A comparative study of diffraction of shallow-water waves by high-level IGN and GN equations
A comparative study of diffraction of shallow-water waves by high-level IGN and GN equations
复制标题
高阶IGN和GN方程对浅水波衍射的比较研究
DOI：
10.1016/j.jcp.2014.11.020
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发表时间：
2015-02
影响因子：
4.1
通讯作者：
W.Y. Duan
中科院分区：
文献类型：
--
作者：
B.B. Zhao;R.C. Ertekin;W.Y. Duan
本文采用两种相关的理论，即经典的Green-Naghdi（GN）方程和无旋Green-Naghdi（IGN）方程，对浅水波撞击水下障碍物的非线性绕射问题进行了分析。近年来，高阶Green-Naghdi方程已被应用于某些波变换问题。在过去的十年中，高层次IGN方程也被用来研究某些波的传播问题。然而，过去的工作，这些理论使用不同的数值方法来解决这些非线性和不稳定的微分方程组，并在不同的水平。此外，过去已经解决了不同的物理问题。因此，迄今为止，人们无法理解这两套理论所产生的差异及其适用范围。因此，我们的动机，使这些理论产生的结果进行直接比较，通过使用相同的数值方法来解决物理上相同的波浪绕射问题。本文着重用相似的程序对这两种理论进行了比较，只是所用的方程不同，但程序的其他部分，如造波机、阻尼区、离散方法、矩阵求解器等，都是一样的通过这种方式，我们消除了许多可能由不同方程的解产生的差异的潜在来源。物理问题包括存在各种水下障碍物，例如可以用作防波堤或代表大陆架。数值波浪水槽的一端放置造波机，另一端放置消波海滩。非线性和非定常微分方程组用有限差分法求解。结果与不同的方程以及与现有的实验数据进行了比较。
This work is on the nonlinear diffraction analysis of shallow-water waves, impinging on submerged obstacles, by two related theories, namely the classical Green–Naghdi (GN) equations and the Irrotational Green–Naghdi (IGN) equations, both sets of equations being at high levels and derived for incompressible and inviscid flows. Recently, the high-level Green–Naghdi equations have been applied to some wave transformation problems. The high-level IGN equations have also been used in the last decade to study certain wave propagation problems. However, past works on these theories used different numerical methods to solve these nonlinear and unsteady sets of differential equations and at different levels. Moreover, different physical problems have been solved in the past. Therefore, it has not been possible to understand the differences produced by these two sets of theories and their range of applicability so far. We are thus motivated to make a direct comparison of the results produced by these theories by use of the same numerical method to solve physically the same wave diffraction problems. We focus on comparing these two theories by using similar codes; only the equations used are different but other parts of the codes, such as the wave-maker, damping zone, discretion method, matrix solver, etc., are exactly the same. This way, we eliminate many potential sources of differences that could be produced by the solution of different equations. The physical problems include the presence of various submerged obstacles that can be used for example as breakwaters or to represent the continental shelf. A numerical wave tank is created by placing a wavemaker on one end and a wave absorbing beach on the other. The nonlinear and unsteady sets of differential equations are solved by the finite-difference method. The results are compared with different equations as well as with the available experimental data.
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DOI：
10.1115/1.4000503
发表时间：
2010-05
影响因子：
1.6
作者：
J. W. Kim;R. Ertekin;K. Bai
通讯作者：
J. W. Kim;R. Ertekin;K. Bai
影响因子：
4.4
作者：
Yao Zhang;A. Kennedy;N. Panda;C. Dawson;J. Westerink
通讯作者：
Yao Zhang;A. Kennedy;N. Panda;C. Dawson;J. Westerink
影响因子：
4.4
作者：
M. Gobbi;J. Kirby
通讯作者：
M. Gobbi;J. Kirby
影响因子：
4.3
作者：
R. Ertekin;M. Hayatdavoodi;Jang Whan Kim
通讯作者：
R. Ertekin;M. Hayatdavoodi;Jang Whan Kim
更高层次的GN理论在一些波动变换问题中的应用
影响因子：
4.4
作者：
B. B. Zhao;W. Y. Duan;R. C. Ertekin
通讯作者：
R. C. Ertekin