A numerical method for solving convection-reaction-diffusion multivalued equations in fire spread modelling

A numerical method is developed for fire spread simulation modelling. The two dimensional surface model presented takes into account moisture content, radiation, wind and slope effects, which are by far the most important mechanisms in fire spread. We consider the combustion of a porous solid, where the energy conservation equation is applied. The influence of moisture content and eventually heat absorbtion by pyrolysis, can be represented as two free boundaries, and are treated here using a multivalued operator representing the enthalpy. The maximal monotone property of this operator allows the implementation of a numerical algorithm with good convergence properties.