A mass and momentum flux-form high-order discontinuous Galerkin shallow water model on the cubed-sphere

A well-balanced discontinuous Galerkin (DG) flux-form shallow-water (SW) model on the sphere is developed and compared with a nodal DG SW model cast in the vector-invariant form for accuracy and conservation properties. A second-order diffusion scheme based on the local discontinuous Galerkin (LDG) method is added to the viscous version of the SW model and tested for conservation behaviors. The inviscid flux-form SW model is found to have better conservation of total energy and zonal angular momentum while the vector-invariant form provides better ability of conserving potential enstrophy. The inviscid flux-form tends to generate spurious vorticity but the LDG scheme combined with a well-balanced treatment can effectively eliminate the small-scale noise and generate smooth and accurate results.