Wave propagation on uniformly sloped beaches is a canonical coastal engineering topic that has been studied extensively in the past few decades. However, most of these studies treat beaches as solid boundaries even though they are often made of porous materials, such as sediment and vegetation. Permeable beaches struck by tsunami-like waves have not been adequately investigated. It is expected that the degree of permeability plays a crucial role in mitigating the impact of the wave. This study examines solitary wave run-ups on sandy beaches using an incompressible smoothed particle hydrodynamics (ISPH) model. The permeability of the beach is considered to be directly related to the diameter of its constituent sand particles. To obtain a satisfactory pressure field, which cannot be achieved using the original ISPH algorithm, the source term of the pressure Poisson equation has been modified based on a higher-order source-term expression. Flows within the porous medium are computed in the same framework as those outside the porous medium. In the current model, no transition zone is needed at the boundary of the porous structure. The wave-attenuation effect of the porous medium is discussed, with a particular focus on the relationship between the run-up height and grainsize.

中文翻译：

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渗透波海滩上孤波传播的不可压缩SPH模拟

波浪在均匀倾斜的海滩上的传播是沿海工程的一个典型主题，在过去的几十年中已经进行了广泛的研究。但是，尽管这些海滩通常是由多孔材料制成的，例如沉积物和植被，但大多数研究仍将海滩视为坚固的边界。海啸般的波浪袭击的渗透性海滩尚未得到充分调查。可以预期，渗透率的程度在减轻波浪的影响方面起着至关重要的作用。这项研究使用不可压缩的平滑粒子流体动力学（ISPH）模型研究了沙滩上的孤立波上升。海滩的渗透率被认为直接与其组成的沙粒的直径有关。为了获得令人满意的压力场，这是使用原始ISPH算法无法实现的，泊松方程的源项已根据高阶源项表达式进行了修改。多孔介质内的流量与多孔介质外的流量在相同的框架内计算。在当前模型中，在多孔结构的边界处不需要过渡区域。讨论了多孔介质的波衰减效应，特别关注了毛坯高度与晶粒尺寸之间的关系。