Analysis of the anisotropy of finite difference schemes

Abstract

Numerical differencing schemes are subject to dispersive and dissipative errors, which in one dimension are functions of wavenumber. When these schemes are applied in two or three dimensions, the errors become functions of both wavenumber and the direction of wave propagation. Spectral analysis and numerical examples using the scalar advection equation are used to assess two finite difference schemes on two-dimensional grids of varying aspect ratio. It is shown that waves can not only propagate at the wrong speed-as per the dispersive errors seen in the one dimensional case-but also in the wrong direction.