Abstract This article develops novel analytical solutions to oblique wave scattering by porous rubble-mound structures based on linear potential theory. The novelty of the solutions is that the usual complex root finding algorithm is avoided by applying a contour integral technique. In the solving procedure, the whole fluid domain is divided into multiple regions, and the series solution of the velocity potential in each region is obtained using the separation of variables. A linear equation system for the expansion coefficients is achieved by matching the interface conditions between adjacent regions. The matrix elements, which initially include the complex roots of complex dispersion relations, are evaluated by applying the contour integral technique. The evaluation process is free of complex roots, and thus the difficulties arising in solving the complex dispersion relations in traditional solutions are avoided. Case studies show that the series solution converge rapidly, and the calculation results of the new solutions agree well with those of previous analytical solutions with complex roots and multi-domain boundary element method (BEM) solutions. Besides providing a simple and elegant approach for analyzing the hydrodynamic performance of porous structures, the new solutions can be extended to water wave problems involving other dissipative coastal structures.

中文翻译：

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多孔防波堤/海堤的斜波散射：基于等高线积分的新型解析解，无需求复根

摘要 本文提出了基于线性势理论的多孔瓦砾丘结构斜波散射的新解析解。解决方案的新颖之处在于通过应用轮廓积分技术避免了通常的复杂求根算法。在求解过程中，将整个流体域划分为多个区域，通过变量分离得到各区域速度势的级数解。通过匹配相邻区域之间的界面条件来实现膨胀系数的线性方程组。矩阵元素最初包括复杂色散关系的复杂根，通过应用等高线积分技术进行评估。评估过程没有复杂的根，从而避免了传统方案在求解复杂色散关系时遇到的困难。案例研究表明，级数解收敛速度很快，新解的计算结果与以前的复根解析解和多域边界元法（BEM）解的计算结果吻合良好。除了提供一种简单而优雅的方法来分析多孔结构的水动力性能外，新的解决方案还可以扩展到涉及其他耗散沿海结构的水波问题。新解的计算结果与以前的复根解析解和多域边界元法（BEM）解的计算结果吻合较好。除了提供一种简单而优雅的方法来分析多孔结构的水动力性能外，新的解决方案还可以扩展到涉及其他耗散沿海结构的水波问题。新解的计算结果与以前的复根解析解和多域边界元法（BEM）解的计算结果吻合较好。除了提供一种简单而优雅的方法来分析多孔结构的水动力性能外，新的解决方案还可以扩展到涉及其他耗散沿海结构的水波问题。