  A nonhydrostatic dynamical core has been developed by using the multi-moment
finite volume method that ensures the rigorous numerical conservation. To
represent the spherical geometry free of polar problems, the cubed-sphere grid
is adopted. A fourth-order multi-moment discretization formulation is applied
to the nonhydrostatic governing equations cast in local curvilinear coordinates
on each patch of cubed sphere through a gnomonic projection. In vertical
direction, the height-based terrain-following grid is used to represent the
topography. To get around the CFL stability restriction imposed by relatively
small grid spacing in the vertical direction, the dimensional-splitting time
integration using the HEVI (Horizontal Explicit and Vertical Implicit) strategy
is implemented by applying the IMEX Runge-Kutta scheme. The proposed dynamical
core preserves the fourth-order accuracy in spherical geometry and has been
verified by the widely-used benchmark tests. The results of our numerical
experiments show that the present numerical core has superior solution quality
and great practical potential as a platform for atmospheric models. A new
unified model for numerical weather prediction and global atmospheric
circulation simulation based on this dynamical core is under development.
