Adaptive numerical modeling of tsunami wave generation and propagation with freefem++

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.