A Comparison of Finite-Difference Methods for the Solution of the Transient Heat Conduction Equation in Inhomogeneous Media.

Abstract

The transient heat conduction equation is solved for inhomogeneous media using the Explicit, Pure-Implicit, Crank-Nicolson and Douglas finite-difference methods, and the numerical solutions are investigated with respect to accuracy and stability. The inherent discontinuity between the initial and boundary conditions is accounted for by mesh refinement. For the two versions of the problem for which the four numerical methods are investigated, all four methods are found to be of equivalent accuracy for small values of the Fourier Modulus. While the Pure-Implicit, Crank-Nicolson and Douglas methods are unconditionally stable, the Crank-Nicolson and Douglas methods are very inaccurate at large values of the Fourier Modulus due to oscillatory behavior. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Mar 01, 1982
Accession Number
ADA115500

Entities

People

  • Kenneth William Blevins

Organizations

  • Air Force Institute of Technology

Tags

Communities of Interest

  • Advanced Electronics
  • Cyber
  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Accuracy
  • Air Force
  • Boundaries
  • Computations
  • Computer Programs
  • Computers
  • Conductivity
  • Difference Equations
  • Differential Equations
  • Discontinuities
  • Engineering
  • Equations
  • Error Analysis
  • Heat Transfer
  • Materials
  • Partial Differential Equations
  • Two Dimensional

Fields of Study

  • Mathematics

Readers

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