We describe a numerical implementation of star formation in disk galaxies, in which the conversion of cooling gas to stars in the multiphase interstellar medium is governed by the rate at which molecular clouds are formed and destroyed. In the model, clouds form from thermally unstable ambient gas and get destroyed by feedback from massive stars and thermal conduction. Feedback in the ambient phase cycles gas into a hot galactic fountain or wind. We model the ambient gas hydrodynamically using smoothed particle hydrodynamics (SPH). However, we cannot resolve the Jeans mass in the cold and dense molecular gas and, therefore, represent the cloud phase with ballistic particles that coagulate when colliding. We show that this naturally produces a multiphase medium with cold clouds, a warm disk, hot supernova bubbles and a hot, tenuous halo. Our implementation of this model is based on the Gadget N-Body code. We illustrate the model by evolving an isolated Milky Way-like galaxy and study the properties of a disk formed in a rotating spherical collapse. Many observed properties of disk galaxies are reproduced well, including the molecular cloud mass spectrum, the molecular fraction as a function of radius, the Schmidt law, the stellar density profile and the appearance of a galactic fountain.
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