| The shallow water equations are a simplified form of the momentum and continuity equations in the Navier-Stokes system. They are used in many atmospheric models because the solution mimics the horizontal aspects of the atmospheric dynamics, and the simplicity of the equations make them useful for numerical experiments. Further, relaxing the hydrostatic assumption yields a full 3D model. This study describes a high-order element-based Galerkin method for the global shallow water equations using absolute vorticity, divergence, and fluid depth (atmospheric thickness) as the prognostic variables.;The numerical method employed to solve the shallow water system is based on the discontinuous Galerkin and spectral element methods. The discontinuous Galerkin method, which is inherently conservative, is used to solve the equations governing two conservative variables -- absolute vorticity and atmospheric thickness (equivalent to mass). The spectral element method is used to solve the divergence equation and the Poisson equations for the velocity potential and the stream function. Time integration is done with an explicit strong stability-preserving second-order Runge-Kutta scheme and the wind field is updated directly from the vorticity and divergence at each stage.;The method is scalable across large distributed memory parallel computers and parallelization techniques are discussed. The computational domain is the cubed sphere, a grid obtained by inscribing a cube in a sphere and projecting points from the surface of the sphere onto the faces of the cube. The domain is free of singularities and well-suited for parallel computing.;A stable steady-state test is run and convergence results are provided, showing that the method is high-order accurate. Additionally, two tests without analytic solutions are run with comparable results to previous high-resolution runs found in the literature. |
