AN INVESTIGATION OF CONVERGENCE TECHNIQUES FOR IMPLICIT NUMERICAL SOLUTION OF THE DIFFUSION EQUATION FOR TRANSIENT HEAT TRANSFER

Abstract

The practical application of two convergence techniques designed to increase the rate of convergence of the method of successive displacements (Gauss-Siedel) for the implicit numerical solution of the diffusion equation of transient heat transfer is investigated. A sample problem of determining the temperature distribution in a cube with a constant internal heat source and fixed boundary temperatures is solved to provide the necessary data. The results provide a theoreticas for the adapted Wegstein technique. This theoretical basis brings to light the fact that successive overrelaxation and the adapted Wegstein technique are based on the same theoretical background. A procedure based on estimating the maximum eigenvalue of the method of successive displacements is used to make an approximation of the relaxation factor for successive overrelaxation.

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Document Details

Document Type
Technical Report
Publication Date
Aug 01, 1963
Accession Number
AD0419310

Entities

People

  • Robert T. Poppe

Organizations

  • Air Force Institute of Technology

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  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Air Force
  • Computational Fluid Dynamics
  • Computational Science
  • Computer Programming
  • Computer Programs
  • Computers
  • Difference Equations
  • Differential Equations
  • Digital Computers
  • Engineering
  • Equations
  • Heat Energy
  • Heat Transfer
  • Partial Differential Equations
  • Simultaneous Equations
  • Three Dimensional
  • Two Dimensional

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