On a wildland fire model with radiation

The 2-D simpli ed wildland re 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 e ect 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 di usion 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 xed parameters of the equations. The approximate solution is obtained using a mixed nite element method. This preserves the continuity of the ux 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 e ciency of the algorithm in capturing the re front, even for critical values of the parameters