Abstract Sea dikes, as a commonly used type of coastal protection structures, are often attacked or damaged by violent waves overtopping under tsunamis and storm surges. In this study, the behavior of solitary waves traveling on a sloping sea dike is simulated, and solitary wave overtopping characteristics are analyzed using a complete Lagrangian numerical method, the moving particle semi-implicit (MPS) method. To better describe the complicated fluid motions during the wave overtopping process, the original MPS method is modified by introducing a new free surface detection method, i.e., the area filling rate identification method, and a modified gradient operator to provide higher precision. Meanwhile, the approximation method for sloping boundaries in particle methods is enhanced, and a smooth slope approximation method is proposed and recommended. To verify the improved MPS method, a solitary wave traveling over a steep sloping bed is studied. The entire solitary wave run-up and run-down processes and exquisite water movements are reproduced well by the present method, and are consistent with the corresponding experimental results. Subsequently, the improved MPS method is applied to investigate the overtopping process of a single solitary wave over a sloping sea dike. The results show that the hydraulic jump phenomenon is also possible to occur during the run-down motion of the solitary wave overtopping. Finally, the characteristics of the propagation and overtopping of two successive solitary waves on a sloping sea dike are discussed. The result manifests that the interaction between adjacent solitary waves affects wave overtopping patterns and overtopping velocities.

中文翻译：

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基于粒子法的倾斜海堤孤波漫顶数值模拟

摘要 海堤作为一种常用的海岸防护结构，在海啸和风暴潮的作用下，经常受到猛烈的海浪的袭击或破坏。在本研究中，模拟了在倾斜海堤上传播的孤立波的行为，并使用完整的拉格朗日数值方法——移动粒子半隐式（MPS）方法分析了孤立波的越顶特性。为了更好地描述波浪漫顶过程中复杂的流体运动，对原有的MPS方法进行了改进，引入了一种新的自由表面检测方法，即区域填充率识别方法，以及改进的梯度算子，以提供更高的精度。同时，增强了粒子方法中倾斜边界的近似方法，并提出并推荐了一种平滑斜率逼近方法。为了验证改进的 MPS 方法，研究了一个在陡坡上传播的孤立波。本方法再现了整个孤立波的起落过程和细腻的水流运动，与相应的实验结果一致。随后，应用改进的 MPS 方法研究了单个孤立波在倾斜海堤上的漫顶过程。结果表明，在孤波翻越的滑行运动过程中也有可能发生水跃现象。最后讨论了两个连续孤立波在倾斜海堤上的传播和越顶特性。