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

Simulating large-scale free-surface flow 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 to 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 enables canonically consistent two-way coupling, allowing information to pass smoothly across the 2D-3D interface. Our 2D solver reduces mean wave-height error by factors of 1.7–5× relative to SWE, BEM, and Airy baselines while running more than 10 3 × 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 full-domain GPU NB-FLIP simulation.