A Discontiuous 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.

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Document Details

Document Type
Technical Report
Publication Date
Nov 02, 2007
Accession Number
ADA637498

Entities

People

  • Doerthe Handorf
  • Francis Giraldo
  • Klaus Dethloff
  • Matthias Laeuter

Organizations

  • Naval Postgraduate School

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Accuracy
  • Coordinate Systems
  • Energy Conservation
  • Equations
  • Galerkin Method
  • Geometry
  • Grids
  • Integrals
  • Jet Streams
  • Mathematics
  • Polynomials
  • Runge Kutta Method
  • Shallow Water
  • Steady State
  • Three Dimensional
  • Triangles
  • Two Dimensional

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)

Technology Areas

  • Space