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A nonhydrostatic dynamical core has been developed by using the multi-momentfinite volume method that ensures the rigorous numerical conservation. Torepresent the spherical geometry free of polar problems, the cubed-sphere gridis adopted. A fourth-order multi-moment discretization formulation is appliedto solve the governing equations cast in the local curvilinear coordinates oneach patch of cubed sphere through a gnomonic projection. In verticaldirection, the height-based terrain-following grid is used to deal with thetopography and a conservative finite difference scheme is adopted for thespatial discretization. The dynamical core adopts the nonhydrostatic governingequations. To get around the CFL stability restriction imposed by sound wavepropagation and relatively small grid spacing in the vertical direction, thedimensional-splitting time integration algorithm using the HEVI(horizontally-explicit and vertically-implicit) strategy is implemented byapplying the IMEX (implicit-explicit) Runge-Kutta method. The proposed modelwas checked by the widely-used benchmark tests in this study. The numericalresults show that the multi-moment model has superior solution quality andgreat practical potential as a numerical platform for development of theatmospheric general circulation models.

A nonhydrostatic atmospheric dynamical core on cubed sphere using hybrid  multi-moment finite-volume/finite difference methods: formulations and  preliminary tests