Analysis of anisotropy of numerical wave solutions by high accuracy finite difference methods

Fourier analysis is used to quantitatively assess the resolution, and in particular the isotropy of wave solution using finite difference spatial discretization schemes along with fourth order Runge–Kutta temporal scheme. Aspect ratio of the grid in two-dimension, along with the angle of wave propagation are the parameters varied to qualitatively and quantitatively assess the anisotropy of the solutions for (a) a skewed one-dimensional wave convecting in two-dimensions following the standard convection equation and (b) a wave propagating following the two-dimensional linearized rotating shallow water equations. Results show the effect of changing the aspect ratio and the propagation angle on the directional nature of the solution as obtained by different methods for the above non-dispersive and dispersive wave system.