The tsunami generated by the Great East Japan Earthquake (GEJE) caused serious damage to the coastal areas of the Tohoku district. Numerical simulations are used to predict damage caused by tsunamis. Shallow-water equations are generally used in numerical simulations of tsunami propagation from the open sea to the coast. This research focuses on viscous shallow-water equations and attempts to generate a computational method using finite-element techniques based on the previous investigations of Kanayama and Ohtsuka (1978). First, the viscous shallow-water equation system is derived from the Navier-Stokes equations, based on the assumption of hydrostatic pressure in the direction of gravity. The derived equations have the horizontal viscosity term hereditary from the original Navier-Stokes equations. Next, a numerical finite element scheme is shown. Finally, tsunami simulations of Tohoku-Oki are shown using the above-mentioned approach. Our main concern in this chapter is how to set the boundary condition on the open boundary.
Part of the book: Tsunami