A nonhydrostatic atmospheric dynamical core on cubed sphere using multi-moment finite-volume method

Abstract

A nonhydrostatic dynamical core has been developed by using the multi-moment finite volume method that ensures the rigorous numerical conservation of mass in this study. To represent the spherical geometry free of the polar problems, the cubed-sphere grid is adopted. A fourth-order multi-moment discretization formulation is applied to solve the governing equations cast in the local curvilinear coordinates on each patch of the cubed sphere through a gnomonic projection. In the vertical direction, the height-based terrain-following coordinate is used to deal with the topography and a finite difference scheme, also assuring the conservation of mass, is adopted for the spatial discretization. The proposed dynamical core adopts the nonhydrostatic governing equations. To get around the CFL stability restriction imposed by the sound wave and the relatively small grid spacing in the vertical direction, the dimensional splitting time integration algorithm using the HEVI (horizontally-explicit and vertically-implicit) strategy is implemented by applying the IMEX (implicit-explicit) Runge-Kutta method. The proposed model was checked by the widely-used benchmark tests in this study. The numerical results show that the multi-moment model has the comparable solution quality in comparison with the existing advanced ones and the great practical potential as a numerical platform for development of the atmospheric general circulation models.