Abstract Predicting the propagation and transformation of the solitary wave is very important in coastal engineering. This paper presents a numerical investigation of the solitary wave breaking over a slope by using a finite particle method (FPM), which is an enhanced smoothed particle hydrodynamics (SPH). We firstly conduct a comparative study on SPH and FPM in modelling solitary wave and it is demonstrated that FPM performs better than SPH qualitatively and quantitatively. A modified particle shifting technique (PST) is integrated into FPM to avoid possible ill corrective matrix due to extremely disordered particle distribution. We find that the artificial viscous coefficient can greatly influence the wave run-up and propose an empirical equation to quickly determine the optimal value of the artificial viscous coefficient used in the FPM simulations. The solitary wave breaking is then modelled for scenarios with relative wave heights and slopes, and three typical breaking types, including surging breaker (SU), plunging breaker (PL) and spilling breaker (SP), are analyzed. The result indicates that SP affects the pressure field more extensive than PL and SU. When the breaker type transits from SP to SU, the breaker tends to break at a narrower region close to the shoreline, the breaking depth decreases, the breaking index gradually turns into an unstable value, and the relative run-up height of breaking waves becomes larger. Although the wave celerity at breaking has no clear relationship with breaker types, the wave celerity at breaking increases with the increase of the relative wave height and slightly decreases with a steeper slope.

中文翻译：

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单波突破斜坡的有限粒子法数值研究

摘要 对孤立波的传播和变换进行预测在海岸工程中具有重要意义。本文介绍了通过使用有限粒子方法 (FPM) 对斜坡上孤立波的数值研究，这是一种增强的平滑粒子流体动力学 (SPH)。我们首先对 SPH 和 FPM 在孤波建模方面进行了比较研究，结果表明 FPM 在定性和定量上都优于 SPH。改进的粒子移动技术 (PST) 被集成到 FPM 中，以避免由于极端无序的粒子分布而可能出现的不良校正矩阵。我们发现人工粘性系数可以极大地影响波浪爬高，并提出了一个经验方程来快速确定 FPM 模拟中使用的人工粘性系数的最佳值。然后针对具有相对波高和坡度的场景对孤立波破碎进行建模，并分析了三种典型的破碎类型，包括涌动破碎机 (SU)、下沉破碎机 (PL) 和溢出破碎机 (SP)。结果表明，SP 对压力场的影响比 PL 和 SU 更广泛。当破浪类型从SP过渡到SU时，破浪趋向于在靠近海岸线的较窄区域破断，破断深度减小，破断指数逐渐变为不稳定值，破浪相对爬高高度变为更大。