This paper studies the use of ADE methods for solving diffusion equations in non-Cartesian coordinates. To retain unconditional stability and greater accuracy of computation when solving diffusion equations in non-Cartesian coordinates, a new explicit algorithm is developed by combining the advantages of those originally proposed by Saul’ev, Larkin, Barakat and Clark. Analysis of accuracy shows that the new algorithm can be as accurate as either that of Larkin or that of Barakat and Clark. Stability analysis is also carried out “locally” based on the spectral stability, and this shows unconditional stability of the generalised algorithm. Numerical examples on transient heat conduction are used to support the conclusions from the analysis.
1.
Anderson, D. A. et al, 1984, Computational Fluid Mechanics and Heat Transfer, Hemisphere Publishing Corp., Bristol, PA.
2.
Barakat, H. Z., and Clark, J. A., 1966, “On the Solution of the Diffusion Equations by Numerical Methods,” ASME JOURNAL OF HEAT TRANSFER, pp. 421–427.
3.
Larkin, B. K., 1964, “Some Stable Explicit Difference Approximations to the Diffusion Equation,” Mathematics of Computations, pp. 196–202.
4.
Richtmyer, R. D., and Morton, K. W., 1967, Difference Methods for Initial-Value Problems, Interscience Publishers, New York.
5.
Saul’ev
K.
1957
, “On a Method of Numerical Integration of the Equation of Diffusion
,” Doklady Akad. Nauk USSR
, Vol. 115
, pp. 1077
–1079
.6.
Saul’ev
K.
1958
, “Methods of Increased Accuracy and Two-Dimensional Approximations to Solutions of Parabolic Equations
,” Doklady Akad. Nauk USSR
, Vol. 118
, pp. 1088
–1090
.7.
Wang, X. M., and Crawford, R. J., 1997, “Splitting-up Algorithms for Solving Diffusion Equations in Arbitrary Regions,” in press.
This content is only available via PDF.
Copyright © 1997
by The American Society of Mechanical Engineers
You do not currently have access to this content.
