A Spectral Element Shallow Water Model on Spherical Geodesic Grids

Abstract

The spectral element method for the two-dimensional shallow water equations on the sphere is presented. The equations are written in conservation form and the domains are discretized using quadrilateral elements obtained from the generalized icosahedral grid introduced previously (Giraldo FX. Lagrange-Galerkin methods on spherical geodesic grids: the shallow water equations. Journal of Computational Physics 2000; 160: 336 368). The equations are written in Cartesian co-ordinates that introduce an additional momentum equation, but the pole singularities disappear. This paper represents a departure from previously published work on solving the shallow water equations on the sphere in that the equations are all written, discretized, and solved in three-dimensional Cartesian space. Because the equations are written in a three-dimensional Cartesian co-ordinate system, the algorithm simplifies into the integration of surface elements on the sphere from the fully three-dimensional equations.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 2001
Accession Number
ADA486947

Entities

People

  • Francis Giraldo

Organizations

  • Naval Postgraduate School

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Accuracy
  • Boundaries
  • Computational Fluid Dynamics
  • Computational Science
  • Computations
  • Equations
  • Finite Element Analysis
  • Fluids
  • Geometry
  • Grids
  • Shallow Water
  • Solid Bodies
  • Steady State
  • Stratified Fluids
  • Three Dimensional
  • Two Dimensional
  • Water

Readers

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

Technology Areas

  • Space