SUMMARYPart I of this work presents a detailed multi-methods comparison of the spatial errors associated with the one-dimensional 每nite di erence, 每nite element and 每nite volume semi-discretizations of the scalar advection-di usion equation. In Part II we extend the analysis to two-dimensional domains and also consider the e ects of wave propagation direction and grid aspect ratio on the phase speed, and the discrete and arti每cial di usivities. The observed dependence of dispersive and di usive behaviour on propagation direction makes comparison of methods more di cult relative to the one-dimensional results. For this reason, integrated (over propagation direction and wave number) error and anisotropy metrics are introduced to facilitate comparison among the various methods. With respect to these metrics, the consistent mass Galerkin and consistent mass control-volume 每nite element methods, and their streamline upwind derivatives, exhibit comparable accuracy, and generally out-perform their lumped mass counterparts and 每nite-di erence based schemes. While this work can only be considered a 每rst step in a comprehensive multi-methods analysis and comparison, it serves to identify some of the relative strengths and weaknesses of multiple numerical methods in a common mathematical framework.