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

Large-scale water has always been a balancing act between fidelity and cost. Pure 3D fluid simulation is expensive, while the 2D surface models commonly used in games are fast but often too simple, especially once waves become strongly nonlinear or need to interact cleanly with a 3D region near the camera or shoreline.

This work introduces a 2D wave model built on the canonical Zakharov formulation, where surface height and surface potential form a Hamiltonian pair. That structure matters because it lets the 2D and 3D solvers exchange information in a way that stays mathematically consistent, reducing the reflections and seam artifacts that usually show up at the boundary between the two systems.

In testing, the 2D solver reduced mean wave-height error by 1.7–5× versus SWE, BEM, and Airy baselines, while running more than 10^3× faster than BEM. When coupled to a 3D Navier–Stokes solver, the full system suppressed visible seams in dispersion-matching and Kelvin-wake experiments and still ran over 4× faster than a pure GPU NB-FLIP simulation on the same domain.

For game teams, the practical takeaway is straightforward: hybrid water can become less of a compromise. Graphics programmers working on oceans, wakes, and shoreline transitions get a path to better nonlinear behavior without paying full 3D costs everywhere, which could make hybrid pipelines more viable for real-time projects that need both scale and close-up detail.