Mathematical Problems in Engineering
Volume 4 (1998), Issue 2, Pages 115-133

On a numerical model for diffusion-controlled growth and dissolution of spherical precipitates

R. Van Keer1 and J. Kačur2

1Department of Mathematical Analysis, Faculty of Engineering, University of Ghent, Galglaan 2, Gent 9000, Belgium
2Institute of Numerical Analysis and Optimalization, Comenius University, Mlynská Dolina, Bratislava 842 15, Slovakia

Received 18 October 1996

Copyright © 1998 R. Van Keer and J. Kačur. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper deals with a numerical model for the kinetics of some diffusion-limited phase transformations. For the growth and dissolution processes in 3D we consider a single spherical precipitate at a constant and uniform concentration, centered in a finite spherical cell of a matrix, at the boundary of which there is no mass transfer, see also Asthana and Pabi [1] and Caers [2].

The governing equations are the diffusion equation (2nd Fick's law) for the concentration of dissolved element in the matrix, with a known value at the precipitate-matrix interface, and the flux balans (1st Fick's law) at this interface. The numerical method, outlined for this free boundary value problem (FBP), is based upon a fixed domain transformation and a suitably adapted nonconforming finite element technique for the space discretization. The algorithm can be implemented on a PC. By numerous experiments the method is shown to give accurate numerical results.