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CivilComp Proceedings
ISSN 17593433 CCP: 80
PROCEEDINGS OF THE FOURTH INTERNATIONAL CONFERENCE ON ENGINEERING COMPUTATIONAL TECHNOLOGY Edited by: B.H.V. Topping and C.A. Mota Soares
Paper 4
A Numerical Algorithm for Solving a Multivalued Equation arising in Fire Spread Modelling L. Ferragut, I. Asensio and S. Monedero
Departement of Applied Mathematics, University of Salamanca, Spain L. Ferragut, I. Asensio, S. Monedero, "A Numerical Algorithm for Solving a Multivalued Equation arising in Fire Spread Modelling", in B.H.V. Topping, C.A. Mota Soares, (Editors), "Proceedings of the Fourth International Conference on Engineering Computational Technology", CivilComp Press, Stirlingshire, UK, Paper 4, 2004. doi:10.4203/ccp.80.4
Keywords: fire, radiation, moisture, pyrolysis, wind, slope.
Summary
Many existing physical models for fire spread in porous fuel bed
use the principle of energy conservation applied to the preheated
fuel. Generally, radiation is considered as the dominant mechanism
of the fuel preheating. On the other hand slope and wind effects
as well as the initial vegetation moisture have to be taken into
account in order to obtain reliable rates of fire spread.
Physical models from fundamental conservation equations and
complex physics have been developed [1]. These valuable
approaches are computationally expensive and too slow to be used
in real time mode, even with fast and parallel processing.
Besides, several works have appeared recently where one or two
dimensional physical models are considered in order to simulate
fire spread in small computers, with moderate simulation times,
see for example [2].
This paper is a contribution to generally applicable models of fire spread through fuel beds, by means of simple models, but taking into account local radiation, moisture content and wind and slope effects. Particularly the influence of the moisture content and eventually heat absorption by pyrolysis, can be represented as two free boundaries, and are treated in this paper using a multivalued operator representing the enthalpy. The maximal monotone property of this operator allows the implementation of a numerical algorithm with wellknown convergence properties. The non dimensional equations governing the fire spread in a region with boundary are: with the corresponding boundary conditions. The unknowns , and are the enthalpy, temperature and mass fraction of solid fuel, respectively. The enthalpy is an element of a multivalued operator given by: The numerical algorithm is a semiimplicit scheme by discretizing the total derivative. The basic idea is to treat implicitly the positive terms. At each time step the resulting nonlinear equations are solved by means of the Yosida aproximation of the multivalued operator and the BermúdezMoreno algorithm. [5]. We consider the series of experiments that were carried out in a low speed wind tunnel by [6]. They were performed in order to observe wind driven effects, slope and moisture content effects in fire across pine needles beds. As in the experimental results, qualitatively, numerical results are similar for low and high fuel moisture content, but the rate of spread is always lower for the later. In absolute terms the difference increase with increasing wind velocity. The higher the fuel moisture content, the lower the combustion temperatures reached, which lowers the rate of spread. References
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