Journal cover Journal topic
Geoscientific Model Development An interactive open-access journal of the European Geosciences Union
Geosci. Model Dev., 7, 2803-2816, 2014
© Author(s) 2014. This work is distributed
under the Creative Commons Attribution 3.0 License.
Development and technical paper
27 Nov 2014
The spectral element method (SEM) on variable-resolution grids: evaluating grid sensitivity and resolution-aware numerical viscosity
O. Guba1, M. A. Taylor2, P. A. Ullrich3, J. R. Overfelt2, and M. N. Levy4 1Department of Mathematics and Statistics, University of New Mexico, Albuquerque, New Mexico, USA
2Sandia National Laboratories, Albuquerque, New Mexico, USA
3Department of Land, Air and Water Resources, University of California Davis, Davis, California, USA
4National Center for Atmospheric Research, Boulder, Colorado, USA
Abstract. We evaluate the performance of the Community Atmosphere Model's (CAM) spectral element method on variable-resolution grids using the shallow-water equations in spherical geometry. We configure the method as it is used in CAM, with dissipation of grid scale variance, implemented using hyperviscosity. Hyperviscosity is highly scale selective and grid independent, but does require a resolution-dependent coefficient. For the spectral element method with variable-resolution grids and highly distorted elements, we obtain the best results if we introduce a tensor-based hyperviscosity with tensor coefficients tied to the eigenvalues of the local element metric tensor. The tensor hyperviscosity is constructed so that, for regions of uniform resolution, it matches the traditional constant-coefficient hyperviscosity. With the tensor hyperviscosity, the large-scale solution is almost completely unaffected by the presence of grid refinement. This later point is important for climate applications in which long term climatological averages can be imprinted by stationary inhomogeneities in the truncation error. We also evaluate the robustness of the approach with respect to grid quality by considering unstructured conforming quadrilateral grids generated with a well-known grid-generating toolkit and grids generated by SQuadGen, a new open source alternative which produces lower valence nodes.

Citation: Guba, O., Taylor, M. A., Ullrich, P. A., Overfelt, J. R., and Levy, M. N.: The spectral element method (SEM) on variable-resolution grids: evaluating grid sensitivity and resolution-aware numerical viscosity, Geosci. Model Dev., 7, 2803-2816, doi:10.5194/gmd-7-2803-2014, 2014.
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