Approximating one-dimensional coupled shallow-water equations for predicting tsunami wave propagation using finite difference method

Abstract

Several countries on the Indian Ocean are hit by the tsunami on 26th December 2004. The tsunami is a rare phenomenon compared to other natural hazards. In order to enhance the preparedness of the people due to the tsunami, the tsunami wave propagation is predicted. Hence one-dimensional shallow-water equations are used in this study since the tsunami is considered as a shallow-water wave. The shallow-water equations are discretized using explicit finite difference method. Then, the numerical method is validated with the θ − method and analytical solution for free surface wave damping problem as to ensure that the proposed method is suitable for solving one-dimensional shallow-water equations. The tsunami wave heights and effects show a high variability along the coastline. One way to study this complexity is by simulating the tsunami wave propagation. To simulate the tsunami, the boundary conditions, initial conditions, spatial and time step size, as well as the shallow-water equations in finite difference form, are coded into MATLAB software. The results showed that the tsunami wave is propagating towards the coastline as the time increases. The simulation results had successfully predicted the behaviour of tsunami wave propagation near the coastline.