Building the next generation of deformable-impact software

Spectral contact dynamics for drops impacting a bath

Contact is the model

In deformable impact, the contact law can decide the result. I build solvers that move pressure, contact extent, and interface motion from prescribed inputs into the dynamics.

Bath-impact simulation. The dark-blue region is the bath, the pale-blue region the drop, and the red arc the solved contact patch. The inset plots pointwise pressure as a diagnostic, not as a converged field.

What each model removed

The line began with a rigid sphere and elastic membrane, published in 2022 ((Agüero et al., 2022)). It then made the impactor liquid, then made the target liquid ((Gabbard et al., 2025)). Each transition removed a convenience assumption: fixed impactor shape, rigid target, or prescribed contact.

Simulation of a rigid sphere impacting an elastic membrane
Simulation of the 2022 rigid-sphere / elastic-membrane model.

The solid-substrate branch then isolated non-Newtonian constitutive behaviour. Contact-dynamics work made pressure and contact extent explicit unknowns. Those reductions made clear which assumptions had been carrying the prediction.

Spectral contact dynamics

SpectralKM.jl is the current Newtonian, non-coalescing drop–bath formulation. It represents the bath with Fourier–Bessel modes, the drop with Legendre modes, and contact pressure with shifted-Legendre modes. A feasibility-filtered outer search selects the contact patch.

It removes three choices that can otherwise decide a rebound prediction: a prescribed pressure profile, a mesh-level contact search, and a fixed liquid interface. The bath, drop, pressure supported on the patch, and contact extent are solved together. A disagreement can then be traced to an explicit physical assumption instead of an opaque contact switch.

The pressure inset is diagnostic, not a polished field to over-interpret. Rebound dynamics can settle before a pointwise pressure trace does.

Controlled rheology on a solid

DropRebound.jl isolates how constitutive behaviour changes rebound on a solid substrate. SpectralKM.jl carries the contact problem to two moving liquid interfaces. The videos are separate numerical cases, not a benchmark.

Numerical Oldroyd-B case.
Numerical Carreau case.

Open source as research infrastructure

Open source is part of the research method here: package code, tests, executable derivations, diagnostics, validation records, parameter sweeps, and rendering scripts live together. A reader can reproduce a result, inspect an assumption, or challenge a conclusion without reconstructing the workflow from a paper.

References

2025

  1. Drop rebound at low Weber number
    Chase T. Gabbard, Elvis A. Aguero, Radu Cimpeanu, and 5 more authors
    2025

2022

  1. PRSA
    Impact of a rigid sphere onto an elastic membrane
    Elvis A Agüero, Luke Alventosa, Daniel M Harris, and 1 more author
    Proceedings of the Royal Society A, 2022