(5)Efficient numerical scheme based on the method of lines for the shallow water equations

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Mohamed M. Mousa ^a,b,∗

^a Department of Basic Science, Faculty of Engineering at Benha, Benha University, Benha 13512, Egypt 

^b Department of Mathematics, College of Sciences and Human Studies at Howtat Sudair, Majmaah University, 11952, Saudi Arabia 

Received 14 August 2018; received in revised form 22 October 2018; accepted 24 October 2018 

Available online 28 October 2018 

Abstract 

    In this paper, a nonlinear shallow-water model of tsunami wave propagation at different points along a coastline of an ocean has been numerically simulated using method of lines. The simulation is carried out for various coastal slopes and the ocean depths. The effects of the coast slope and sea depth on the tsunami wave run-up height and velocity are illustrated. The accuracy of the mathematical model is verified by solving a classical test problem with known analytic solution. The computed run-up height and velocity show satisfactory agreement with the tsunami wave physics. 

© 2018 Shanghai Jiaotong University. Published by Elsevier B.V. 

This is an open access article under the CC BY-NC-ND license. (http://creativecommons.org/licenses/by-nc-nd/4.0/)  

Keywords: Shallow-water equation; Tsunami wave; Run-up height; Method of lines.