CelerisLab/docs/validation/leontini_viv_predeclare.md

# Single-cylinder free transverse VIV — PREDECLARATION DRAFT (not frozen)

Stage goal (Yanqi via TRON): prescribed Dütsch case + one VIV case both
"reasonably close" to a predeclared reference = development-stage success, then
cleanup. The frozen Dütsch settling failure (0/28 pairs at 31.25 T) stays on
record. Practical closeness is not a formal validation claim. No code until
this page is jointly agreed.

## Primary case (one case)

- Reference: Qin et al., arXiv:2003.12186, §4.5 (maximum amplitudes at
  U_red = 3…8: .075, .551, .520, .459, .370, .084 D in the text, as quoted by
  Grok/Astra) for the target; setup from Kolahdouz et al., arXiv:2003.12046,
  §4.1.1 (read 2026-10-30 via ar5iv): U* sweep 3–8 with amplitudes only in
  Fig. 3(b) (no text values), domain [−30, 45] D × [−30, 30] D with the
  cylinder "initially at rest and centered at the origin", uniform inflow on
  the left, zero normal traction and tangential velocity at the outlet, zero
  normal velocity and tangential traction on y = ±30 D; no initial
  perturbation and no total simulated time stated.
- Re = 150, U* = U/(f_n D) = 5, m/(rho D²) = 2 (m* = rho_s/rho_f = 8/pi),
  zeta = 0, f_n = sqrt(K/M)/(2 pi) in vacuum. Transverse DOF only.
- Target: A_max = .520 D (peak amplitude, Qin §4.5). Multi-code reference
  (Kolahdouz ILE-NS, Qin II-LBM). Reference uncertainty: not stated; the
  spread between codes is not quantified here.

## Our reproduction (declared differences)

- D = 40, MRT, dense double buffer; U_lat = .04, nu = U D / 150 = .010667,
  tau = .532.
- Box [0, 75 D] × [0, 60 D] (3000 × 2400) with the cylinder centre at
  (30 D, 30 D): 30 D from the inlet, 45 D from the outlet, centred in y
  (Kolahdouz §4.1.1). Qin's own box ([0, 40 D] × [0, 20 D], centre (10 D, 10 D))
  is the target paper's, not ours.
- Boundaries: uniform Zou–He inlet, NEQ outlet (rho = 1, backflow clamp),
  free-slip y walls. Kolahdouz uses a traction outlet: declared mismatch.
- Qin's own VIV box (40 D × 20 D) is not used; a smaller box would be a
  declared cost cut with more blockage, not "the same case".
- Allowed y offset ±1.5 D; peak transverse speed ≈ .026 cells/step (bound .5).

## Structure, coupling and time levels

- M = 2 rho D² (lattice rho = 1), f_n = U/(5 D) = 2e-4 per step, K = M (2 pi f_n)²,
  zeta = 0. Equation of motion uses the structural mass only.
- Time levels (binding): the target y^{n+1} must be set before step n runs
  (`set_body`, then `run(1)`), so step n moves the body with (y^n, v^n) that
  were advanced using F^{n-1} from the previous fluid step; step n measures
  F^n. One step of explicit lag, declared.
- Structural update over one step with constant force F = F^{n-1} (exact
  harmonic solution, zeta = 0): y_e = F/K, w = 2 pi f_n,
  y^{n+1} = y_e + (y^n − y_e) cos w + (v^n / w) sin w,
  v^{n+1} = −(y^n − y_e) w sin w + v^n cos w.
- Primary RHS (single coupled run): CME + Wen (theory-motivated stage choice:
  Galilean-invariant link correction; G4 could not separate it from CME).
  Raw CME and the node terms are logged as diagnostics of that trajectory;
  the node impulse is not added. A run with CME-only as RHS is a separate,
  labelled sensitivity case, decided separately. Neither RHS is claimed proven.

## Window, failure semantics, acceptance (engineering, development stage)

- Start (source-faithful): fluid at rest except the uniform inlet, body at
  rest at the declared centre, y(0) = v(0) = 0.
- Seed policy (conditional, declared): exact mirror symmetry can suppress
  lift. If max |y| over the last 5 T_n before t = 40 T_n (200,000 steps) is
  below .01 D, apply one labelled seed at that step: body centre displaced by
  +.01 D in y (v = 0), `seed_applied=true` and its step logged; the run
  continues under the same cap. Missing shedding is a diagnostic, never an
  "A = 0 pass"; the seed is not changed or repeated after seeing results.
- Response cycles: delimited by consecutive upward zero crossings of y about
  its running mean; per-cycle peak = max |y − mean| in that cycle.
- Settled when the per-cycle peak changes ≤ 2 % between consecutive 10-cycle
  windows and the last 5 cycle peaks agree within 1 %. Budget: 150 response
  cycles from the start of motion, including the 20 scoring cycles, so
  settling must complete by response cycle 130; the score uses the first 20
  cycles after settling. Cap miss → FAIL-CLOSED.
- Durations reported: total steps, t U/D, N_resp, measured T_resp (mean
  upward-crossing interval); N_resp / f_n only as a labelled secondary clock,
  never as the settling unit.
- Growth transient vs instability: an envelope that rises and then saturates
  under the settling windows is a physical transient. Instability =
  |y| > 1.0 D (about twice the largest reference peak, .551 D), a non-finite
  value, the offset box being reached, or an envelope still growing at the
  cap.
- FAIL-CLOSED and reported (no sub-iteration, no RHS or parameter retune):
  unsettled at the cap, instability as defined above (possible weak-coupling
  instability at m* ≈ 2.55), or no_donor > 0.
- Score over the 20 cycles after settling: A_max/D (mean of cycle peaks) and
  f/f_n (reported; no target).
- Acceptance: |A_max − .520 D| ≤ .052 D (±10 %), stated together with the
  boundary mismatch and the absence of a quoted reference uncertainty. A pass
  is "reasonably close" for the stage: not grid convergence, not force-RHS
  validation, and it does not touch the Dütsch settling record.
- Driver reads force and the small diagnostics per step only; field reads
  only at a few predeclared snapshots. Cost from Astra's no-dump timing on
  this grid.

## Queued, not in this stage

Leontini et al. JFS 22 (2006) Re = 200, m* = 10, zeta = 0.01, U* = 5.0 (needs
the owners' c_crit convention and a Fig. 1 digitization). D80, literature
claims, pinball, AMR, BC redesign, threshold changes.