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Time-Space Decoupled Explicit Method for Fast Numerical Simulation of Tsunami Propagation

机译：时空解耦显式方法用于海啸传播的快速数值模拟

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This study presents a novel explicit numerical scheme for simulating tsunami propagation using the exact solution of the wave equations. The objective of this study is to develop a fast and stable numerical scheme by decoupling the wave equation in both the time and space domains. First, the finite difference scheme of the shallow-water equations for tsunami simulation are briefly introduced. The time-space decoupled explicit method based on the exact solution of the wave equation is given for the simulation of tsunami propagation without including frequency dispersive effects. Then, to consider wave dispersion, the second-order accurate numerical scheme to solve the shallow-water equations, which mimics the physical frequency dispersion with numerical dispersion, is derived. Lastly, the computation efficiency and the accuracy of the two types of numerical schemes are investigated by the 2004 Indonesia tsunami and the solution of the Boussinesq equation for a tsunami with Gaussian hump over both uniform and varying water depths. The simulation results indicate that the proposed numerical scheme can achieve a fast and stable tsunami propagation simulation while maintaining computation accuracy.
机译：这项研究提出了一种新颖的显式数值方案，它使用波动方程的精确解来模拟海啸传播。这项研究的目的是通过在时域和空间域中解耦波动方程，从而开发出一种快速，稳定的数值方案。首先，简要介绍了海啸模拟中的浅水方程组的有限差分格式。给出了基于波动方程精确解的时空解耦显式方法，用于海啸传播的模拟，而没有考虑频率分散效应。然后，考虑波的频散，推导了用浅水方程模拟物理频率频散和数值频散的二阶精确数值解法。最后，利用2004年印度尼西亚海啸以及在水深均匀且变化的高斯峰的海啸中，研究了两种数值方法的计算效率和精度。仿真结果表明，所提出的数值方案可以在保持计算精度的同时，实现快速稳定的海啸传播模拟。

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