We formulate a large-scale network model for the dynamics and stability of a planar (gas-liquid) foam with low liquid fraction composed of approximately polygonal gas bubbles. We restrict attention to clean liquids (free of surfactants and colloidal particles) as a model for molten metallic foams produced using batch-processing techniques for manufacturing porous-metal solids. The liquid is primarily confined within highly curved regions around the bubble vertices, Plateau borders, interconnected by thin liquid films that form the edges of the bubbles and drain due to capillary-viscous suction. The model incorporates direct coupling between the pressure and area of the bubbles, surface-tension forces on the gas-liquid interfaces and draining and elongational flows in the films. The model also explicitly accounts for van der Waals instabilities that grow to rupture a liquid film once it becomes sufficiently thin, leading to bubble coalescence and hence coarsening of the foam. We consider foams confined within a rectangular box which is prewetted with a thin film of liquid. Initially, the foam is composed of regular polygonal bubbles with equal pressure, but the first film breakage triggers a dynamic coalescence process where the mean bubble area increases quickly; numerical simulations elucidate the large-scale topological rearrangement as the foam coarsens. (C) 2012 The Society of Rheology. [http://dx.doi.org/10.1122/1.3695029]