Note on the determination of the ignition point in forest fires propagation using a control algorithm

摘要

This paper is devoted to the determination of the origin point in forest fires propagation using a control algorithm. The forest fires propagation are mathematically modelled starting from a reaction diffusion model. A volume of fluid (V.O.F.) formulation is also used to determine the fraction of the area which is burnt. After having developed the objective functional and its derivative, results from an optimization process based on the simplex method is presented. It is shown that the ignition point and the final time of the fire propagation are precisely recovered, even for a realistic, non-horizontal, terrain.