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

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.