Adaptive Numerical Modelling of Tsunami Wave Generation and Propagation with FreeFem++

Georges Sadaka; Denys Dutykh

doi:10.20944/preprints202008.0616.v1

Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Version 1 : Received: 26 August 2020 / Approved: 27 August 2020 / Online: 27 August 2020 (12:17:44 CEST)

A simplified nonlinear dispersive system of BBM-type, initially derived by D. Mitsotakis, is employed here in order to model the generation and propagation of surface water waves over variable bottom. The simplification consists in applying the so-called Boussinesq approximation. Using the finite element method and the FreeFem++ software, we solve numerically this system 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 rather as a tutorial paper even if it contains the description of completely new adaptation techniques.

tsunami wave; finite elements; mesh adaptation; domain adaptation; co-seismic displacements; tsunami wave energy; FreeFem++; unstructured meshes

MATHEMATICS & COMPUTER SCIENCE, Numerical Analysis & Optimization

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Adaptive Numerical Modelling of Tsunami Wave Generation and Propagation with FreeFem++

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