Dispersion-Correction Finite Difference Model for Simulation of Transoceanic Tsunamis

Abstract

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.

Capturing Physical Dispersion Using a Nonlinear Shallow Water Model

“…The accuracy of the numerical solution of NLSWEs in NAMI DANCE is tested through simulation of a Gaussian hump tsunami as initial free surface [5,6] on a constant uniform bottom. In this section, the water surface displacement at certain time steps along horizontal, vertical and diagonal directions are computed and compared with the analytical solution of the linear BTEs [3,27].…”

“…In a separate study, Yoon et al in 2007 [6] improved the numerical scheme to reproduce the physical dispersion effects and tested on a uniform bottom domain with different water depths [6]. Shown in Figure 4 (Figure 4e,f).…”

“…Shown in Figure 4 (Figure 4e,f). In the second case, the grid size is selected as ∆x = 2086 m according to [6]. Figure 4a [3] results, since the dispersion correction term in the diagonal direction is not considered in the solutions.…”

“…He proposed a hidden grid system in which the local water depth determines the grid size for the capturing of dispersion effects. Subsequently, Yoon et al [6] developed another scheme using an explicit finite difference method to solve the linearized BTEs and to improve the physical frequency dispersion effects. The linearized BTEs model considers the frequency dispersion effects from shallow to intermediate water regimes accurately [7][8][9][10][11][12][13][14].…”

“…A brief explanation of NAMI DANCE is presented in the next section. In this study, the ability of NAMI DANCE to capture dispersion effects is examined with several bathymetry profiles or case studies taken from the literature [5,6]. The bathymetry profiles are: (i) uniform bottom, (ii) slowly varying depth and (iii) submerged circular shoal.…”