Spectral transform solutions to the shallow water test set
Journal of Computational Physics
Journal of Computational Physics
The spectral element method for the shallow water equations on the sphere
Journal of Computational Physics
The Runge-Kutta discontinuous Galerkin method for conservation laws V multidimensional systems
Journal of Computational Physics
Terascale spectral element algorithms and implementations
SC '99 Proceedings of the 1999 ACM/IEEE conference on Supercomputing
Runge–Kutta Discontinuous Galerkin Methods for Convection-Dominated Problems
Journal of Scientific Computing
Terascale spectral element dynamical core for atmospheric general circulation models
Proceedings of the 2001 ACM/IEEE conference on Supercomputing
Nodal high-order discontinuous Galerkin methods for the spherical shallow water equations
Journal of Computational Physics
Semi-Implicit Spectral Element Atmospheric Model
Journal of Scientific Computing
Multiscale Geophysical Modeling Using the Spectral Element Method
Computing in Science and Engineering
Partitioning with Space-Filling Curves on the Cubed-Sphere
IPDPS '03 Proceedings of the 17th International Symposium on Parallel and Distributed Processing
Journal of Computational Physics
High-order Galerkin methods for scalable global atmospheric models
Computers & Geosciences
Journal of Computational Physics
Journal of Computational Physics
A Fully Implicit Domain Decomposition Algorithm for Shallow Water Equations on the Cubed-Sphere
SIAM Journal on Scientific Computing
Journal of Computational and Applied Mathematics
Journal of Computational Physics
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An efficient and scalable Discontinuous Galerkin shallow water model on the cubed sphere is developed by extending the transport scheme of Nair et al.The continuous flux form nonlinear shallow water equations 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 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. is used to validate the model.It is observed that the numberical 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.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 is presented. Sustained performance in excess of 10% of peak is observed out to 64 processors on a Linux cluster.