非线性波与三维流的哈密顿双向耦合
Hamiltonian Two-Way Coupling of Nonlinear Waves and 3D Flows
AI总结：
该研究提出基于Zakharov公式的非线性色散二维波模型，实现与三维流的哈密顿双向耦合，解决二维-三维流体耦合的界面伪影问题，提升模拟精度与效率。
AI中文摘要：
长期以来，通过将局部三维流体求解器与更轻量的二维表面模型耦合来模拟大规模自由表面水时，一直存在波动力学不匹配的问题：图形学中使用的高效二维波模型通常是线性的或非色散的。这些模型速度快、结构简单，在平静、小振幅海面场景下精度较高，但将它们与强非线性三维求解器耦合时，会在二维-三维界面产生明显的反射和伪影。我们通过引入一种基于经典Zakharov公式的非线性色散二维波模型来解决该问题。该模型具有哈密顿结构，其中表面高程和表面势构成由波能控制的经典对（η, ψ），支持经典一致的双向耦合方案，使信息能在二维-三维界面平滑传递。我们的二维求解器与SWE、BEM和Airy基准相比，平均波高误差降低了1.7至5倍，同时运行速度比BEM快1000倍以上；与SWE和Airy相比，它具有更高的非线性精度和耦合保真度，仅在速度和稳定性上有轻微损失。将其与三维Navier-Stokes求解器耦合后得到的完整系统，在色散匹配和开尔文尾流测试等一系列实验中可抑制明显的接缝伪影，且在相同计算域上的运行速度比纯GPU NB-FLIP模拟快4倍以上。
英文摘要：
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$\times$ over SWE, BEM, and Airy baselines while running more than $10^3\times$ 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$\times$ faster than a pure GPU NB-FLIP simulation on the same domain.
