A General Mathematical Framework for Modeling Two-Dimensional Wildland Fire Spread

Abstract

This work considers the modelling of two dimensional fire spread for heterogeneous fuel and meteorological conditions. Differential equations are used as the modelling form, and a set of partial differential equations that describes fire growth in terms of the rate of spread at each point on the perimeter is derived. These equations require the specification of the rate of spread as a function of the variables affecting it, and form a general modelling framework into which such a function can be placed. To model the relationship between the rate of spread and its affecting factors an analysis of point source ignition fires for homogeneous fuel and meteorological conditions is made. Based on this analysis a spread rate model for heterogeneous conditions is proposed. The resulting differential equations require a sophisticated computer solution, however there are a number of nontrivial fire situations for which solutions can relatively easily be obtained, and example solutions are presented.