A numerical algorithm is presented which allows three-dimensional time-dependent simulations of Czochralski and other crystal growth processes. Besides the computation of turbulent flow and heat transfer in the melt, it includes the movement of the crystallization interface between melt and crystal, the dynamics of the melt free surface with the meniscus and the variation of the three-phase boundary. Thus, there is the potential that crystal diameter variations, which occur during growth of the start and the end cone can be predicted. This is illustrated by results of sample computations. © 2010 Elsevier B.V.