ON THE STABILITY ANALYSIS OF AN IMPLICIT DIFFERENCE ANALOG OF THE TWO-DIMENSIONAL DIFFUSION EQUATION WITH CONCENTRATION DEPENDENT DIFFUSIVITY

Abstract

A procedure has been demonstrated by which variations in the diffusion coefficient in a two dimensional diffusion equation can be introduced into the solution at every time step in the alternating direction method of solution. This can be accomplished provided that the change in the dimensionless parameter (analogous to the inverse of the Fourier modulus in heat transfer) falls within specified ranges as indicated, or that an adjustment in the time step can be made to compensate for a portion of the change in the diffusion coefficient so that the allowable bounds on the change are not violated. The conditions as de eloped for this problem using the von Neumann criterion are sufficient to insure stability of the difference analog. (Author)

Document Details

Document Type
Technical Report
Publication Date
Mar 01, 1961
Accession Number
AD0256982

Entities

People

  • Bertram Bussell

Organizations

  • University of California, Los Angeles

Tags

DTIC Thesaurus Topics

  • Coefficients
  • Diffusion
  • Diffusion Coefficient
  • Diffusivity
  • Equations
  • Heat Transfer
  • Mathematics
  • Physical Properties
  • Two Dimensional

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)