A Discontinuous Galerkin Method for the Shallow Water Equations in Spherical Triangular Coordinates
Abstract
A global barotropic model of the atmosphere is presented governed by the shallow water equations and discretized by a Runge-Kutta discontinuous Galerkin method on an unstructured triangular grid. The shallow water equations on the sphere, a two-dimensional surface in R3, are locally represented in terms of spherical triangular coordinates, the appropriate local coordinate mappings on triangles. On every triangular grid element, this leads to a two-dimensional representation of tangential momentum and therefore only two discrete momentum equations. The discontinuous Galerkin method consists of an integral formulation using a Rusanov numerical flux. A strong stability-preserving third order Runge-Kutta method is applied for the time discretization. The polynomial space of order k on each curved triangle of the grid is characterized by a Lagrange basis and requires high-order quadature rules for the integration over elements and element faces. For the presented method no mass matrix inversion is necessary, except in a preprocessing step.
Document Details
- Document Type
- Technical Report
- Publication Date
- Nov 01, 2007
- Accession Number
- ADA486696
Entities
People
- Doerthe Handorf
- Francis Giraldo
- Klaus Dethloff
- Matthias Laeuter
Organizations
- Naval Postgraduate School