Abstract
Different grid distributions or different equidistantly subdivided coordinate frames, nonlinearly depending on each other, imply different truncation errors, thus different results. This is well known, and (for given coordinates) discussions of truncation errors of difference approximations to differential systems are obligatory. However, it is also customary to use altitude as well as pressure for the vertical coordinate, to use equi-angular polar-coordinate grids in addition to (Kurihara-type) equi-area grids, to use σ-coordinates for avoiding difficulties with a lower topographic boundary, or even to use transformed coordinates in order to parameterize subgrid structures. The reasons of numerical simplicity and stability and of adaptation to special physical structures usually motivate the special choice.
The deviations due to grids of equal degree of resolution but with different types of distributions, and their importance, are studied for some examples of initial-value differential problems, and some inferences are given. For example, the fulfilment of a few conservative properties (as mass and energy) proves to be quite insufficient to overcome the deviations. Instead of grids with special distributions, spectral representation and orthogonal truncation processes are employed in order to achieve the greatest accuracy (like separation from truncation errors due to differencing) and utility.
