Abstract
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.
Highlights
In climate and weather forecast applications, there is an increased demand for variable-resolution capabilities
We focus on the multi-resolution approach made possible by the spectral element method (SEM)
We evaluate this approach using the shallow-water equations on the sphere with the two-dimensional version of High-Order Method Modeling Environment (HOMME)’s spectral element dynamical core
Summary
In climate and weather forecast applications, there is an increased demand for variable-resolution capabilities. We use the shallow-water equations to show some deficiencies with this approach and that better results are obtained with a tensor-based hyperviscosity operator, which can better represent both length scales within non-square spectral elements. Grid smoothing is performed via straightforward application of spring dynamics in threedimensional geometry (Persson and Strang, 2004) Grids obtained via this technique exhibit several improved characteristics, including greater uniformity in the transition region, and elements with angles that are closer to 90 ◦. In the refined region, the multi-resolution simulation can resolve the same scales as the uniform xhigh resolution simulation With hyperviscosity, this requires a resolutionaware formulation, which locally matches what would be used in a uniform resolution simulation. The rest of the paper is organized as follows: in Sect. 2, we introduce two dissipation mechanisms – scalar and tensor hyperviscosity; in Sect. 3, we discuss grid refinement techniques; in Sect. 4, we describe shallow-water test cases; in Sect. 5, we present numerical results
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
