Error Prediction for the Implicit Numerical Solution of the Heat Conduction Equation

Abstract

The results of an investigation of time- and space-truncation errors inherent in the implicit numerical analysis of the heat conduction equation are presented. Curves showing the percentage of error as a function of Biot and Fourier number for both step-function and ramp-function boundary conditions are given. Acceleration techniques, over-relaxation, and a direct tridiagonal matrix solution are presented. Methods are developed for automatic determination and printout of spatial- and time-truncation error, for extending ramp-function responses for either analytical or numerical solutions, and for synthesizing ramps of different slopes from a given transient response. An automatic time- step generator that maintains a specified error level is described and coded. Preliminary studies correlating the delta first derivative with spatial-truncation error, and accelerating the solution of a three-dimensional implicit transient solution through the use of a one-dimensional approach are given.

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Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1971
Accession Number
AD0729652

Entities

People

  • Alohn F. Stanley
  • J. T. Anderson
  • William Van Tassel

Organizations

  • University of Nevada, Reno

Tags

Communities of Interest

  • Energy and Power Technologies
  • Space
  • Weapons Technologies

DTIC Thesaurus Topics

  • Applied Mathematics
  • Chebyshev Polynomials
  • Computations
  • Computer Programs
  • Difference Equations
  • Differential Equations
  • Error Analysis
  • Geometry
  • Heat Transfer
  • Heat Transfer Coefficients
  • Mathematical Analysis
  • Numerical Analysis
  • Numerical Integration
  • Partial Differential Equations
  • Smoothing (Mathematics)
  • Surface Temperature
  • Thermal Conductivity

Readers

  • Computer Science.
  • Linear Algebra
  • Thermal Physics or Thermal Science.

Technology Areas

  • Space
  • Space - Hall-Effect Thruster