A MODIFIED LEAP-FROG SCHEME FOR LINEAR SHALLOW-WATER EQUATIONS

摘要

A new leap-frog finite difference scheme is proposed to solve the linear shallow-water equations. The accuracy of propagation speed in diagonal direction is improved through the inclusion of frequency dispersion correction terms in linear shallow-water equations. The two-dimensional linear Boussinesq equations are recovered when the proper spatial grid size and time step size are chosen. As a result, more accurate simulation can be made for the transoceanic propagation of tsunamis. The scheme is stable when the Courant number is less than 0.866.