Grid nesting for dispersion-correction finite difference model for tsunami simulation

Abstract

A grid nesting scheme for dispersion-correction finite difference model is developed to simulate the propagation of distant tsunamis. The dispersion-correction finite difference model developed by Yoon et al. (2007) solves a linear Boussinesq-type wave equation with correct dispersion effects for relatively long waves. However, the dispersion-correction becomes degraded when the grid size is much greater than the water depth. To extend the applicability of the finite difference model a nesting between coarse and fine grids is indispensable. The present grid nesting scheme employs the third order interpolation in space and the second order interpolation in time. In order to examine the applicability of the present grid nesting scheme, the propagation of tsunamis is simulated for a submerged circular shoal. The numerical results are compared with the numerical solutions of the linearized Boussinesq equations. The comparisons show that the agreements are satisfactory.