Author(s)

F. Lasaponara, F. Camilli

Abstract

In this paper we propose a numerical model for the simulation of tsunami wave propagation in a coastal region. The model can simulate the wave transformation due to refraction, shoaling, diffraction and breaking phenomena that take place in the surf zone and can simulate the wet front progress on the mainland. The above mentioned model is based on the numerical integration of the Fully Non-linear Boussinesq Equations in the deep water region and of the Non-linear Shallow Water Equations in the surf zone. These equations are expressed in an integral contravariant formulation and are integrated on a generalized curvilinear boundary conforming grid that can reproduce the complex morphology of the coastline. The numerical integration of the model equations is implemented by a high order Upwind WENO numerical scheme that involves an exact Riemann Solver. For the simulation of the wet front progress on the dry bed, the exact solution of the Riemann problem for the wet-dry front is used. The capacity of the proposed model to simulate the wet front progress velocity is tested by numerically reproducing the dam-break problem on a dry bed. The capacity of the proposed model to correctly simulate the tsunami wave evolution and propagation on the coastal region is tested by numerically reproducing a benchmark test case about tsunami wave propagation on a conic island.

Keywords

coastal flooding, fully non-linear Boussinesq equations, non-linear shallow water equations, contravariant formulation, upwind WENO scheme, run up