Explicit FE Modeling of Indian Ocean Tsunami Using Unstructured Mesh

Abstract

Propagation of the Indian Ocean Tsunami has been simulated using Shallow Water Equations. The three dimensional shallow water equations are reduced, by a process of vertical integration relating to the pertinent variables, to obtain equivalent equations in two dimensions. An Unstructured Explicit Finite Element Model is adopted for solution of the governing equations. The method of weighted residuals, in particular the Galerkin method, coupled with the finite element discretisation technique is then used to obtain a set of integral equations which can be assembled in a matrix form. The domain is discretised with 9-noded lagrangian isoparametric elements. Simpson’s 9-point integration rule, used to integrate over the 9-noded elements, leads to an explicit form of the assembled matrix (diagonal matrix). The above mentioned Unstructured Explicit Finite Element Method requires less computational resources and ensures higher order representation of the solution.
A computational domain (Bay of Bengal and northern part of the Indian Ocean) has been considered for simulation with an initial disturbance which resembles the type and location of the 2004 Indian Ocean Tsunami. The wave elevations and deformations as well as time of travel of tsunami are reproduced. The computed runup heights along Tamil Nadu coast of India were compared with the signature data and the agreement was found to be reasonable.