Spurious numerical refraction

Abstract

AbstractThe purpose of this paper is to investigate the effect of a non‐uniform mesh in two dimensions (2D). A change in mesh size will, in general, result in spurious refraction (and reflection) which is entirely numerical (rather than physical) in origin. To facilitate the analysis, the mesh geometry has been highly simplified in that only a single change in mesh size is considered. The analysis is based on a finite element wave model.The domain consists of two conterminous regions discernible only by their different nodal spacings in the x‐direction. The interface between the two regions is internal to the mesh and is a straight line. The model is based upon the Crank‐Nicolson linear finite element scheme applied to the second order wave equation. The results of the analysis are confirmed by numerical experiments. It is shown that under particular numerical conditions total internal reflection may occur and when this is the case, the transmitted wave is evanescent. An analysis of the energy flux associated with the incident, reflected and trasmitted waves shows that energy is conserved across the interface between the two regions.