# Moving-boundary force spikes: evidence and source index

Updated 2026-10-31.

This note indexes supplied audited observations and primary-source extractions.
It does not report a newly measured cure or implement an alternative method.
Paper details below were supplied by the parent investigation; no new source
retrieval or independent paper verification was performed for this note.

## Current implementation and interpretation

- Celeris M1 reconstructs a fresh node as `feq(rho_bar, u_wall) + donor NEQ`.
- In exact arithmetic, the donor non-equilibrium component has zero mass and
  momentum when formed against the donor's own equilibrium moments.
- Re-projecting that same reconstruction onto the same wall velocity therefore
  does not, by itself, change its mass or momentum or supply a cure for spikes.
- Floating-point residuals should be measured separately from this algebraic fact.
- Peng's alternative differs upstream: extrapolate PDFs from three donors, then
  replace selected moments. It is not simply another projection of current M1.
- PPO interval-force observations and native per-step FSI right-hand-side forces
  are distinct signals; comparisons must identify which signal is being used.

## Audited run observations supplied to this note

- D40 revision: `e9213dd2cc9cfed0e8487a3cf4ebdd94d23dc64d`.
- Window: first `97.303 D/U` of physical time.
- Maximum displacement: `max |y|/D = 0.304893`.
- Maximum native force-coefficient increment: `max |ΔCy| = 0.66688`.
- D20 over the same physical-time window: `max |ΔCy| = 1.80735`.
- The largest D40 event involved 30 nodes.
- These are supplied audited observations, not measurements made for this note.
- Time steps and trajectories differ between runs. This comparison establishes
  neither spatial convergence nor a unique cause for the force spikes.

Evidence locations supplied by the investigation:

- Horsea: `/tmp/celeris-results-pinball-resolution`.
- Mac: `validation-evidence/pinball-force-diagnosis`.

These locations index run evidence, not local copies of the cited papers.

## Tao, Hu, and Guo (2016): time-step decoupling

Computers & Fluids **133**, 1–14. DOI:
[10.1016/j.compfluid.2016.04.009](https://doi.org/10.1016/j.compfluid.2016.04.009).
[Publisher abstract](https://www.sciencedirect.com/science/article/pii/S0045793016301116).

- Abstract-level support only: non-equilibrium refill reduces oscillations.
- With local iteration, the compared refill methods give similar oscillation magnitudes.
- Time-step decoupling reduces oscillations further in the reported sedimentation,
  Couette, and Poiseuille examples.
- The exact decoupling schedule and time-step ratios have not been verified.
- This abstract does not establish equivalence to an arbitrary force filter.
- Do not implement a claimed reproduction until the actual methods are available.

## Marson et al. (2021): local iterations

Physical Review E **103**, 053308. DOI:
[10.1103/PhysRevE.103.053308](https://doi.org/10.1103/PhysRevE.103.053308).
[Open repository record](https://archive-ouverte.unige.ch/unige:151868).

- §VI, p. 18 discusses pressure waves associated with fresh nodes.
- Appendix E.3, p. 25 and Fig. 18, p. 24 describe the local procedure.
- Copy a local sublattice, perform local collision and streaming, write the fresh
  nodes, and repeat before the global collision and streaming operation.
- One to three iterations performed best in the reported tests; this is not a
  universal iteration-count recommendation.
- The reported smoothed torque-noise assessment is qualitative here.
- Its thin-shell setting differs from the current moving-body configuration.

## Peng (2016): extrapolation and moment replacement

Computers & Mathematics with Applications **72**, 349–374. DOI:
[10.1016/j.camwa.2015.08.027](https://doi.org/10.1016/j.camwa.2015.08.027).

- §5.1.2, Eq. (50), p. 368: extrapolate PDFs along an outward normal direction:
  `f_new(x) = 3 f(x + e) - 3 f(x + 2e) + f(x + 3e)`.
- §5.1.3, Eq. (51): wall equilibrium plus donor non-equilibrium is the family
  containing the current M1 reconstruction.
- §5.1.4, Eqs. (52)–(54): in MRT space, replace momentum with `j = rho0 u_wall`,
  preserve the other moments, then apply the inverse transform.
- A compressible Celeris adaptation must choose the appropriate density;
  copying the paper's `rho0` blindly is not justified.
- Three valid donors require new eligibility checks and fallback behavior beyond
  the current one-link shared-body clearance rule.
- §§5.2–5.3 retain nonzero fluctuations in specific configurations; these results
  do not promise elimination of force spikes in the present problem.

## Bounded next investigation

1. Retain current M1 as the baseline and compare matched prescribed trajectories
   over matched physical-time windows.
2. Record raw force RHS, node crossings, donor moments, mass and momentum changes,
   impulse, spectra, and trajectory response together.
3. Evaluate local iterations, Peng-style reconstruction, and force filtering as
   separate interventions, with explicit definitions and diagnostics.
4. Obtain the actual time-step-decoupling methods before implementing that method.

The current task indexes evidence only; it makes no alternative-method change.