High-order Galerkin methods for scalable global atmospheric models

  • Authors:

  • Michael N. Levy;Ramachandran D. Nair;Henry M. Tufo

  • Affiliations:

  • Department of Applied Mathematics, University of Colorado at Boulder, 526 UCB Boulder, CO 80309-0526, USA;Institute for Mathematics Applied to Geosciences (IMAGe), The National Center for Atmospheric Research, P.O. Box 3000 Boulder, CO 80307-3000, USA;Computational & Information Systems Laboratory (CISL), The National Center for Atmospheric Research, P.O. Box 3000 Boulder, CO 80307-3000, USA

  • Venue:
  • Computers & Geosciences
  • Year:
  • 2007

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Abstract

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 L"2 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.