Abstract
The tsunami generated by the Great East Japan Earthquake 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 (Coast Eng Jpn 21:157–171, 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. Next a numerical scheme is shown. Finally, tsunami simulations of Hakata Bay and Tohoku-Oki are shown using the approach.
Highlights
The coastal areas of the 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]
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 simulated by a finite element computation
Summary
This appendix summarizes contents of Kanayama and Ushijima [15,16] for selfcontainedness. First we introduce a linearized system [15] of the viscous shallowwater equations. After the derivation of the model problem, we reformulate the linear initial-boundary value problem within the framework of Hilbert space theory. The existence and uniqueness of the solution of the reformulated problem follows from Hille–Yosida theorem. This appendix concerns the finite element analysis of linearized viscous shallow-water equations [16]. The derivation of a linearized viscous shallow-water system Let us consider the following nonlinear stationary problem. We assume the existence of a sufficiently smooth solution pair {U0, ζ0} of the above problem (16)–(18). As a model linear initial-boundary value problem, we adopt the following linearized viscous shallow-water equations (20) and (21):. Conditions (17), (18) and (19) will be assumed, and (16) will not be used
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