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
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.
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.
On the modelling of forest fire propagation.
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.
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
Some developments in premixed combustion modeling.
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.