Machinery invariants — asserted at every resolution.
    assert!(
        result.worst_conservation < 1e-10,
        "load transfer lost force: {:.3e}",
        result.worst_conservation
    );
    assert!(result.final_state_finite, "flag state went non-finite");
    assert!(
        result.mean_subiterations < 10.0,
        "coupling is grinding: {:.1} subiterations/step",
        result.mean_subiterations
    );
    // Stalls at the noise floor are tolerated but must stay the exception;
    // a coupling stalling on most steps is not converging, it is drifting.
    assert!(
        result.stalled_steps * 5 < result.coupled_steps.max(1),
        "coupling stalled on {} of {} steps (worst residual {:.2e})",
        result.stalled_steps,
        result.coupled_steps,
        result.worst_stall
    );

    // Physics bands, by horizon and configuration. The march is
    // deterministic, so short horizons carry tight regression bands;
    // long horizons pin MEASURED attractors — which attractor depends on
    // the coupling (see the module docs): the loosely-coupled default
    // (Aitken, subcycle 8) locks the wake-forced 3.73 Hz / ±17.3 mm
    // state at BOTH grids; the IQN / subcycle-2 configuration locks the
    // benchmark's mode-2 flapping cycle, grid-converged at ±57 mm /
    // 2.23 Hz. If a change moves any of these numbers, that is a finding
    // either way and must be loud. Smoothing changes the load path and
    // is pinned nowhere (measured to change nothing that matters).
    // Every physics band below was measured at the BENCHMARK case; an
    // overridden u_mean (the TWIN-1 sweep) or e_s (the TWIN-2 sweep)
    // pins nothing here — those bands live in the campaigns' composition
    // harnesses. The machinery invariants above stay asserted at every
    // inflow and stiffness.
    let benchmark_case =
        case.u_mean.to_bits() == FSI2.u_mean.to_bits() && case.e_s.to_bits() == FSI2.e_s.to_bits();
    let default_coupling = benchmark_case && smooth_in_h == 0.0 && config.coupler == "aitken";
    let mode2_coupling =
        benchmark_case && smooth_in_h == 0.0 && config.coupler == "iqn" && subcycle == 2;
    let s1_coupling =
        benchmark_case && smooth_in_h == 0.0 && config.coupler == "iqn" && subcycle == 1;
    if default_coupling
        && ny == 62
        && flag_nx == 35
        && (t_end - 7.0).abs() < 1e-9
        && (t_release - 6.0).abs() < 1e-9
    {
        // The committed default: the release response over [6, 7] s,
        // measured 2026-08-21 as uy mid 3.773 mm, amp 3.792 mm. The band
        // is ±35% for cross-platform floating-point drift in a growing
        // transient, not an accuracy claim.
        assert!(
            (2.4e-3..5.2e-3).contains(&w.uy_mid),
            "uy release-response mid {:.4e} outside the measured band [2.4e-3, 5.2e-3]",
            w.uy_mid
        );
        assert!(
            (2.4e-3..5.2e-3).contains(&w.uy_amp),
            "uy release-response amp {:.4e} outside the measured band [2.4e-3, 5.2e-3]",
            w.uy_amp
        );
    } else if default_coupling && t_end >= 25.0 {
        // Study horizons: the measured attractor of the loosely-coupled
        // (subcycle 8) march — f = 3.729 / 3.728 Hz and uy amp 17.3 mm at
        // ny = 62 / 82 (2026-08-21).
        if let Some(f) = w.frequency {
            assert!(
                (f - 3.73).abs() / 3.73 < 0.10,
                "uy frequency {f:.3} left the measured 3.73 Hz attractor \
                 (benchmark reference {REF_UY_FREQ}) — a material change"
            );
        }
        assert!(
            (12e-3..24e-3).contains(&w.uy_amp),
            "uy amplitude {:.4e} left the measured ±17.3 mm attractor band [12e-3, 24e-3]",
            w.uy_amp
        );
    } else if mode2_coupling && flag_nx == 35 && t_end >= 16.0 {
        // Study horizons, the mode-2 configuration: the flapping cycle
        // measured 2026-08-21 at t_end = 16 (ny = 62: uy 3.71 ± 57.6 mm
        // at 2.227 Hz), t_end = 20 (ny = 82: 1.99 ± 57.1 mm at 2.236 Hz)
        // and t_end = 30 (ny = 62: 3.68 ± 55.9 mm at 2.224 Hz) — two-grid
        // agreement 0.9% in amplitude, 0.4% in frequency, stable over 24 s.
        // The bands are wide enough for a settled cycle at either grid
        // and narrow enough that the wake attractor (3.73 Hz, ±17 mm)
        // or the reference itself (1.93 Hz, ±82 mm) would both fail:
        // either would be a material change to report.
        if let Some(f) = w.frequency {
            assert!(
                (2.05..2.45).contains(&f),
                "uy frequency {f:.3} left the measured mode-2 cycle band \
                 [2.05, 2.45] Hz (benchmark reference {REF_UY_FREQ})"
            );
        }
        assert!(
            (45e-3..70e-3).contains(&w.uy_amp),
            "uy amplitude {:.4e} left the measured mode-2 cycle band [45e-3, 70e-3] \
             (benchmark reference {REF_UY_AMP})",
            w.uy_amp
        );
    } else if s1_coupling && ny == 62 && flag_nx == 35 && t_end >= 16.0 {
        // Study horizons, subcycle 1: THE BENCHMARK CYCLE, hit 2026-08-24
        // (run 3, floor 4e-6, MAXSUB 30; measured over [13, 16] s:
        // uy 3.17 ± 81.68 mm at 1.925 Hz vs reference 1.30 ± 81.6
        // [1.93] — 0.1% in amplitude, 0.26% in frequency; full record in
        // omni-cortex solver_status.md §"C2 closed in displacement").
        // The bands are deliberately generous: the s = 1 trajectory
        // shifts legitimately whenever a structural-Newton rescue
        // engages mid-march (runs 1 and 2 DIED where run 3's coupler
        // fixes carried it), and the mode-2 s = 2 cycle (±57.6 mm at
        // 2.23 Hz) still fails both bands — losing the benchmark cycle
        // stays loud.
        if let Some(f) = w.frequency {
            assert!(
                (1.85..2.0).contains(&f),
                "uy frequency {f:.3} left the benchmark-cycle band [1.85, 2.0] Hz \
                 (measured 1.925, reference {REF_UY_FREQ})"
            );
        }
        assert!(
            (70e-3..92e-3).contains(&w.uy_amp),
            "uy amplitude {:.4e} left the benchmark-cycle band [70e-3, 92e-3] \
             (measured 81.68e-3, reference {REF_UY_AMP})",
            w.uy_amp
        );
    }
}