Keywords: fire spread, free boundary, multivalued operators, radiation.

A numerical method is developed for fire spread simulation modelling. The model is a variant of the models in chapter one of reference [2], Model I in [1] or the model in [3] where we have introduced the influence of the moisture content and radiation. We consider the combustion of a porous solid, where a simplified energy conservation equation is applied.

The rate of loss of fuel is given by

Which is coupled to the temperature by the arrhenius law through the term

The effect of the vegetation moisture and endothermic pyrolysis is incorporated in the model by means of a multivalued function representing the enthalpy.

Where the and are the non-dimensional evaporation heat and pyrolysis heat and , the temperatures of evaporation and pyrolysis.

The resolution of this multivalued operator is done using the Yosida approximation of a perturbed multivalued operator

Which gives explicit values of and without the need of an iterative algorithm.

The nonlocal radiation term from the flames above the vegetable is based on a 3D transfer equation involving 2D calculations and taking into account the absortion by the gases.

We present two ways of computing the approximate solution of the radiative equation, by use of the characteristic method combined with a discrete ordinate method, and by the discontinuous Galerkin method together with a modified Runge-Kutta method [5].

Finally several representative examples are solved and compared with experimental data [4].

1

Margerit J, Séro Guillaume O. Modelling forest fires. Part II: reduction to two-dimensional models and simulation of propagation, Int. J. Heat and Mass Transfer 2002; 45:1723-1737. doi:10.1016/S0017-9310(01)00249-6

2

Cox G. Combustion Fundamentals of Fire. Academic Press, London, 1995.

3

Simeoni A, Larini M, Santoni PA, Balbi JH. Coupling of a simplified flow with a phenomenological fire spread model. C.R. Mecanique 2002; 330:783-790. doi:10.1016/S1631-0721(02)01532-2

4

J. Ventura, J.Mendes-Lopes, L. Ripado Temperature-Time curves in fire propagating in beds of pine needles. III International Confer. on Forest Fires Research.

5

B.Cockburn, G.E.Karniadakis, C.-W. Shu. Discontinuous Galerkin Methods. Lecture Notes in Computational Science and Engineering 11, Springer.

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