Atmospheric flow modelling using some finite difference methods

Abstract

In this work, we compare the performance of some finite difference methods in order to solve an advection-diffusion equation which models atmospheric flows. This flow problem was solved by Clancy [3] using Forward-Time Central Space (FTCS) scheme and it is a rather challenging problem to simulate due to large errors in phase and amplitude which are generated especially over long propagation times. We use the following methods namely, FTCS, Lax-Wendroff (LW), Crank-Nicolson (CN) and a non-standard finite difference scheme (NSFD). To improve the results, we derive a new composite scheme consisting of three applications of Lax-Wendroff followed by one application of NSFD. The latter acts likes a filter to remove the dispersive oscillations from Lax-Wendroff. We further improve the composite scheme by computing the optimal temporal step size which minimises the dispersion error.