Grid Effect on Spherical Shallow Water Jets Using Continuous and Discontinuous Galerkin Methods
Abstract
Element-based Galerkin methods are not constrained by the logical structure of the computational grid. In this paper, the behavior of the continuous and discontinuous Galerkin solutions of the shallow water equations on the sphere is analyzed for three different grids of ubiquitous use in atmospheric modeling: (A) hexahedron (or cubed sphere), (B) reduced latitude-longitude, and (C) icosahedron. Conforming and nonconforming mesh configurations are adopted. The nonconforming grids are based on a quad-tree structure. The analysis is performed on the mid-latitude zonal flow problem suggested by Galewsky et al. [An initial-value problem for testing numerical models of the global shallow-water equation, Tellus 2004; 56A:429-440]. This test is sufficiently simple in its implementation, yet sufficiently complex to capture some important modes that arise on the global scales of real atmospheric dynamics. 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 are compared. The study shows that not only the resolution, but the grid alignment with respect to the flow is important in order to obtain an accurate solution. This is especially true if the governing equations are not regularized by the addition of a sufficiently large, fully artificial, diffusion mechanism; we give a brief (not exhaustive) analysis of the effect of viscosity on the solution quality. The flexibility and accuracy of element-based Galerkin methods on general spherical geometries is illustrated; we particularly emphasize the excellent properties of the reduced Lat-Lon configuration in comparison with the cubed-sphere on the one hand, and with the more regular and uniform icosahedral grid on the other.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 2013
- Accession Number
- ADA603963
Entities
People
- F. X. Giraldo
- Michal A. Kopera
- S. Marras
Organizations
- Naval Postgraduate School