The production and dispersal of airborne dust is an important issue in both environmental and industrial contexts. Dust pollution is a major environmental concern, and long exposure in occupational settings has been linked with numerous respiratory health issues. Industrial dust pollution can also present a significant explosion hazard, even in facilities with dust extraction systems. Computational models for dust generation and dispersal have, however, generally been formulated for specific geophysical applications and restricted to static, two-dimensional, approaches. Here, we present a method for simulating dust production from a dynamic granular bed by using a three-dimensional coupled discrete element method and Navier–Stokes computational model. Dust production is based on an energy formulation in which micro-scale dust particles are assumed to overcome cohesion to macro-scale grains. This model is used over the entire range of energies present within the system, from macro-scale collisions to aerodynamic entrainment and bombardment of micro-scale particles. The dust concentration is modelled as a scalar density field, which is advected and diffused through turbulence in the gas flow field. The model is tested against empirical predictions for two test cases, a slug of granular material dropped from a set height and air flow over a granular stockpile. Both give good agreement to the empirical relations, showing that the model can accurately predict the production and subsequent dispersal of dust from a dynamic granular bed. Copyright © 2012 John Wiley & Sons, Ltd.