Open AccessA finite-element numerical approach for modeling tsunamis
Author(s) -
Stefano Tinti,
Ivan Gavagni,
A. Piatanesi
Publication year - 1994
Publication title -
annals of geophysics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.394
H-Index - 60
eISSN - 2037-416X
pISSN - 1593-5213
DOI - 10.4401/ag-4189
Subject(s) - discretization , finite element method , nonlinear system , shallow water equations , grid , spacetime , boundary value problem , numerical integration , mathematics , boundary (topology) , computer science , geology , mathematical analysis , geometry , physics , quantum mechanics , thermodynamics
A numerical scheme suitable for modeling tsunamis is developed and tested against available analytical solutions. The governing equations are the shallow water nonlinear nondispersive equations that are known to be appropriate for tsunami generation and propagation in coastal waters. The integration scheme is based on a finite-element space discretization, where the basic elements are triangles and the shape functions are linear. The time integration is a double step algorithm that is accurate to the second order in the time step ?t. The boundary conditions are pure reflectivity and complete transmissivity on the solid and open boundaries respectively and are implemented by modifying the time integration scheme in a suitable way. The model performance is evaluated by comparing the results with the analytical solutions in selected cases and is quite satisfactory, even when the grid has a coarse spatial resolution