Numerical study of the effects of tsunamis using a finite element method

Effects of tsunamis generated in water areas surrounding Japan are studied numerically. Partial differential equations consisting of momentum equations and a continuity equation are reduced to a system of ordinary differential equations with discretisation based on a finite element mesh. An ordinary differential equation solver is applied to the resultant system to generate numerical solutions. Depth data formulated in terms of longitude and latitude in the horizontal direction are transformed to generate input data in terms of projected coordinates by the Gauss--Kruger projection. Numerical results are visualised, and effects of tsunamis such as wave heights and propagation speeds are illustrated. Numerical techniques to simulate tsunamis are described, and numerical results are introduced. References I. Aida. Numerical experiments for the tsunamis generated off the coast of the Nankaido district. Bull. Earthquake Research Institute, 56:713--730, 1981. J. D. Lambert. Computational Methods in Ordinary Differential Equations. John Wiley and Sons, Chichester, 1973. L. Mansinha and D. E. Smylie. The displacement fields of inclined faults. Bulletin of the Seismological Society of America, 61(5):1433--1440, October 1971. A. R. Mitchell and R. Wait. The Finite Element Method in Partial Differential Equations. John Wiley and Sons, Chichester, 1977. Geospatial Information Authority of JAPAN. The Niigata--Kobe tectonic zone. http://cais.gsi.go.jp/Virtual_GSI/Tectonics/Niigata_Kobe/niigata_kobe.html, January 14, 2011. T. Okamoto, M. Kawahara, N. Ioki, and H. Nagaoka. Two-dimensional wave run-up analysis by selective lumping finite element method. International Journal for Numerical Methods in Fluids, 14(1992):1219--1243, 1992. N. Shuto, F. Imamura, S. Koshimura, K. Satake, and H. Matsutomi. Encyclopedia of Tsunami. Asakura Shoten, 2007 (in Japanese)