We report on numerical simulations of a vibrated granular bed including the effect of the ambient air, generating the famous Faraday heaps known from experiment. A detailed analysis of the forces shows that the heaps are formed and stabilized by the airflow through the bed while the gap between bed and vibrating bottom is growing, confirming the pressure gradient mechanism found experimentally by Thomas and Squires [Phys. Rev. Lett. 81, 574 (1998)], with the addition that the airflow is partly generated by isobars running parallel to the surface of the granular bed. Importantly, the simulations also explain the heaping instability of the initially flat surface and the experimentally observed coarsening of a number of small heaps into a larger one.