Dispersion-Correction Finite Difference Model for Simulation of Transoceanic Tsunamis

A finite difference numerical model, which can correctly consider dispersion effect of waves over a slowly varying water depth, is developed for the simulation of tsunami propagation. The present model employs a linear Boussinesq-type wave equation that can be solved more easily than typical Boussinesq equations. In the present model numerical dispersion is minimized by controlling the dispersion-correction parameter determined by the time step, grid size and local water depth. In order to examine the applicability of the present model to dispersive waves, the propagation of tsunamis is simulated for an initial water surface displacement of Gaussian shape for the cases of several constant water depths and a submerged circular shoal. The numerical results are compared with analytical solutions or numerical solutions of linearized Boussinesq equations. The comparisons show that satisfactory agreement is obtained.