Modeling radiation and moisture content in fire spread

A numerical method for a 2-dimensional surface fire model taking into account moisture content and radiation is developed. We consider the combustion of a porous solid, where a simplified energy conservation equation is applied. The effects of the moisture content and the endothermic pyrolysis of the vegetation are introduced in the model by means of a multivalued function representing the enthalpy. Its resolution is based on the Yosida approximation of a perturbation of this operator. The radiation term allows us to cope with wind and slope effects. In order to avoid heavy time consuming computations, this term is approximated using the characteristic method, combined with a discrete ordinate method. Finally, the approximate solution of the energy equation in the porous solid is obtained using a finite element method together with a semi-implicit Euler algorithm in time.