The large scale hydrodynamics of laser accelerated thin disks (foils) are studied numerically using a 2-D, evolutionary Lagrangian fluid code. The laser and target parameters considered are relevant to direct drive laser fusion, in the classical interaction regime. Peculiar 2-D features observed in the experiments are recovered in the simulations; agreement with experimental data is found for a series of experiments concerning foils of different thickness. Scaling laws for the design of hydrodynamically equivalent experiments are tested, with the effects of non-scaled processes turning out to be fairly small, although observable, and qualitatively in agreement with the relevant theory. Simulations also indicate the adequacy of foil acceleration experiments driven by non-uniform (but controlled) beams to the quantitative study of the smoothing of the irradiation non-uniformities.