  A simple numerical model which calculates the kinetics of crystallization
involving randomly distributed nucleation and isotropic growth is presented.
The model can be applied to different thermal histories and no restrictions are
imposed on the time and the temperature dependencies of the nucleation and
growth rates. We also develop an algorithm which evaluates the corresponding
emerging grain size distribution. The algorithm is easy to implement and
particularly flexible making it possible to simulate several experimental
conditions. Its simplicity and minimal computer requirements allow high
accuracy for two- and three-dimensional growth simulations. The algorithm is
applied to explore the grain morphology development during isothermal
treatments for several nucleation regimes. In particular, thermal nucleation,
pre-existing nuclei and the combination of both nucleation mechanisms are
analyzed. For the first two cases, the universal grain size distribution is
obtained. The high accuracy of the model is stated from its comparison to
analytical predictions. Finally, the validity of the
Kolmogorov-Johnson-Mehl-Avrami model is verified for all the cases studied.
