**4. Concluding remarks**

In this study, the viscous shallow-water equations have again been derived from the Navier-Stokes equations in which the hydrostatic pressure in the direction of gravity is assumed. Tsunami propagation is then simulated by a finite-element computation. In the study of

**Figure 7.** Structural analysis in the case of tsunami attack [9].

Kanayama and Dan [9] using the Hakata Bay model, in which the tsunami-generating area was taken to be the epicenter of the West off Fukuoka Prefecture Earthquake (2005), tsunami propagation from the open sea to the coastal area might be produced. This is an example in which the conventional open boundary condition Eq. (10) is still valid. In this chapter, however, in the second Tohoku-Oki model, the open boundary condition is changed from Eq. (10) to Eq. (16) to overcome artificial reflection. In addition, we have reconstructed a system in which the tsunami arrival time and the wave height at the time of tsunami attack can be obtained from numerical results. Since our analysis takes the viscosity term into account, this study can also be considered to be a preliminary study for future planned stress analyses of tsunamis (see **Figure 7**). We still want to check whether the hydrostatic pressure is always the dominant force in the case of tsunami attack compared with other forces including the viscous force.
