Abstract
A simplified nonlinear dispersive Boussinesq system of the Benjamin–Bona–Mahony (BBM)-type, initially derived by Mitsotakis (2009), is employed here in order to model the generation and propagation of surface water waves over variable bottom. The simplification consists in prolongating the so-called Boussinesq approximation to bathymetry terms, as well. Using the finite element method and the FreeFem++ software, we solve this system numerically for three different complexities for the bathymetry function: a flat bottom case, a variable bottom in space, and a variable bottom both in space and in time. The last case is illustrated with the Java 2006 tsunami event. This article is designed to be a pedagogical paper presenting to tsunami wave community a new technology and a novel adaptivity technique, along with all source codes necessary to implement it.
Highlights
Tsunami waves represent undeniably a complex natural process
This article is designed as a tutorial paper in order to show to the readers how these processes can be modeled in the framework of the FreeFem++, which is a free software
The FreeFem++ programming framework offers the advantage of hiding all technical issues related to the implementation of the finite element method [2]
Summary
Tsunami waves represent undeniably a complex natural process. they represent a major risk for exposed coastal areas, including the local populations, infrastructure, etc. This class of models is distinguished by the application of the so-called B OUSSINESQ approximation [7] They can be used to study a variety of water wave phenomena in harbors, coastal dynamics, and, tsunami generation and propagation problems [8,9,10,11,12]. With this code, we simulate the propagation of a tsunami-like wave generated by the moving bottom (e.g., an earthquake). We consider the J AVA island region with real world bathymetry We apply this solver to simulate a realistic example of a tsunami wave near the J AVA island which took place in 2006.
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