同源分析法(HAM)和变分迭代法(VIM)求解浅水中非线性波传播方程的比较

M. Soltani, R. Amirabadi
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引用次数: 0

摘要

本研究旨在研究两种常用的数值方法——同伦分析法(HAM)和变分迭代法(VIM)的能力,提出更有效的浅水非线性表面波传播控制方程的近似求解方法。为了做到这一点,与深度均匀的开放海洋相连的半平坦、中等和陡峭的海岸暴露在初始波高H=2,静止高程d=20的孤立波中。然后,确定了这些剖面的地表高程和速度曲线,并用HAM和VIM进行了比较。为了验证数值模拟的正确性,考虑了半平坦和中等坡度两种坡度,并在Flow-3D中进行了建模。然后利用相关系数对地表高程结果进行比较。斜率的相关系数表明结果吻合得很好。最后,尽管两种方法的结果非常相似,但强烈建议使用HAM而不是VIM,因为它使求解过程快速收敛并且更加精简。
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Comparison between Homotopy Analysis Method (HAM) and Variational Iteration Method (VIM) in Solving the Nonlinear Wave Propagation Equations in Shallow Water
Article History: Received: 3 Feb. 2019 Accepted: 17 Mar. 2019 This study aims to investigate the capability of two common numerical methods, Homotopy Analysis Method (HAM) and Variational Iteration Method (VIM), and to suggest more efficient approximate solution method to the governing equations of nonlinear surface wave propagation in shallow water. To do so, semi-flat, moderate, and sharp slope of shore which are connected to an open ocean with a uniform depth are exposed to a solitary wave with initial wave height H=2 and stationary elevation d=20. Then, the surface elevation and velocity curves for these profiles are determined and compared by HAM and VIM. To verify the numerical modeling, two slopes i.e. semi-flat and moderate slope are considered and modeled in Flow-3D. Afterwards, the results of surface elevations are compared to each other by using correlation coefficient. The correlation coefficients for the slopes represent that the results coincide well. Ultimately, although the results of both methods are quite similar, using HAM is highly recommend rather than VIM since it makes solution procedure fastconverging and more abridged.
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