The numerical modelling of long wave propagation in the framework of non-linear dispersion models

Abstract

The work is devoted to the questions of numerical modelling of long wave propagation, in particular tsunami waves, in the framework of non-linear dispersion models of the Boussinesq and Korteweg-de Vries type. The first part of the work includes a classification of some known mathematical models, in terms of dispersion correlation, phase and group velocities. Problems arising on the construction of finite-difference approximations of non-linear dispersion models are discussed in the second part of the work, special attention is given to the questions of constructing discrete boundary conditions. In the conclusion the results obtained in the course of numerical experiments and estimation of specifics of finite-difference models, and the contribution of non-linear dispersion effects in the process of wave propagation in the coastal zone, are discussed. The results of calculations of tsunami wave propagation in a wave tube with real bathymetry, are given.