Accuracy and efficiency of two numerical methods of solving the potential flow problem for highly nonlinear and dispersive water waves
Accuracy and efficiency of two numerical methods of solving the potential flow problem for highly nonlinear and dispersive water waves
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DOI：
10.1002/fld.3992
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发表时间：
2015-04
影响因子：
1.8
通讯作者：
M. Yates;M. Benoit
中科院分区：
文献类型：
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作者：
M. Yates;M. Benoit
通过三种不同的单水平维（1DH）测试案例，比较了两种方法求解非线性波精确势流问题的精度和效率。这两种模型方法在水平维度上使用高阶有限差分格式，在垂直维度上使用不同的分辨率。第一个模型也在垂直方向上使用高阶有限差分格式，而第二个模型则采用谱方法。这两种模型的收敛性、准确性和效率与时间、水平和垂直分辨率有关：(1)规则非线性波在周期域中的传播；(2)非线性驻波在全反射边界域中的运动；(3)一列波浪在斜坡上的传播和浅滩化。光谱模型方法作为垂直分辨率的函数收敛得更快。此外，在垂直分辨率相当的情况下，光谱模型方法在实际模型应用的参数范围内显示出更高的精度和效率。版权所有©2015 John Wiley & Sons， Ltd
The accuracy and efficiency of two methods of resolving the exact potential flow problem for nonlinear waves are compared using three different one horizontal dimension (1DH) test cases. The two model approaches use high‐order finite difference schemes in the horizontal dimension and differ in the resolution of the vertical dimension. The first model uses high‐order finite difference schemes also in the vertical, while the second model applies a spectral approach. The convergence, accuracy, and efficiency of the two models are demonstrated as a function of the temporal, horizontal, and vertical resolutions for the following: (1) the propagation of regular nonlinear waves in a periodic domain; (2) the motion of nonlinear standing waves in a domain with fully reflective boundaries; and (3) the propagation and shoaling of a train of waves on a slope. The spectral model approach converges more rapidly as a function of the vertical resolution. In addition, with equivalent vertical resolution, the spectral model approach shows enhanced accuracy and efficiency in the parameter range used for practical model applications. Copyright © 2015 John Wiley & Sons, Ltd.