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

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Abstract

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.

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Acknowledgments

The financial support from the National Natural Science Foundation of China, the Fundamental Research Funds for the Central Universities, and the Research Fund for the Doctoral Program of Higher Education of China with Grant Nos. 51222808, HIT.BRETIV.201320 and 20122302110057, respectively, are greatly appreciated by the authors. We are also grateful to P.L.F. Liu, S.B. Woo, Y.S. Cho at Cornell University for their open-source code for COMCOT, as well as H. Liu and Zh.P. Liao. The computing program presented in this study is partially based on their work.

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  1. Ministry-of-Education Key Laboratory of Structural Dynamic Behavior and Control, School of Civil Engineering, Harbin Institute of Technology, Harbin, 150090, China

    Anxin Guo, Shengchao Xiao & Hui Li

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  1. Anxin Guo
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  2. Shengchao Xiao
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  3. Hui Li
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Correspondence to Anxin Guo.

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Guo, A., Xiao, S. & Li, H. Time–Space Decoupled Explicit Method for Fast Numerical Simulation of Tsunami Propagation. Pure Appl. Geophys. 172, 569–587 (2015). https://doi.org/10.1007/s00024-014-0848-1

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