A global nonhydrostatic dynamical core on cubed sphere using multi-moment finite volume method: formulation and preliminary test

TL;DR

This paper introduces a high-order nonhydrostatic dynamical core on a cubed-sphere grid using a multi-moment finite volume method, demonstrating its accuracy and potential for atmospheric modeling.

Contribution

It develops a fourth-order multi-moment discretization for nonhydrostatic equations on a cubed-sphere, ensuring conservation and high accuracy in spherical geometry.

Findings

Verified with benchmark tests showing high solution quality

Achieved fourth-order accuracy in spherical coordinates

Implemented HEVI scheme for vertical stability

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 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.