Accuracy of Finite Difference Methods for Solution of the Transient Heat Conduction (Diffusion) Equation.

Abstract

The two-dimensional transient heat conduction (diffusion) equation was solved using the fully explicit, fully implicit, Crank-Nicholson implicit, and Peaceman-Rachford alternating direction implicit (ADI) finite difference methods (FDMTHs). The general stability condition for the same FDMTHs was derived by the matrix, coefficient, and a probabilistic method. The matrix, coefficient, and probabilistic methods were found to be equivalent in that each lead to the same general stability condition. Oscillatory behavior of the fully explicit FDMTH was as predicted by the general stability condition. Though the Crank-Nicholson implicit and the Peaceman-Rachford ADI FDMTHs were expected to be unconditionally stable, unstable oscillations were observed for large sizes of time step. For large numbers of time steps and sizes of time steps for which all FDMTHs considered are stable, the Crank-Nicholson implicit FDMTH is the more accurate. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Feb 01, 1983
Accession Number
ADA124846

Entities

People

  • Thomas Sidney Chivers Jr

Organizations

  • Air Force Institute of Technology

Tags

Communities of Interest

  • C4I

DTIC Thesaurus Topics

  • Accuracy
  • Air Force
  • Boundaries
  • Boundary Value Problems
  • Coefficients
  • Computer Programs
  • Difference Equations
  • Differential Equations
  • Diffusion
  • Engineering
  • Equations
  • Error Analysis
  • Materials Laboratories
  • Oscillation
  • Stability Conditions
  • Three Dimensional
  • Two Dimensional

Readers

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