Discontinuous Galerkin Method for Atmospheric Modeling

Ram Nair

NCAR Scientific Computing Division

Recent paradigm shifts in large-scale scientific computing have motivated investigations into numerical methods which are more suitable for distributed-memory parallel computing.  Discontinuous Galerkin (DG) method, a hybrid approach combining the finite-element and the finite-volume methods, is an ideal numerical method to meet this requirement for atmospheric modeling. An efficient and scalable DG shallow water model on the cubed-sphere is developed, within the High-Order Method Modeling Environment (HOMME) framework at SCD/NCAR. The continuous flux form nonlinear shallow water equations in curvilinear coordinates are used. Spatial discretization is a nodal or modal basis set of Legendre polynomials. Fluxes along internal element interfaces are approximated by a Lax-Friedrichs scheme. A third-order total variation diminishing Runge-Kutta scheme is applied for time integration, without any filter or limiter. The standard shallow-water test suite of Williamson et al. (1992, JCP) is used to validate the model and it is observed that the numerical solutions are comparable to or even better than a high-order spectral element model.  There are no spurious oscillations in a test case where zonal flow impinges a mountain, and the model conserves mass to machine precision.