Computational properties of a new horizontal staggered grid

Abstract

This paper presents a new horizontal staggered grid (LE grid), which defines h at a gridpoint, and both u and v at the same mid-gridpoint along the x and y directions. A general method is used to deduce the dispersion relationships of describing inertia gravity waves on LE grid and Arakawa A―E grids, which are then compared with the analytical solution (AS) in resolved or under-resolved cases, using two-order central difference or four-order compact difference scheme from the frequency and group velocity. Results show that in both resolved and under-resolved cases, no matter whether two-order central difference or four-order compact dif-ference scheme is used, the frequency and group velocity discrete errors on LE grid in describing inertia gravity waves are smaller than those of Arakawa A―E grids. At the same time, it is only on LE or Arakawa grid C that the employment of a compact difference scheme of higher difference precision can improve their accuracy in describing inertia gravity waves. However, as for the other four grids (Arakawa A,B,D and E), when the difference precision increases, the accuracy of simulating inertia gravity waves decreases.