A dispersion-corrected finite element model for simulation of distant tsunamis

Abstract

A dispersion-corrected finite element model is developed to simulate the propagation of distant tsunamis over a slowly varying topography. A linear Boussinesq wave equation is solved to consider the dispersion effect of tsunami waves by employing a linear triangular mesh and an explicit time integration scheme. The numerical dispersion associated with the explicit scheme is minimized by adjusting both the mesh size and the dispersion-correction parameter. In order to test the present model, numerical simulations for the propagation of an initial Gaussian hump over various constant depths are conducted,and the numerical results are compared with analytical solutions of the linear Boussinesq equations. The present model is also tested for the propagation of tsunamis over a sub merged circular shoal and the numerical results are compared with the numerical solutions obtained using an other Boussinesq model. The present model is shown to be efficient and considerably accurate.