Numerical dispersion in non-hydrostatic modeling of long-wave propagation
Numerical dispersion in non-hydrostatic modeling of long-wave propagation
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DOI：
10.1016/j.ocemod.2019.05.002
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发表时间：
2019-06-01
期刊：
影响因子：
3.2
通讯作者：
Cheung, Kwok Fai
中科院分区：
文献类型：
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作者：
Li, Linyan;Cheung, Kwok Fai
众所周知，有限差分格式的数值离散化会在海啸研究和灾害测绘中常用的深度积分长波模型中引入频散。虽然以前的研究主要集中在线性浅水方程的数值色散，我们包括非静水压力和垂直速度通过凯勒箱计划，并调查所产生的系统的性质与流体静力学模型。离散化的控制方程的傅立叶分析引起的色散关系的水深参数以及时间步长，网格大小，和波的方向。色散关系是由泰勒级数展开式导出的超前阶近似以及涉及驻波和前进波的均匀水深的数值实验来说明的。空间离散和非静力项之间的相互作用导致浅水范围外的数值色散显着减少。由于空间分辨率的有效增加，波传播斜向计算网格的数值色散也降低。时间步长抵消了空间离散的数值色散，在柯朗数的适用范围内只具有次要影响。由于从凯勒箱方案推导出的非流体静力模型的控制方程往往低估了浅水中的弥散，因此数值效应在产生更接近艾里波理论的解方面是互补的。2011年东北海啸的案例研究说明了网格的敏感性和收敛特性在现实世界中的应用。一个适当选择的网格大小可以实现一个准确的描述波传播的水深参数范围广泛的海洋。
Numerical discretization with a finite-difference scheme is known to introduce frequency dispersion in depth-integrated long-wave models commonly used in tsunami research and hazard mapping. While prior studies on numerical dispersion focused on the linear shallow-water equations, we include the non-hydrostatic pressure and vertical velocity through a Keller box scheme and investigate the properties of the resulting system in relation to a hydrostatic model. Fourier analysis of the discretized governing equations gives rise to a dispersion relation in terms of the water-depth parameter as well as the time step, grid size, and wave direction. The dispersion relation is illustrated by its lead-order approximation derived from Taylor series expansions as well as numerical experiments involving standing and progressive waves with uniform water depth. Interaction between the spatial discretization and non-hydrostatic terms leads to significant reduction of numerical dispersion outside the shallow-water range. Numerical dispersion also decreases for wave propagation oblique to the computational grid due to effective increase in spatial resolution. The time step, which counteracts numerical dispersion from spatial discretization, only has secondary effects within the applicable range of Courant numbers. Since the governing equations of the non-hydrostatic model derived from the Keller box scheme tend to underestimate dispersion in shoaling water, the numerical effects are complementary in producing a solution closer to Airy wave theory. A case study of the 2011 Tohoku tsunami illustrates the grid sensitivity and convergence properties in real-world applications. A properly selected grid size can achieve an accurate description of wave propagation over a wide range of water-depth parameters across the ocean.