The spectral element method (SEM) on variable-resolution grids: evaluating grid sensitivity and resolution-aware numerical viscosity
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 h...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Copernicus Publications
2014-11-01
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| Series: | Geoscientific Model Development |
| Online Access: | http://www.geosci-model-dev.net/7/2803/2014/gmd-7-2803-2014.pdf |
| Summary: | 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. |
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| ISSN: | 1991-959X 1991-9603 |