Development and Evaluation of a Hydrostatic Dynamical Core Using the Spectral Element/Discontinuous Galerkin Methods

摘要

In this paper, we present a dynamical core for the atmospheric primitive hydrostatic equations using a unified formulation of spectral element (SE) and discontinuous Galerkin (DG) methods in the horizontal direction with a finite difference (FD) method in the radial direction. The CG and DG horizontal discretization employs high-order nodal basis functions associated with Lagrange polynomials based on Gauss-Lobatto-Legendre (GLL) quadrature points, which define the common machinery. The atmospheric primitive hydrostatic equations are solved on the cubed-sphere grid using the flux form governing equations three-dimensional (3D) Cartesian space. By using Cartesian space, we can avoid the pole singularity problem due to spherical coordinates and this also allows us to use any quadrilateral-based grid naturally. In order to consider an easy way for coupling the dynamics with existing physics packages, we use a FD in the radial direction. The models are verified by conducting conventional benchmark test cases: the Rossby-Haurwitz wavenumber 4 Jablonowski-Williamson tests for balanced initial state and baroclinic instability, and Held- Suarez tests. The results from those tests demonstrate that the present dynamical core can produce numerical solutions of good quality comparable to other models.