有限深度和无限深度的两条不对称沟槽的斜波散射组合

Swagata Ray, Soumen De
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引用次数: 0

摘要

本研究的重点是在线性化理论框架内研究斜波散射,尤其关注涉及有限深度和无限深度非对称海沟的情况。通过采用特征函数展开法,物理问题被转化为等效边界值问题。这个新提出的问题由四个弱奇异积分方程组构成,它们与位于沟槽边缘上方的间隙中的速度水平分量有关。这些积分方程的求解是通过使用多期 Galerkin 近似方法实现的。这种方法使用超球面格根鲍尔多项式作为基函数进行展开,再加上适当的加权函数,以解决三分之一奇异性问题。采用图形表示法来描述各种非尺寸参数的反射和透射系数的数值评估。这些可视化效果有助于深入了解这些系数在不同条件下的行为和依赖关系。为了验证当前模型的准确性,我们将其与以前发表的文献结果进行了比较。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Oblique wave scattering by a combination of two asymmetric trenches of finite and infinite depth
The focal point of the current study lies in investigating oblique wave scattering within the framework of linearized theory, with particular attention to scenarios involving asymmetric trenches of both finite and infinite depths. By employing the eigenfunction expansion method, the physical problem undergoes a transformation into an equivalent boundary value problem. This newly formulated problem is characterized by a system of four weakly singular integral equations, which pertain to the horizontal component of velocity across the gaps situated above the edges of the trenches. The solution to these integral equations is achieved through the utilization of a multi-term Galerkin approximation method. This approach involves expansions using ultraspherical Gegenbauer polynomials as basis functions, coupled with the appropriate weight functions tailored to address the one-third singularity. Graphical representations are employed to depict the numerical evaluations of reflection and transmission coefficients across various non-dimensional parameters. These visualizations offer insight into the behavior and dependencies of these coefficients under different conditions. To validate the accuracy of the current model, it is compared against previously published results available in the literature.
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