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

TL;DR

This paper introduces a nonhydrostatic atmospheric dynamical core on a cubed-sphere grid using multi-moment finite-volume methods, demonstrating high accuracy and stability through benchmark tests for potential use in general circulation models.

Contribution

It develops a novel nonhydrostatic dynamical core employing multi-moment finite-volume methods on a cubed-sphere grid with a hybrid time integration scheme, improving conservation and stability.

Findings

Achieved high solution accuracy in benchmark tests.

Demonstrated stability with the HEVI-IMEX time integration.

Showed potential for development of atmospheric general circulation models.

Abstract

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 solve the governing equations cast in the 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 deal with the topography and a conservative finite difference scheme is adopted for the spatial discretization. The dynamical core adopts the nonhydrostatic governing equations. To get around the CFL stability restriction imposed by sound wave propagation and 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 superior solution quality and great practical potential as a numerical platform for development of the atmospheric general circulation models.