Department of Mechanical Engineering
University of Kentucky, Lexington, KY USA 40506-0503
E-mail: jmmcd@uky.edu
Web page: http://www.engr.uky.edu/ ∼ acfd
Abstract
A new approach to simulation of wildland fire spread is outlined, and preliminary results of computations and parallelization of the algorithms are presented and discussed. The fire spread model is based on a porous medium representation of the forest with heat source terms replacing treatment of detailed chemistry. The formulation is implemented in conjunction with a synthetic-velocity form of large-eddy simulation (LES) which is capable of producing far more detailed results than can be obtained with usual forms of LES, but yet is very efficient and easily parallelized.
Key words: Large-eddy simulation, Parallelization, Forest fire spread
1 Background
Wildland fires result in billions of dollars (USD) in financial losses annually on a global basis. In the US alone, more than a billion USD are spent per year simply on containment and extinguishment aspects of wildland fires. The amount of financial loss can be expected to rise in the coming years in developed regions of the world due to rapidly increasing extent of the wildland/urban interface, leading to far higher property losses in the form of homes and businesses in the path of wildland fires, and at the same time increased potential for loss of human and domestic animal life as seen in the fires in Southern
California during the Autumn 2003 fire season. At the same time, both the length of the yearly fire seasons and the extent of geographic territory subject to fires is expected to increase in response to global warming. Beyond this is the fact that setting forest fires is one of the most easily accomplished acts of terrorism, and the social upheaval caused by widespread forest fires, if nothing else, provides an effective diversion allowing even more sinister activities to go undetected.
Preprint submitted to Elsevier Science 22 April 2005

It is not difficult to recognize that the key to more effective control of wildland fire behavior is prediction—both a priori , in the sense of identifying the most likely times and places that fires might begin and/or spread rapidly once started, and in the ability to provide details of fire behavior during evolution of the fire. The first of these is widely practiced with at least a fair degree of effectiveness, worldwide. On the other hand, ability to predict fire spread in a useful fully-deterministic way is not yet available. In the US forms of the
BEHAVE code of Andrews et al.
[1] are widely used. These are easily employed via a graphical user interface (GUI) and can be executed in the field on laptop PCs—and the output is graphical and easily interpreted. But the computed results are for the most part no better than qualitative because they are produced entirely from phenomenological models of the type developed by Rothermel [2] and executed with some probabilistic features. Thus, despite the fact that such results can be computed very rapidly, they are of little value in guiding the almost instant-to-instant changes in tactics often demanded in control of fires, especially at the wildland/urban interface.
In the present work we describe current progress on a more intensive approach to simulating wildland fire evolution, and specifically, we consider parallelization of the corresponding large-eddy simulation (LES) code. In particular, we contend that to obtain results that are truly useful to firefighters, the model employed must be completely deterministic in that fluid motion and heat transfer must be computed from (at least) the
Navier–Stokes (N.–S.) and thermal energy equations. Moreover, this must be done for a range of scales that spans the important details of the forest (including locations of houses and other structures at the wildland/urban interface) and at the same time covers distances corresponding to at least microscale meteorology. In very large fires mesoscale meteorology, and the fire’s interaction with it, must be simulated because such fires are able to create their own weather, and this is a critical component in the physics of their spread, as has been emphasized by Clark et al.
[3] and others. All this clearly implies a need for dedicated massively-parallel supercomputing, either in the form of a very large shared-memory symmetric multiprocessor (SMP) or an extremely large PC cluster—or possibly some combination of these. We remark that it does not seem likely that use of the Tera Grid would be consistent with the faster-than-real-time (FTRT) computing needs of a firefighting scenario in the near future, but it could be extremely valuable in the context of data transfers once computations have been completed and for generating large numbers of a priori predictions mentioned above.
For the required FTRT simulations of large-scale fires it is clear that certain details would necessarily be ignored, and it is the specifics of choices related to this that distinguishes one model from another and at the same time sets the practical effectiveness of any particular model. For example, the level of detail embodied in models such as that of S´ero-Guillaume and Margerit [4] could not possibly lead to FTRT results on any hardware in the foreseeable future. For the sake of brevity, in the present work we will only outline the features of the model now being developed since in the present context it is parallel performance that is tantamount. We also observe that with regard to performance, the current model still is at least two orders of magnitude too slow. In particular, it should be clear that, in general, fire spread predictions must be available at least a half hour in advance to permit
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their use in altering firefighting tactics. Nevertheless, we believe the overall structure and nature of the proposed model will in time lead to such capability through nothing more than the natural progression of improvement in computing hardware.
2 Form of model
It is rather easy to see from the standpoint of CFD for forest fire spread that there are at least two things that a model capable of very fast execution cannot contain. The first is intricate details of the forest, per se —imagine attempting grid generation, even unstructured, for a detailed individual tree, accounting for limbs, branches, leaves and bark; and these details would change rapidly as the tree is consumed by fire and subjected to highly-swirling, turbulent winds created by the fire. So attempting this for thousands, possibly even tens of thousands, of trees is completely hopeless. The second is detailed chemistry. At any particular time and place during a forest fire it is impossible to know precisely what, if anything, is actually burning. Thus, even the most sophisticated combustion models are doomed to be incorrect in detail most of the time and in most spatial locations, and of course even the simplest such models significantly slow computations.
At the same time there are several items that must be included in the physical model if it is to be predictive in the necessary sense. The first is heat release rate due to all forms of combusting materials, and associated with this the induced fluid motion from buoyancy.
Second is the turbulent cross flow in wind-aided fires, and in particular interaction of this with the turbulent buoyant thermal plume created by the fire—and then, ultimately, interaction of all of this with microscale, and possibly mesoscale, meteorology. Third, again especially within the framework of wind-aided fires, is the creation and transport of firebrands, and then the initiation and spread of new fires caused by their spotting.
Fourth, an effective model must be able to simulate the separate types of wildland fire: ground fires, crown fires and general conflagrations consisting of combinations of these— and one would hope for sufficient physical realism to allow predictions of transition from any one of these types to another. Finally, especially from the standpoint of firefighter safety, the model should be capable of predicting density and spatio-temporal distribution of smoke, effects of fire suppressants and generation and movement of fire whirls within the overall fire. The model we present here has, in principle, the potential to meet all such requirements, but in its present form only the first and second have been implemented.
3 Analysis
Our forest fire model is constructed on the basis of three main ideas. First, replace the forest with a porous medium of very high porosity as was first done by Costa et al.
[5], and somewhat later, and independently, by McDonough and Garz´on [6] in only two space dimensions. Second, ignore all details of combustion chemistry, and simply focus on the
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main outcome of that chemistry, heat release. Finally, implement these ideas within the framework of a modern “synthetic velocity” large-eddy simulation (LES) formalism, as described by McDonough and Yang [7].
Within this framework, the governing equations for fluid motion and heat transfer take the form
ρ
0
1 ϕ
∂ U
∂t
+
ρ
0 c p
∂T
∂t
1
∇ · U = 0 ,
!
ϕ 2
U · ∇ U
+ U · ∇ T
!
=
=
−∇
∇ · ( p k
+ e
∇
µ ϕ
∆ U −
T ) +
µ
K
µ
K
U −
C
F
ρ
K
0
| U | U + δρg e
2
,
+
C
F
ρ
K
0
!
U · U + S .
(1)
(2)
(3)
In these equations U is the velocity vector and e
2 denotes the vertical direction Cartesian basis vector; T is temperature, and ρ and p are density and pressure, respectively. Dynamic viscosity is denoted by µ , and the effective thermal conductivity is represented by k e
; c p is an effective specific heat for the porous region. Observe that the effects of the porous medium are carried through the porosity ϕ and the permeability K , which are related as described in Garz´on et al.
[8], and a coefficient C
F appearing in what is often termed the
Forchheimer term. This is essentially a drag coefficient that in many current forest fire models is used to account for presence of trees in a very unsophisticated way.
The source term S in the third of the above equations controls the heat input, both temporally and spatially and thus, in general, must include effects of chemistry and radiation; in the present state of the model these effects have not been explicitly included. Presently, we use source term S defined as follows:
S = (1 − ϕ ) Q (4)
It should be noted that only the forested part of the domain can have a non-zero source term. We assume that once the temperature of the forest reaches 500 ◦ C at any location, the fire is started (at that location), and after 200 seconds of burning, the forest material is assumed to have been consumed. During the burning period, the value of at 450 (in units of ◦ C/second); otherwise, it is zero.
S/ρ
0 c p is set
The form of LES employed differs from usual treatments in three ways: i) solutions are filtered, rather than equations, ii) subgrid-scale (SGS) physical variables are modeled instead of their statistics, and iii) the complete velocity is constructed incorporating both large- and small-scale parts of the solution, in contrast to usual discarding of the smallscale part. The usual LES decomposition of dependent variables still is employed:
Q ( x , t ) = ˜ ( x , t ) + q ∗ ( x , t ) , x ∈ R
3 , (5) where Q is the complete solution vector, ˜ is the filtered large-scale part, and q ∗ is the SGS part of the solution. The large scale, ˜ , is computed directly from Eqs. (1), (2) and (3),
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and then filtered after each time step. The SGS part is obtained from a model consisting of the product of an amplitude factor and a discrete dynamical system (DDS). The former is computed for each dependent variable based on generalized Kolmogorov power laws as described by Holloway and McDonough [9], and the DDSs are obtained from a singlemode Galerkin approximation to the governing equations presented by McDonough and
Huang [10].
Equations (1), (2) and (3) are solved by rather standard, well-known methods consisting of trapezoidal integration in time, centered-differencing in space, Douglas and Gunn time splitting [11], and δ -form quasilinearization, all implemented in the context of a projection method to handle pressure-velocity coupling. Spatial filtering applied to the computed solution, as described by Yang and McDonough [12], is employed to handle aliasing arising from under resolution that occurs for very-high Reynolds number simulations.
4 Parallelization and Results
Parallelization of the discretization of the above equations has been performed using MPI for maximum portability. The parallel algorithm has been executed on the HP Integrity
SuperDome 224-processor SMP at the University of Kentucky, and on a 64-processor PC cluster, also at the University of Kentucky. Details of parallelization of the numerical algorithms associated with the above equations, in the absence of the thermal energy equation, have been reported by McDonough et al.
[13], and for the sake of brevity we merely note that in principle the same techniques were employed in the present study.
Figure 1 presents results of simulating a rather small forest fire burning on a 7 km ×
1 .
5 km flat region with simulations extending vertically to 2 km. The figure displays only the lower portion of this because little of interest is occurring above the height shown in the present simulation. A steady two km/sec crosswind is blowing from left to right in the figure, and the computed thermal plume is shown after a physical time of 10 minutes after initiation of a spot fire. One can see that a puff is just beginning to pinch off from the main smokey region, and that the wind field is being significantly altered by the buoyant plume.
In Fig. 2 we provide an indication of the gridding used for the reported simulations.
Figure 1. Simulated spot fire 10 minutes into burn.
This grid consisted of 144 × 64 × 35 points with equal spacing of ∆ x ∼ 49 m, ∆ z ∼ 44 m in the flow and cross flow directions, respectively, and non-uniform spacing in the vertical
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direction, as shown in the figure. The first 12 grid cells starting from the forest floor have a height of 1.5 m each and are shown here near the center of the fire. In this region the porosity is set to 0.98 to account for presence of trees, etc . Then beginning with the thirteenth grid cell fairly rapid stretching is used with a maximum of ∆ y ∼ 74 m attained for the last few cells at the top of the computational domain (not shown). Figure 2 also displays streamlines of SGS velocity, shaded with SGS vorticity magnitude to emphasize an important feature of our synthetic-velocity SGS modeling approach. In particular, one can see a complete range of sizes of flow structures in this figure. In the lower left-hand part of the figure a long region of swirling flow is seen. This covers more than a single grid cell in the flow direction while extending over several cells vertically, and over only a small fraction of a cell in the lateral direction. In the lower right-hand corner of the figure is a flat vortex spanning approximately three quarters of a cell in the flow and lateral directions, and a couple cells vertically. Finally, throughout the part of the forested region near the fire one can see single streamlines exhibiting significant twisting. We hypothesize that these various structures are related to onset of firewhirls often observed in actual forest fires.
35
30
25
20
15
10
5
Figure 2. Small-scale streamlines within burning region of forest.
0
0 5 10 15 20 25 30 35
Number of Processors
Figure 3. Speedup as a function of processors on HP SuperDome.
Figure 3 presents speedup as a function of number of processors for the HP Integrity
SuperDome. It is clear that scalability is extremely good through 16 processors, and still quite acceptable for 32 processors, despite the fact that we were not running in a
“dedicated” environment. It is worthwhile to comment that scaling indicated here is far better than that achieved on any previous HP SMP, and it is also far superior to that achieved on the PC cluster. It is evident, however, that the main shortcoming of the cluster employed was the relatively slow interprocessor communication, which is expected to continue to improve.
Acknowlegdements
The authors wish to express their gratitude to the University of Kentucky Computing
Center for the generous availability of their HP SuperDome computer. The second author
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would also like to thank the University of Kentucky Center for Computational Sciences for support of a significant part of his post-doctoral studies.
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