Hamiltonian Two-Way Coupling of Nonlinear Waves and 3D Flows

Simulating large-scale free-surface water by coupling a localized 3D fluid solver to a cheaper 2D surface model has long faced a mismatch in wave dynamics: efficient 2D wave models used in graphics are typically either linear or non-dispersive. These models are fast, simple, and accurate for calm, small-amplitude seas, but coupling them with strongly nonlinear 3D solvers produces visible reflections and artifacts at the 2D–3D interface. We address this problem by introducing a nonlinear and dispersive 2D wave model based on the canonical Zakharov formulation. Its Hamiltonian structure, in which the surface elevation and surface potential form a canonical pair (η, ψ) governed by the wave energy, enables a canonically consistent two-way coupling scheme, allowing information to pass smoothly across the 2D–3D interface. Our 2D solver reduces mean wave-height error by 1.7–5× over SWE, BEM, and Airy baselines while running more than 10³× faster than BEM; it achieves greater nonlinear accuracy and coupling fidelity than SWE and Airy, with minor losses in speed and stability. Coupling it with a 3D Navier–Stokes solver yields a full system that suppresses visible seam artifacts across a range of experiments, including dispersion-matching and Kelvin-wake tests, and runs over 4× faster than a pure GPU NB-FLIP simulation on the same domain.


@article{wang2026hamiltonian,
title={Hamiltonian Two-Way Coupling of Nonlinear Waves and 3D Flows},
author={Wang, Sinan and Wang, Ruicheng and Zhang, Taiyuan and Feng, Fan and He, Jinjin and Sun, Yuchen and Li, Zhiqi and Zhu, Bo},
journal={ACM Transactions on Graphics (TOG)},
volume={45},
number={6},
pages={1--20},
year={2026},
publisher={ACM New York, NY, USA},
doi={10.1145/3842540}
}