Adaptive numerical modelling of tsunami wave generation and propagation with FreeFem++
Résumé
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.
Domaines
Mécanique des fluides [physics.class-ph] Dynamique des Fluides [physics.flu-dyn] Physique Atmosphérique et Océanique [physics.ao-ph] Physique Classique [physics.class-ph] Physique Numérique [physics.comp-ph] Physique Générale [physics.gen-ph] Océan, Atmosphère Géophysique [physics.geo-ph] Océanographie Equations aux dérivées partielles [math.AP] Analyse numérique [math.NA] Modélisation et simulation Logiciel mathématique [cs.MS] Analyse numérique [cs.NA] Systèmes Solubles et Intégrables [nlin.SI]
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