Computational Dispersion Properties of 3D Staggered Grids for a Nonhydrostatic Anelastic System

Abstract

Computational dispersion properties of centered-difference schemes, in terms of frequency and group velocity components, are examined for an anelastic system using a variety of candidates for practically meaningful staggered 3D grids. The numerical analysis is done for dry nonhydrostatic inviscid gravity?inertia wave equations in a Boussinesq system, linearized about a statically stable resting base state with and without Coriolis force. The most advantageous 3D grids are obtained by combining the best horizontal grids, such as the Eliassen and Arakawa C grids, with the best vertical grids, such as the Lorenz and Charney?Phillips grids, and their time-staggemd versions. These best staggered 3D grids provide twice the effective spatial resolution of the regular (unstaggered) 3D grid. The obtained results provide practical guidance for the optimal choice of a grid for anelasfic mesoscale atmospheric models.