Modelling the dynamics of wildfires is very computationally challenging. Although three-dimensional computational fluid dynamics (CFD) models have been successfully applied to wildfires, the computational time required makes them currently impractical for operational usage. In this study, we develop a two-dimensional propagation model coupled to a ‘pyrogenic’ potential flow formulation representing the inflow of air generated by the fire. This model can accurately replicate features of fires previously unable to be simulated using current two-dimensional models, including development of a fire line into a parabolic shape, attraction between nearby fires and the observed closing behaviour of ‘V’ shaped fires. The model is compared to experimental results with good agreement. The pyrogenic potential model is orders of magnitude faster than a full CFD model, and could be used for improved operational wildfire prediction.