Journal of Materials Science

, Volume 16, Issue 11, pp 3122–3130

Efficient numerical modelling of hydrogen diffusion with trapping

  • Peter G. Thomas
  • Ellen J. Stern


In view of the growing interest both in numerical solutions of the McNabb and Foster model for hydrogen diffusion with trapping, and the computational scheme proposed by Caskey and Pillinger, a more efficient, simpler scheme is presented which more closely replaces this model. Further techniques are presented which reduce the cost of the computations yet increase the accuracy of the results. Using a formulation better adapted to analysis, and with readily comprehensible variables, bounds are given on the numerical mesh sizes which ensure the stability of the scheme. For cases where these bounds are overly restrictive, alternative numerical tests are suggested. Finally, driving equations are given on which an approximation to the McNabb and Foster model in which the concentration of traps varies with time may be validly based.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    A. McNabb and P. K. Foster, Trans. Metal. Soc. 227 (1963) 618.Google Scholar
  2. 2.
    G. R. Caskey Jr and W. L. Pillinger, Metall. Trans. A 6A (1975) 467.Google Scholar
  3. 3.
    R. C. Frank, C. W. Wert and H. K. Birnbaum, ibid. 10A (1979) 1627.Google Scholar
  4. 4.
    J. Crank and P. Nicolson, Proc. Camb. Phil. Soc. Math. Phys. Sci. 43 (1947) 50.Google Scholar
  5. 5.
    L. Fox, “Numerical Solution of Ordinary and Partial Differential Equations” (Pergamon Press, Oxford, 1962).Google Scholar
  6. 6.
    S. H. Crandall, J. Ass. Comput. Mach. 2 (1955) 42.Google Scholar

Copyright information

© Chapman and Hall Ltd. 1981

Authors and Affiliations

  • Peter G. Thomas
    • 1
  • Ellen J. Stern
    • 1
  1. 1.Faculty of MathematicsThe Open UniversityMilton KeynesUK

Personalised recommendations