分散性浅水波建模。第四部分：在全局球形几何上的数值模拟
Dispersive shallow water wave modelling. Part IV: Numerical simulation on a globally spherical geometry
AI总结：
本文研究了在旋转全局球形几何上分散性波模拟的问题，采用分裂方法提出了一种两步预测-校正方案，通过理想化情境和实际案例验证了该算法在球形几何上处理分散性波传播的能力。
摘要：
在本文中，我们考虑了在旋转的全局球形几何上进行分散性波模拟的问题。在本第四部分中，我们专注于数值方面，而模型推导已在第三部分中描述。我们提出的算法基于分裂方法。即，方程被分解为一个均匀椭圆方程，用于分散压力分量，以及一个带有源项的球形浅水方程的双曲部分。该算法被实现为两步预测-校正方案。在每一步中，我们分别求解椭圆和双曲问题。然后，我们通过理想化情境展示该算法的性能，其中底面是偶数的，我们估计球形性和旋转效应对分散性波传播的影响。分散效应取决于波传播距离和生成区域的线性范围。最后，该数值方法应用于两个真实世界事件。即，我们进行了2007年保加利亚和2010年智利 tsunami 的模拟。在数据可用的情况下，我们的计算结果与实际测量进行对比。
英文摘要：
In the present manuscript, we consider the problem of dispersive wave simulation on a rotating globally spherical geometry. In this Part IV, we focus on numerical aspects while the model derivation was described in Part III. The algorithm we propose is based on the splitting approach. Namely, equations are decomposed on a uniformly elliptic equation for the dispersive pressure component and a hyperbolic part of shallow water equations (on a sphere) with source terms. This algorithm is implemented as a two-step predictor-corrector scheme. On every step, we solve separately elliptic and hyperbolic problems. Then, the performance of this algorithm is illustrated on model idealised situations with an even bottom, where we estimate the influence of sphericity and rotation effects on dispersive wave propagation. The dispersive effects are quantified depending on the propagation distance over the sphere and on the linear extent of generation region. Finally, the numerical method is applied to a couple of real-world events. Namely, we undertake simulations of the Bulgarian 2007 and Chilean 2010 tsunamis. Whenever the data is available, our computational results are confronted with real measurements.
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