A local grid method for modelling real-time quantum dynamical events is formulated. The formulation is straightforward for 1-D systems. For more than one dimension, appeal has to be made to mean-field approximation of the appropriate kind. The simplest mean-field model results in time-dependent Hartree-Fourier grid method. The relationship of the proposed method with some other methods available in the literature is examined. A few examples of numerical applications dealing with (i) the dynamics of dissociation and ionization processes in diatoms and atoms respectively and (ii) tunnelling dynamics in the intramolecular H-atom transfer phenomenon are presented.