A Numerical Method for solving Convection-Reaction-Diffusion Multivalued Equations in Fire Spread Modelling 1 L. Ferragut a,∗ M.I. Asensio a S. Monedero a a Department of Applied Mathematics, University of Salamanca, Pza. Merced s.n. 37008 Salamanca, Spain Abstract A numerical method is developed for fire spread simulation modelling. The two di- mensional 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 conser- vation 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 mono- tone property of this operator allows the implementation of a numerical algorithm with good convergence properties. Key words: fire, radiation, moisture, pyrolysis, wind, slope PACS: 02.60.Cb, 02.60.Lj, 02.70.Dh 1 Introduction Many existing physical models for fire spread in a porous fuel bed use the prin- ciple of energy conservation applied to the preheated fuel. Generally, radiation is considered as the dominant mechanism of the fuel preheating. But in order to obtain reliable rates of fire spread, wind effects and initial vegetation moisture should be taken into account. Physical models from fundamental conservation equations and complex physics have been developed [3,7,9,8]. These valuable ∗ Corresponding author. Email addresses: ferragut@usal.es (L. Ferragut), mas@usal.es (M.I. Asensio), smonedero@usal.es (S. Monedero). 1 Spanish Ministry of Science and Technology, grant number: REN2001-0925-03-03 Preprint submitted to Elsevier Science 19 September 2005