On a wildland fire model with radiation

The 2-D simplified wildland fire model presented here is based on conservation laws and takes into account radiation as the dominant thermal transfer mechanism, as well as convection, which represents the effect of the wind and the slope. The non-dimensional equations are obtained using the Frank-Kamenestkii change of variables. The existence of weak solutions of the non-linear reaction diffusion problem obtained is established as a particular case of more general existence results using a compactness method. The uniqueness of the weak solution is shown for a given initial data and fixed parameters of the equations. The approximate solution is obtained using a mixed finite element method. This preserves the continuity of the flux through the inter-element boundaries and allows to represent high gradients in the solution. Semi-discrete error estimation is presented. The convective term is solved by a splitting technique using Godunov's method. The numerical examples show the efficiency of the algorithm in capturing the fire front, even for critical values of the parameters. Copyright (C) 2002 John Wiley Sons, Ltd.