Development of a high-order global dynamical core using the discontinuous Galerkin method for an atmospheric large-eddy simulation (LES) and proposal of test cases: SCALE-DG v0.8.0

Abstract

Focusing on the future global atmospheric simulations with a grid spacing of O(10-100 m), we developed a global nonhydrostatic atmospheric dynamical core with high-order accuracy by applying a discontinuous Galerkin method (DGM) for horizontal and vertical discretization. Furthermore, considering a global large-eddy simulation (LES), a Smagorinsky-Lilly turbulence model was introduced to the proposed global dynamical core in the DGM framework. By conducting several tests with various polynomial (p) orders, the impact of the high-order DGM on the accuracy of the numerical simulations of atmospheric flows was investigated. To show high-order numerical convergence, a few modifications were made in the experimental setup of existing test cases. In addition, we proposed an idealized test case to verify global-LES models, which is a global extension of an idealized planetary boundary layer (PBL) turbulence experiment performed in our previous studies. The error norms from the deterministic test cases, such as the linear-advection and gravity-wave tests, showed an optimal convergence rate achieved by an approximately p+1-order spatial accuracy when the temporal and round-off errors were sufficiently small. In the climatic test cases, such as the Held-Suarez test, the kinetic energy spectra indicated the advantage of effective resolution when large polynomial orders were used. In the LES experiment, the global model provided a reasonable vertical structure of the PBL and energy spectra because the results under shallow-atmosphere approximation reproduced those obtained in the plane computational domain well.