Simulation of shallow-water jets with a unified element-based continuous/discontinuous Galerkin model with grid flexibility on the sphere

We test the behavior of a unified continuous/discontinuous Galerkin (CG/DG) shallow water model in spherical geometry with curved elements on three different grids of ubiquitous use in atmospheric modeling: (A) the cubed-sphere, (B) the reduced latitude-longitude, and (C) the icosahedral grid. Both conforming and non-conforming grids are adopted including static and dynamically adaptive grids for a total of twelve mesh configurations. The behavior of CG and DG on the different grids are compared for a non-linear mid-latitude perturbed jet and for a linear case that admits an analytic solution. Because the inviscid solution on certain grids shows a high sensitivity to the resolution, the viscous counterpart of the governing equations are also solved and the results compared. The logically unstructured element-based CG/DG model described in this paper is flexible with respect to arbitrary grids. However, we were unable to define a best grid configuration that could possibly minimize the error regardless of the characteristic geometry of the flow. This is especially true if the governing equations are not regularized by the addition of a sufficiently large, fully artificial, diffusion mechanism, as will be shown. The main novelty of this study lies in the unified implementation of two element-based Galerkin methods that share the same numerical machinery and that do not rely on any specific grid configuration to solve the shallow water equation on the sphere.