A Fourth Order Energy and Potential Enstrophy Conserving Difference Scheme

Abstract

A horizontal difference scheme that conserves both potential enstrophy and energy for general flow and, in addition, yields fourth-order accuracy for the advection of potential vorticity in case of non-divergent flow, is derived for the shallow water equations on the staggered grid as a simple extension of the second-order potential enstrophy and energy conserving scheme presented by Arakawa and Lamb (1981). This fourth-order scheme is derived both for a Cartesian grid and for a spherical grid. Comparison by means of numerical experiments between the newly derived scheme and the second-order scheme showed the distinct advantage of the new scheme in giving better development and faster moving speed of the law.

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Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1982
Accession Number
ADA126626

Entities

People

  • Kenji Takano
  • M. G. Wurtele

Organizations

  • University of California, Los Angeles

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Accuracy
  • Advection
  • Air Force
  • Climate Change
  • Computations
  • Energy
  • Equations
  • Fluids
  • Grids
  • Height
  • Kinetic Energy
  • Lisp Programming Language
  • Numerical Integration
  • Shallow Water
  • Topography
  • Two Dimensional
  • Water

Readers

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