The model we developed is a modified version of the dune field evolution model of Werner (1995). Werner (1995) was the first to model the formation of eolian dunes numerically from an initially flat surface. Werner’s (1995) model is based on the iterative entrainment, transport, and deposition of discrete units of sand that are picked up at random, transported a characteristic distance l downwind, and deposited back onto the surface with a probability ps that is, by default, equal to 0·5. Sand units that are not deposited after the first ‘jump’ of distance l are transported repeatedly downwind until

deposition occurs. In this way, the local sand flux depends on the values of l and p_s input  into  the  model.  In Werner’s model, the effect of air flow over incipient dunes is included in a simplified way by defining ‘shadow’ zones where the probability of deposition is one. Shadow zones are defined to be areas located in shadow when the surface is illuminated by a sun angle of 15° from the horizontal and parallel to the wind direction. In Werner’s model, shadow zones provide a simplified representation of the recirculation zone on the lee sides of incipient dunes where wind-driven sediment flux is

low and deposition rates are high. Sand units deposited back down on the bed in Werner’s model roll down the direction of  steepest  descent  if  deposition  causes  an  oversteepened condition (i.e. a slope angle greater than the angle of repose). Werner’s model combines three basic elements that, taken together, are responsible for the complex self-organized behavior observed in the model. First, the stochastic model of entrainment generates structureless, multi-scale relief from aninitially flat bed. Second, shadow zones provide a mechanism for a positive feedback between the topography of incipient dunes and the spatial pattern of erosion and deposition that enhances dune height and spacing over time. Finally, avalanching provides a limitation on dune slope and a mechanism for cross-wind sand transport. Werner’s model is capable of reproducing the four principal dune types (transverse, barchan, star, and linear) by varying sand supply and wind direction variability.

Quoted from: The effects of interdune vegetation changes  on eolian dune field evolution: a numerical modeling case study at Jockey’s Ridge, North 

Carolina, USA