High-order Galerkin methods for scalable global atmospheric models

Three different high-order finite element methods are used to solve the advection problem—two implementations of a discontinuous Galerkin and a spectral element (high-order continuous Galerkin) method. The three methods are tested using a 2D Gaussian hill as a test function, and the relative L2L2 errors are compared. Using an explicit Runge–Kutta time stepping scheme, all three methods can be parallelized using a straightforward domain decomposition and are shown to be easily and efficiently scaled across multiple-processor distributed memory machines. The effect of a monotonic limiter on a DG scheme is demonstrated for a non-smooth solution. Additionally, the necessary geometry for implementing these methods on the surface of a sphere is discussed.