The basic concepts of a deterministic scheme for simulating grain growth or foam coarsening in two dimensions have been presented in Part I. Implementation of the corresponding Laguerre (or weighted Voronoi) diagram in computer manageable practical terms is now presented. The internal constituents of the model are discussed first and include the initial configurations of the cellular network, obtained from different schemes. An internal clock is designed and an arbitrary dimensionless parameter is introduced to provide a relative weight to the rates of change of the generating circle positions with those of their sizes. A criterion for evaluating robustness and consistency of simulations is also presented. Actual simulation experiments are subsequently described as conducted from a range of initial structures built from different numbers of cells-up to 10^5. The essential theoretical attributes of normal grain growth were found to be recoverable in all simulations, notably statistical self-similarity, parabolic kinetic law, and independence from initial structures. It was also found that varying the relative rates of change of circle positions with radii (via the corresponding internal parameter mentioned above) resulted in size and shape distributions ranging from foam-like to polycrystal-like behaviours. It is claimed finally that the present model can be extended to three dimensions without any basic difficulty.