  In this study, we use the cell dynamics method to test the validity of the
Kormogorov-Johnson-Mehl-Avrami (KJMA) theory of phase transformation. This cell
dynamics method is similar to the well-known phase-field model, but it is a
more simple and efficient numerical method for studying various scenarios of
phase transformation in a unified manner. We find that the cell dynamics method
reproduces the time evolution of the volume fraction of the transformed phase
predicted by the KJMA theory. Specifically, the cell dynamics simulation
reproduces a double-logarithmic linear KJMA plot and confirms the integral
Avrami exponents $n$ predicted from the KJMA theory. Our study clearly
demonstrates that the cell dynamics approach is not only useful for studying
the pattern formation but also for simulating the most basic properties of
phase transformation.
