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

• Published in: Journal of computational physics Vol. 271; pp. 224 - 243
• Main Authors: Bao, Lei, Nair, Ramachandran D., Tufo, Henry M.
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 15.08.2014
• Subjects: Angular momentum; Bottom topography; Conservation; Conservative form; Cubed-sphere; Diffusion; Discontinuous Galerkin; Energy conservation; Flux-form; Galerkin methods; Noise generation; Second-order diffusion; Shallow water; Shallow-water equations; Small scale; Well-balanced; Discontinuous Galerkin; Conservative form; Flux-form; Well-balanced; Bottom topography; Second-order diffusion; Cubed-sphere; Shallow-water equations
• ISSN: 0021-9991; 1090-2716
• DOI: 10.1016/j.jcp.2013.11.033

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.