AI 中文总结
该研究提出一种非贴合计算框架，结合高阶多项式修正移位边界近似、保多项式梯度恢复与超粘性，实现无需重网格化的完全非线性水波及与结构的相互作用模拟。
AI 中文摘要
我们提出了一种新颖的非贴合计算框架，用于模拟基于完全非线性势流的水波。针对波传播问题，我们阐述了核心方法，该方法涉及非贴合谱元上的高阶多项式修正移位边界近似。此方法可在简单笛卡尔背景网格上模拟受水深变化影响的弯曲、高度时变（移动且变形）的自由表面，无需重新网格化或对非仿射几何特征进行进一步近似。此外，我们强调采用保多项式技术进行恰当梯度恢复对准确捕捉垂直自由表面速度的重要性。最终目标是开发一种高阶收敛的数值格式，能够长时间模拟高度非线性波，这通过自由表面的任意阶有限差分近似结合额外的超粘性以保证数值稳定性来实现。我们给出了周期域和有限域中波传播的验证与确认测试案例，重点开展了收敛性研究、高阶近似的合理性论证、最优梯度恢复的重要性、高度非线性波的长时间模拟、高度非线性流函数波及大幅值孤子与仿射和弯曲水深变化以及垂直壁的非线性波相互作用等研究。该新颖计算模型为模拟海浪及其与近海结构的相互作用提供了全面的一体化框架，具有显著的几何灵活性，可使自由表面等边界随时间移动和变形，无需贴合边界网格重新网格化。
英文摘要
We present a novel unfitted computational framework for simulating fully nonlinear potential flow-based water waves. Focusing on wave propagation, we describe the core methodology, which involves a high-order polynomial-corrected shifted-boundary approximation on unfitted spectral elements. This approach allows for the simulation of a curved, highly time-dependent (moving and deforming) free surface affected by bathymetric changes. All that on a simple Cartesian background mesh without re-meshing or further approximations of non-affine geometric features. In addition, we highlight the importance of proper gradient recovery using a polynomial-preserving technique to accurately capture the vertical free-surface velocity. Ultimately, the goal is to develop a high-order convergent numerical scheme capable of simulating highly nonlinear waves over long periods. This is achieved through an arbitrary-order finite-difference approximation of the free surface combined with added hyperviscosity for numerical stability. We present verification and validation test cases for wave propagation in both periodic and finite domains. Emphasis is placed on convergence studies, the justification for using high-order approximations, the importance of optimal gradient recovery, long-time simulation of highly nonlinear waves, and nonlinear wave interactions with both affine and curved bathymetry changes, as well as with vertical walls, for highly nonlinear stream function waves and high-amplitude solitons. The novel computational model offers a comprehensive, all-in-one framework for simulating ocean waves and their interactions with offshore structures. It provides significant geometric flexibility, enabling boundaries such as the free surface to move and deform over time without the need to re-mesh a boundary-fitted mesh.
Comments28 pages, 14 figures, 3 tables, 82 references
