Numerical modelling of Tsunami wave equations

Abstract

This report investigates the modelling of tsunami wave using one dimensional shallow water equations (SWEs) by numerical methods namely finite difference method (FDM) and finite volume method (FVM). We have used one dimensional SWEs to model the water wave propagation i.e. we study the variation of water surface elevation with finite distance. We obtained the SWEs from Euler's equation of mass and momentum assuming a long wave approximation. First of all we approximate the SWEs using FDM and then by FVM for showing the behaviour of water surface elevation with distance. After approximating the SWEs using both the numerical method, results have been shown using different schemes viz. FDM as well as FVM. Moreover, in actual practice, we may have incomplete information about the variables being a result of errors in modelling, observations, or by applying different initial as well as boundary conditions etc. Rather than the particular value of water surface we may have only the bounds of the values. These bounds may be given in term of interval. Thus we have developed interval finite volume method (IFVM) also for approximating one dimensional SWEs to model tsunami wave with uncertain (interval) parameter. Next, numerical results have been shown using IFVM. Then a comparision study has been investigated to compare the results of both the method i.e. FDM and FVM. Finally all computed results are shown in terms of tables and plots.