Diffusion experiments with a global discontinuous Galerkin shallow-water model

The shallow-water equations are discretized on the cubed sphere tiled with quadrilateral elements relying on a nonorthogonal curvilinear coordinate system. In the viscous shallow-water model the diffusion terms (viscous fluxes) are approximated with two different approaches: 1) the element-wise localized discretization without considering the interelement contributions and 2) the discretization based on the local discontinuous Galerkin (LDG) method.

In the LDG formulation the advection-diffusion equation is solved as a first-order system. All of the curvature terms resulting from the cubed-sphere geometry are incorporated into the first-order system. The effectiveness of each diffusion scheme is studied using the standard shallowwater test cases.