**1. Introduction**

The coastal areas of Tohoku district suffered serious damage from the tsunami caused by the 2011 off the Pacific Coast of Tohoku Earthquake that occurred on March 11, 2011 [1, 2]. Numerical simulations are used to develop disaster-prevention measures to deal with such tsunami disasters. They are also used to predict potential future tsunami disasters, to design disasterprevention facilities such as coastal breakwaters and levees and to predict tsunami attacks immediately after an earthquake occurs [3, 4]. The Central Disaster Prevention Council [5] prepares a basic disaster prevention plan and participates in the determination of important

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

disaster-prevention matters. If the Tonankai-Nankai earthquake occurs, it may cause considerable damage. Consequently, the council has been performing numerical calculations to predict wave height and arrival time when tsunami reaches the coast.

In this chapter, to let it be self-contained, the viscous shallow-water equations are again derived from the Navier-Stokes equations in which the hydrostatic pressure in the direction of gravity is assumed. In the numerical analysis of tsunamis, the viscosity term is often omitted or simply added [6, 7]. In this study, however, a computational method that does not omit the viscosity term is adopted, that is, because it enables more rigorous analysis to be performed and we intend to include the viscosity term in future stress analysis of tsunamis. The approximation scheme [8] is given below and simulation results [9] for a Tohoku-Oki model are again presented for self-containing. Our main concern in this chapter is how to set the boundary condition on the open boundary, which is completely changed to a new one.
