Title: Numerical Simulation of Wild Fires.

Abstract:

Numerical simulations of wildfires have a long history but it is only recently that numerical models treating the coupled fire-atmosphere problem have been introduced. These models are still in their early stages of development but already show promise of providing a useful tool to the fire community that can be used to better understand fire behaviour and as a result eventually be used for such activities as developing and/or
testing mitigation techniques.

The physics of fires occurs on the molecular scale whereas wild fires themselves can span kilometers in linear scale. The modeler is faced with treating a problem that spans six or more orders of magnitude in scale. Much like treating cloud physics in the modeling of moist convection, the fire modeler must also consider Sub-Grid-Scale parameterizations of the physical processes in order to attain the range of scales needed to treat the full problem in an acceptably efficient manner. Given a SGS fire parameterization the modeler still remains faced with the computational challenge of simulating a physical problem requiring grid sizes of 1 m or better to capture the dynamics of the combustion zone convection and kilometers or more to allow interaction with the larger scale atmospheric flow. The typical computational procedure is to use multiple levels of grid refinement on massively parallel computational platforms.

I will describe the SGS fire parameterizations we are using as well as some current developments underway. The essential components of the SGS fire parameterization are the treatment of fire-atmosphere heat exchange and fire-fuel heat exchange. I will also describe the numerical modeling framework used to numerically simulate fires using multiple levels of grid refinement on distributed memory machines. Examples of fire simulations will be presented. This will be followed with a summary of what I feel are some of the important research questions needing further study.

Title: What is missing from fire ecology?

Abstract:

Simply put fire ecology is missing a good understanding of heat transfer and combustion in wildfires and how these processes are coupled to specific ecological processes. Fire behaviour research has been slow in attracting researchers with the proper backgrounds in applied mathematics, engineering, hydrology and ecology. Further, what efforts have occurred has been in wildfire suppression. Fire suppression research approaches fire as a kind of war in which logistics and technology are the primary concerns. Fire ecology research has been largely descriptive, either of plant community composition recovery from imprecisely defined fire behaviour, landscape ecology patterns left by fires, or apparent plant adaptations to fire. Careful understanding of how wildfires cause the effects observed on population and ecosystem processes has been perused by only a few, most of who were not originally ecologists or foresters. In this talk I will discuss some of what I consider to be the central problems in fire ecology that need research.

Title: On the modelling of forest fire propagation.

Abstract:

In the first part of the talk we will analyze the different scales involved in the propagation of forest fires. They are mainly: The microscopic scale which is the scale of the vegetal cell associated to pyrolysis and drying. The mesoscopic scale is the scale associated to vegetation considered as a porous media. The third scale is the macroscopic scale, at this scale vegetation is considered as an continuous medium. The last scale or "gigascopic" scale is the scale of a developed fire. At this scale the fire interacts with wind and slope. It is clear that it is impossible to describe with just one modelling the fire at all these scales. The choice of the modelling scale depends on the utilisation of the model. For instance the modelling at gigascopic scale is the more adapted for fire fighters. A brief overview of usual models of propagation will be done, especially the description of empirical models. The first type of models is cellular automata .Roughly speaking the cells of the automata can have two or three states, unburned, burning or burnt. The transition probability for a cell to change its state depends on the states of its neighbours. Fire spreading is seen as a percolation process on a two-dimensional lattice. The simulation for these models is very fast. The major interest of this group of models is that they give the critical occupation density above which the fire goes to infinity (under which the fire will die). The main aim of this kind of modeling is to explain forest fire phenomena with universal statistical critical laws (such as percolation density) assuming that these global characteristics of fire are insensitive to the details of physical interactions. Unfortunately, the transition probabilities are not related, a priori, to any measurable physical parameters, such as humidity, heat capacity etc. Therefore these types of models fall in the category of black box models, the output of which is mainly the position of the fire front. Up to now they don't fulfil the purposes cited above. The second group of models is the group of geometrical models. The fire front is seen as a line on a two-dimensional surface. The propagation of the front is calculated by the envelope method. The Huygens principle is the physical background of this method. These models can be very quickly simulated. However, the geometrical parameters are again difficult to relate a priori to physical parameters. The geometrical parameters must be fitted for all kinds of data on real fires. These kinds of modeling suffer from the same drawbacks as statistical ones. The third group of models is composed of the empirical models, a balance of energy is considered at the fire front but the velocity (or the rate of spread) of the front is given by an empirical law. The rate of spread is supposed to be a "scalar" function of the local parameters: load, humidity, slope wind …etc. Computations are still very fast, but the empirical laws are usually obtained from laboratory experiments, not from real fire experiments but because of the lack of similarity the transpositions to real terrain cases can sometimes be irrelevant. It can be shown that the two preceding types of models have a common similar structure. The second part of the talk will be dedicated to the description of the derivation of a model at macroscopic scale. At this scale one can not speak of a propagation model but in a more relevant way of a model of vegetal combustion. In the third part we will investigated the derivation of propagation model from combustion model set at macroscopic scale. The obtained model has the form of a reaction diffusion system. We will at this stage compare this model with the empirical one considered above and show that reaction diffusion models can do at least as well as empirical models. The last part of the talk will be dedicated to the exploration of the ability of the preceding model, to describe properly forest fire propagation at gigascopic scale. The model, a set of non linear reaction diffusion equations, will be set as a free boundary problem which admits a "level-set" formulation. We will show that under a certain value of the initial density of vegetation the fire does not "percolate". We will investigate the rate of spread for this type of models and show that the model can be fitted in order to reproduce experimental rate spread. And at least we will show how the modelling of fire fighting by retardant could be incorporated in the model.

Title: Convection in forest fires.

Abstract:

A model of forest fire propagation coupling the fire equations in a bidimensional domain representing the surface and the air equations in a three dimensional domain representing an air layer is presented. As the air layer thickness is small in front of its length, an asymptotic analysis gives a three dimentional air velocity governed by a quasi-stationary bidimensional equation on a convenient stream function. In that manner, a fire propagation taking into account the 3D air convection is obtained for the cheaper cost of a 2D computation. Numerical simulations are presented.

Title: Some developments in premixed combustion modeling.

Abstract:

Recent theoretical advances in premixed gas combustion are reviewed. The attention is focused on (i) self-acceleration of outward propagating wrinkled flames sustained by the intrinsic flame instability, and interpretation of the 7/3 flame-front fractal dimension, (ii) fragmentation of near-limit cellular flames and formation of self-drifting flame balls, (iii) flame acceleration and extinction by large-scale turbulence, (iv) multiplicity of detonation regimes in hydraulically resisted flows and the phenomenon of shock-free pressure-driven combustion, (v) hydraulic resistance as a mechanism of deflagration-to-detonation transition. A novel drag based mechanism for deflagration-to-detonation transition in long tubes is identified. The presence of drag rules out the conventional constant velocity flame as an equilibrium combustion mode. Yet, under mild ignition conditions and low friction the flame may emerge as a quasi-steady transient mode where the fresh premixture adjacent to the advancing flame front undergoes gradual (drag induced) precompression and preheating resulting in a localized thermal explosion and abrupt flame-to-detonation transition.