Approximating one-dimensional coupled shallow water equation for predicting Tsunami wave propagation using new semi-implicit method

Tsunamis are uncommon events compared to natural hazards. Population growth along the shorelines has increased the statistic of the number of victims affected by the tsunami disaster. In order to help people to be aware about the tsunami disasters, a tsunami wave propagation must be predicted. This study proposed a one dimensional coupled shallow water equation for predicting the tsunami wave propagation. The simulation of numerical modelling was conducted to predict the occurrence of tsunami wave propagation. In order to approximate the shallow water equation, the discretization process was conducted using a new semi-implicit method which is one of the methods in finite difference method. A problem regarding the free surface wave damping problem were used in validating the semiimplicit method. After the validation process, the numerical algorithm was developed in MATLAB software to solve the one dimensional coupled shallow water equation for the tsunami wave propagation. For the purposes of the simulation, the boundary condition and initial condition, the spatial steps and time steps as well as the approximation of shallow water equation were encoded. The simulation results of one dimensional shallow water equation successfully predicted the behaviour of the tsunami propagation near the coastline after the earthquake ground shaking occurred.