Analysis of the Numerical Solution of the Shallow Water Equations

Abstract

This thesis is concerned with the analysis of various methods for the numerical solution of the shallow water equations along with the stability of these methods. Most of the thesis is concerned with the background and formaulation of the shallow water equations. The derivation of the basic equations will be given, in the primative variable and vorticity divergence formulation. Also the shallow water equations will be written in spherical coordinates. Two main types of methods used in approximating differential equations of this nature will be discussed. The two schemes are finite difference method (FDM) and the finite element method (FEM). After presenting the shallow water equations in several formulations, some examples will be presented. The use of the Fourier transform to find the solution of a semidiscrete analog of the shallow water equations is also demonstrated.

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Document Details

Document Type
Technical Report
Publication Date
Sep 01, 1997
Accession Number
ADA338796

Entities

People

  • Thomas A. Hamrick

Organizations

  • Naval Postgraduate School

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Computational Fluid Dynamics
  • Computational Science
  • Difference Equations
  • Differential Equations
  • Equations
  • Finite Element Analysis
  • Fluid Dynamics
  • Fluids
  • Grids
  • Integral Transforms
  • Integrals
  • Mathematics
  • Numerical Analysis
  • Partial Differential Equations
  • Three Dimensional
  • Two Dimensional
  • Water

Fields of Study

  • Mathematics

Readers

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