Methodology for studying the numerical speed of sound in finite differences schemes

Abstract

The space and time discretization inherent to all FDTD schemes introduce non-physical dispersion errors, i.e. deviations of the speed of sound from the theoretical value predicted by the governing Euler differential equations. A generalmethodology for computing this dispersion error via straightforward numerical simulations of the FDTD schemes is presented. The method is shown to provide remarkable accuracies of the order of 1/1000 in a wide variety of twodimensional finite difference schemes.