Development of a Scalable Global Discontinuous Galerkin Atmospheric Model

An efficient and scalable global discontinuous Galerkin atmospheric model (DGAM) on the sphere is developed. The continuous flux form of the nonlinear shallow water equations on the cubed-sphere (in curvilinear coordinates) are developed. Spatial discretization is a nodal basis set of Legendre polynomials. Fluxes along internal element interfaces are approximated by a Lax-Friedrichs scheme. A third-order strong stability preserving Runge-Kutta scheme is applied for time integration. The standard shallow water test suite of Williamson et al. (1992) is used to validate the model. It is observed that the numerical solutions are accurate, the model conserves mass to machine precision, and there are no spurious oscillations in a test case where zonal flow impinges a mountain. The serial execution time of the high-order nodal DG scheme presented here is half that of the modal version DG scheme. Development time was substantially reduced by building the model in the High Order Method Modeling Environment (HOMME) developed at the National Center for Atmospheric Research (NCAR). Performance and scaling data for the steady state geostrophic flow problem Williamson et al. (1992) is presented. Sustained performance of 8% of peak is observed on 2048 processor of a IBM Blue Gene/L supercomputer.