Application of a nonlinear evolution model to fire propagation

Abstract

The numerical simulation of fire in forest has been an important objective in recent researches, The rate of spread and shape of a forest fire front is af8ecte.d by many factors. The most important of these are as follows: fuel type and moisture content, wind velocity and variability, forest topography, fire spread mechanism, fuel continuity and the amount of spotting (cf.[ l-21). The development of Geographic Information Systems allows the incorporation of these data to the developed models, The first models took into account constant factors, continuous uniform fuel type, constant wind velocity, moisture and slope. Under these conditions, a fire ignited at a single point reaches a quasi-steady state and progresses toward the down wind direction and expands at a constant rate. These data cannot give precise predictions under variable conditions but are very useful in order to the intuition of the fire controller. Models capable of being incorporated into the computer simulations of fires under variable conditions have been developed, based on cellular automata (cf. [3-7]), and stochastic process [8]. These models can give useful indicators as to fire behavior under such conditions. Combustion phenomena has been extensively studied [9], unsteady flame propagation has been analyzed [lo]. Models based on combustion theories are very difficult to develop because of the diversity of the fuel type and varied chemical composition within a given fuel type. Because of the complexity of the problem, models based rigorously on combustion theory have not been completely developed. In this preliminary work, a first attempt is done to design a computer code for numerical simulation of forest fire spread in landscapes. Basically a convection-diffusion model for temperature and a mass-consistent model for wind field simulation will be assumed. A two-steps chemical mechanism is simplified in order to obtain the heat source. This proposed 2-D model take into account the convection phenomena due to temperature gradients in vertical direction. A numerical solution of the former model is presented using a finite difference method together with the study of stability. This numerical method is contrasted with an adaptive finite element method using reflnementiderefinement techniques (cf. [ 1 1 - 143}).