Mathematical and Numerical Analysis of a Tsunami Problem

Abstract

In this paper, we present a tsunami model based on the displacement of the lithosphere and the mathematical and numerical analysis of this model. More precisely, we give an existence and uniqueness result for a problem which models the flow and formation of waves at the time of a submarine earthquake in the vicinity of the coast. We propose a model which describes the behavior of the fluid using a bi-dimensional shallow-water model by means of a depth-mean velocity formulation. The ocean is coupled to the Earth's crust whose movement is assumed to be controlled on a large scale by plate equations. Finally, we give some numerical results showing the formation of a tsunami.

A new Savage–Hutter type model for submarine avalanches and generated tsunami

“…and, using the kinematic condition (16) and the boundary condition (22), the following equation is derived:…”

“…As a result, the momentum equation for the fluidized granular material does not contain any coupling terms between the two layers which should appear in the pressure gradient terms. Other systems, named active models, with a dynamic displacement of sea bed are used with a coupling between a shallow-water system and visco-elastic equations, see for instance [16], [17]. The interested reader is referred to [15] and [18] for references around Tsunamis and challenging modeling.…”