Alluvial fan deltas are built by aggrading and avulsing river channels. A numerical model of flow and sediment transport in channels is combined with a condition for channel avulsion to describe evolution of the fan surface. The model combines elements of two recent approaches: (1) diffusional models of depositional basin filling, which describe the evolution of overall morphology, and (2) cellular models of channel evolution, which provide simplified descriptions of channel dynamics. Here the cellular formulation is used simply as a template for discretizing a standard set of equations describing flow and sediment transport within channels. The basic formulation is thus grid-invariant, and the results are in actual rather than arbitrary time and length scales. The model captures the interaction between microscale (channel) morphodynamics, including converging and diverging flow and avulsion, and morphodynamics at the macroscale (fan). It provides a starting point for the study of a wide range of topics, including the three-dimensional stratigraphy of fan delta deposits and the response of fan deltas to engineering activities.