A general circulation model (GCM) is a mathematical climate model of the general circulation of a planet's atmosphere or ocean. It incorporates fluid dynamics (Navier-Stokes equations), rotation, and thermodynamics. Such a model can be analytic or can be fleshed out with computer-based numerical simulations.
Such models have been developed for the Earth, but also adapted to other planets and moons. With the study of extra-solar planets, there is much opportunity for using them.
GCM can also stand for global climate model, and detailed global climate models can be general circulation models.