Heap formations of granular materials in a vertical vibrating bed are studied by a simulation model in which the effect of decrease in local density due to vibration is modeled by the creation of empty sites in the bulk. Dynamics of empty sites are introduced to simulate the bulk how while the surface flow is modeled by rules similar to the sandpile model. Phenomena such as heap formation and downward and upward convection modes can be reproduced. Phase diagrams similar to experimental observations can be constructed. A continuum model based on the empty site dynamics is also proposed. Predictions from the continuum model compare favorably with experimental observations.
