Wildland Fire Propagation Modelling: A Novel Approach Reconciling Models Based on Moving Interface Methods and on Reaction-Diffusion Equations

A novel approach to study the propagation of fronts with random motion is presented. This approach is based on the idea to consider the motion of the front, split into a drifting part and a fluctuating part; the front position is also split correspondingly. In particular, the drifting part can be related to existing methods for moving interfaces, for example, the Eulerian level set method and the Lagrangian discrete event system specification. The fluctuating part is the result of a comprehensive statistical description of the system which includes the random effects in agreement with the physical properties of the system. The resulting averaged process emerges to be governed by an evolution equation of the reaction-diffusion type. Hence, following the proposed approach, when fronts propagate with a random motion, models based on methods for moving interfaces and those based on reaction-diffusion equations can indeed be considered complementary and reconciled. This approach turns out to be useful to simulate random effects in wildland fire propagation as those due to turbulent heat convection and fire spotting phenomena.