High order difference schemes with reduced dispersion for hyperbolic differential equations

摘要

We investigate difference schemes for systems of first order hyperbolic differential equations in two space dimensions, possessing the following characteristics: 1.The spatial discretizations are fourth order accurate.2.The time discretization is of explicit Runge-Kutta type and is also fourth order accurate.3.The scaled stability boundary is approximately 122.4.The weights in the space discretizations and the Runge-Kutta parameters can be adapted in order to reduce the dispersion of dominant Fourier components.This method is illustrated by applying it to the shallow water equations simulating the motion of water in a shallow sea due to tidal forces. Since in such problems the dominant frequencies in the solution are known in advance, the method can take fully advantage of the possibility to tune the various parameters to these dominant frequencies.