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.
Highlights
Tsunamis are ocean water surface waves generated by undersea earthquakes, landslides, volcanic eruptions or even meteoric impact on water surfaces
The primary objective of this study is to develop a highly efficient and relatively accurate two-dimensional finite difference model to simulate the propagation of distant tsunamis over varying topography
4.1 Tsunami Propagation over Constant Depth Regions In order to test the applicability of the present model, the propagation of tsunamis is first simulated with an initial Gaussian shape of the water surface for the case of various constant water depths, and the computed free surface displacements are compared with the analytical solutions of the linear Boussinesq equations (Carrier 1991)
Summary
Tsunamis are ocean water surface waves generated by undersea earthquakes, landslides, volcanic eruptions or even meteoric impact on water surfaces. The physical dispersion is compensated by the numerical dispersion introduced by the truncation error of the numerical scheme This can be done only if the grid size is appropriately selected for the given water depth and the time step satisfying the criterion proposed by Imamura et al (1988). Yoon (2002) developed a new finite difference scheme that uses a uniform grid, but the actual computations are made on a hidden grid of variable size determined from the conditions proposed by Imamura et al (1988) This model satisfies local dispersion relationships of waves for a slowly varying topography. These difficulties can be solved by nesting the near-field model such as full Boussinesq equation model or shallow water equation model with a finer mesh system to the present transoceanic model as described in Yoon (2002)
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