International Journal of Wildland Fire International Journal of Wildland Fire Society
Journal of the International Association of Wildland Fire
REVIEW

Wildland surface fire spread modelling, 1990–2007. 1: Physical and quasi-physical models

Andrew L. Sullivan
+ Author Affliations
- Author Affliations

CSIRO Sustainable Ecosystems and CSIRO Climate Adaptation Flagship, GPO Box 284, Canberra, ACT 2601, Australia. Email: andrew.sullivan@csiro.au

International Journal of Wildland Fire 18(4) 349-368 https://doi.org/10.1071/WF06143
Submitted: 1 November 2006  Accepted: 13 March 2008   Published: 29 June 2009

Abstract

In recent years, advances in computational power have led to an increase in attempts to model the behaviour of wildland fires and to simulate their spread across the landscape. The present series of articles endeavours to comprehensively survey and précis all types of surface fire spread models developed during the period 1990–2007, providing a useful starting point for those readers interested in recent modelling activities. The current paper surveys models of a physical or quasi-physical nature. These models are based on the fundamental chemistry and physics, or physics alone, of combustion and fire spread. Other papers in the series review models of an empirical or quasi-empirical nature, and mathematical analogues and simulation models. Many models are extensions or refinements of models developed before 1990. Where this is the case, these models are also discussed but in much less detail.


Acknowledgements

I would like to acknowledge the CSIRO Sustainable Ecosystems Bushfire Dynamics and Applications (BDA) Team and the CSIRO Centre for Complex Systems Science for supporting the present project; Jim Gould and Rowena Ball for comments on the draft manuscript; Miguel Cruz and Stuart Matthews (BDA) and Grant Pearce (Scion, NZ) for internally reviewing the draft; and the anonymous journal referees who assisted in making this a much better article.


References


Albini FA (1985) A model for fire spread in wildland fuels by radiation. Combustion Science and Technology  42, 229–258.
CrossRef |

Albini FA (1986) Wildland fire spread by radiation – a model including fuel cooling by natural convection. Combustion Science and Technology  45, 101–113.
CrossRef |

Albini FA (1996) Iterative solution of the radiation transport equations governing spread of fire in wildland fuel. Combustion, Explosion, and Shock Waves  32(5), 534–543.
CrossRef |

Albini FA , Stocks BJ (1986) Predicted and observed rates of spread of crown fires in immature jack pine. Combustion Science and Technology  48, 65–76.
CrossRef | CAS |

Anderson DH, Catchpole EA, de Mestre NJ , Parkes T (1982) Modelling the spread of grass fires. Journal of Australian Mathematics Society, Series B  23, 451–466.
CrossRef |

Anderson TB , Jackson R (1967) Fluid mechanical description of fluidized beds: equations of motion. Industrial & Engineering Chemistry Fundamentals  6(4), 527–539.
CrossRef | CAS |

Asensio M , Ferragut L (2002) On a wildland fire model with radiation. International Journal for Numerical Methods in Engineering  54(1), 137–157.
CrossRef |

Asensio M, Ferragut L , Simon J (2005) A convection model for fire spread simulation. Applied Mathematics Letters  18, 673–677.
CrossRef |

Balbi J, Santoni P , Dupuy J (1999) Dynamic modelling of fire spread across a fuel bed. International Journal of Wildland Fire  9(4), 275–284.
CrossRef |

Ball R, McIntosh A , Brindley J (1999) The role of char-forming processes in the thermal decomposition of cellulose. Physical Chemistry Chemical Physics  1, 5035–5043.
CrossRef | CAS |

Blackshear PL (1974) ‘Heat Transfer of Fires: Thermophysics, Social Aspects and Economic Impact.’ (Scripta Book Co.: Washington, DC)

Butler B, Finney M, Andrews P , Albini F (2004) A radiation-driven model for crown fire spread. Canadian Journal of Forest Research  34(8), 1588–1599.
CrossRef |

Byram GM (1959a) Combustion of forest fuels. In ‘Forest Fire Control and Use’. (Ed. K Davis) Ch. 3, pp 61–89 (McGraw-Hill: New York)

Byram GM (1959b) Forest fire behaviour. In ‘Forest Fire Control and Use’. (Ed. K Davis) Ch. 4, pp. 90–123. (McGraw-Hill: New York)

Carrier G, Fendell F , Wolff M (1991) Wind-aided firespread across arrays of discrete fuel elements. I. Theory. Combustion Science and Technology  75, 31–51.
CrossRef |

Catchpole WR, Catchpole EA, Tate AG, Butler B, Rothermel RC (2002) A model for the steady spread of fire through a homogeneous fuel bed. In ‘Proceedings of the IV International Conference on Forest Fire Research 2002 Wildland Fire Safety Summit’, 18–23 November 2002, Luso, Portugal. (Ed. DX Viegas) p. 106. (Millpress Science Publishers: Rotterdam, the Netherlands)

Chandler CC, Storey TG, Tangren CD (1963) Prediction of fire spread following nuclear explosions. USDA Forest Service, Pacific Southwest Research Station, Research Paper PSW-5. (Berkeley, CA)

Cheney NP, Gould JS , Catchpole WR (1993) The influence of fuel, weather and fire shape variables on fire-spread in grasslands. International Journal of Wildland Fire  3(1), 31–44.
CrossRef |

Chetehouna K, Er-Riani M , Séro-Guillaume O (2004) On the rate of spread for some reaction-diffusion models of forest fire propagation. Numerical Heat Transfer, Part A: Applications  46(8), 765–784.
CrossRef | CAS |

Colman JJ, Linn RR (2003) Non-local chemistry implementation in HIGRAD/FIRETEC. In ‘Fifth Symposium on Fire and Forest Meteorology’, 16–20 November 2003, Orlando, FL. (American Meteorological Society: Boston, MA)

Colman JJ, Linn RR (2005) Separating combustion from pyrolysis in HIGRAD/FIRETEC. In ‘Sixth Symposium on Fire and Forest Meteorology’, 25–27 October 2005, Canmore, AB. (American Meteorological Society: Boston, MA)

Colman JJ , Linn RR (2007) Separating combustion from pyrolysis in HIGRAD/FIRETEC. International Journal of Wildland Fire  16(4), 493–502.
CrossRef |

Consalvi JL, Porterie B , Loraud JC (2002) A formal averaging procedure for radiation heat transfer in particulate media. International Journal of Heat and Mass Transfer  45(13), 2755–2768.
CrossRef |

Croba D, Lalas D, Papadopoulos C, Tryfonopoulos D (1994) Numerical simulation of forest fire propagation in complex terrain. In ‘Proceedings of the 2nd International Conference on Forest Fire Research, Vol. 1’, November 1994, Coimbra, Portugal. (Ed. DX Viegas) pp. 491–500. (DX Viegas: Coimbra, Portugal)

Cunningham P , Linn RR (2007) Numerical simulations of grass fires using a coupled atmosphere–fire model: dynamics of fire spread. Journal of Geophysical Research – Atmospheres  112, D05108.
CrossRef |

Curry JR , Fons WL (1938) Rate of spread of surface fires in the Ponderosa pine type of California. Journal of Agricultural Research  57(4), 239–267.


Curry JR , Fons WL (1940) Forest-fire behaviour studies. Mechanical Engineering  62, 219–225.


de Mestre NJ, Catchpole EA, Anderson DH , Rothermel RC (1989) Uniform propagation of a planar fire front without wind. Combustion Science and Technology  65, 231–244.
CrossRef |

Di Blasi C (1993) Modeling and simulation of combustion processes of charring and non-charring solid fuels. Progress in Energy and Combustion Science  19(1), 71–104.
CrossRef | CAS |

Di Blasi C (1998) Comparison of semi-global mechanisms for primary pyrolysis of lignocellulosic fuels. Journal of Analytical and Applied Pyrolysis  47(1), 43–64.
CrossRef | CAS |

Drysdale D (1985) ‘An Introduction to Fire Dynamics.’ (Wiley: Chichester, UK)

Dupuy J (1995) Slope and fuel load effects on fire behaviour: laboratory experiments in pine needle fuel beds. International Journal of Wildland Fire  5(3), 153–164.
CrossRef |

Dupuy JL (2000) Testing two radiative physical models for fire spread through porous forest fuel beds. Combustion Science and Technology  155, 149–180.
CrossRef | CAS |

Dupuy J , Larini M (1999) Fire spread through a porous forest fuel bed: a radiative and convective model including fire-induced flow effects. International Journal of Wildland Fire  9(3), 155–172.
CrossRef |

Dupuy JL , Morvan D (2005) Numerical study of a crown fire spreading toward a fuel break using a multiphase physical model. International Journal of Wildland Fire  14(2), 141–151.
CrossRef |

Emmons H (1963) Fire in the forest. Fire Research Abstracts and Reviews  5(3), 163–178.


Emmons HW (1966) Fundamental problems of the free-burning fire. Fire Research Abstracts and Reviews  8(1), 1–17.


Evans DD, Rehm RG, McPherson EG (2003) Physics-based modelling of wildland–urban intermix fires. In ‘Proceedings of the 3rd International Wildland Fire Conference’, 3–6 October 2003, Sydney. (CD-ROM) (3rd International Wildland Fire Conference and Exhibition 2003)

Fernandes PAM (2001) Fire spread prediction in shrub fuels in Portugal. Forest Ecology and Management  144(1–3), 67–74.
CrossRef |

Ferragut L, Asensio MI , Monedero S (2007) A numerical method for solving convection-reaction-diffusion multivalued equations in fire spread modelling. Advances in Engineering Software  38(6), 366–371.
CrossRef |

Ferziger JH, Perić M (1996) ‘Computational Methods for Fluid Dynamics.’ (Springer-Verlag: Berlin, Germany)

Fons WL (1946) Analysis of fire spread in light forest fuels. Journal of Agricultural Research  72(3), 93–121.


Forbes LK (1997) A two-dimensional model for large-scale bushfire spread. Journal of the Australian Mathematical Society. Series B. Applied Mathematics  39(2), 171–194.
CrossRef |

Gisborne HT (1927) The objectives of forest fire-weather research. Journal of Forestry  25(4), 452–456.


Gisborne HT (1929) The complicated controls of fire behaviour. Journal of Forestry  27(3), 311–312.


Grishin AM (1984) Steady-state propagation of the front of a high-level forest fire. Soviet Physics, Doklady  29(11), 917–919.


Grishin AM (1997) ‘Mathematical Modeling of Forest Fires and New Methods of Fighting Them. English Translation Edition.’ (Ed. F Albini) (Publishing House of Tomsk State University: Tomsk, Russia) [Translated from Russian by M Czuma, L Chikina, L Smokotina]

Grishin AM , Shipulina OV (2002) Mathematical model for spread of crown fires in homogeneous forests and along openings. Combustion, Explosion, and Shock Waves  38(6), 622–632.
CrossRef |

Grishin AM, Gruzin AD , Zverev VG (1983) Mathematical modeling of the spreading of high-level forest fires. Soviet Physics, Doklady  28(4), 328–330.


Grishin AM, Gruzin AD , Gruzina EE (1984) Aerodynamics and heat exchange between the front of a forest fire and the surface layer of the atmosphere. Journal of Applied Mechanics and Technical Physics  25(6), 889–894.
CrossRef |

Hanson HP, Bradley MM, Bossert JE, Linn RR , Younker LW (2000) The potential and promise of physics-based wildfire simulation. Environmental Science & Policy  3(4), 161–172.
CrossRef |

Hawley LF (1926) Theoretical considerations regarding factors which influence forest fires. Journal of Forestry  24(7), 756–763.


Incropera FP, DeWitt DP (1985) ‘Introduction to Heat Transfer.’ (Wiley: New York)

Jiménez J (2006) The numerical computation of turbulence. In ‘Lecture Notes on Turbulence and Coherent Structures in Fluids, Plasmas and Non-linear Media’ (Eds M Shats, H Punzmann) Vol. 4. Lecture Notes in Complex Systems, Ch. 6, pp. 281–307. (World Scientific: Singapore)

Karplus WJ (1977) The spectrum of mathematical modeling and systems simulation. Mathematics and Computers in Simulation  19(1), 3–10.
CrossRef |

Koo E, Pagni P, Woycheese J, Stephens S, Weise D, Huff J (2005) A simple physical model for forest fire spread. In ‘Fire Safety Science, Proceedings of 8th International Symposium’, 18–23 September 2005, Tsinghua University, Beijing, China. (Eds D Gottuk, B Lattimer) pp. 851–862. (International Association of Fire Safety Science)

Larini M, Giroud F, Porterie B , Loraud JC (1998) A multiphase formulation for fire propagation in heterogeneous combustible media. International Journal of Heat and Mass Transfer  41(6–7), 881–897.
CrossRef | CAS |

Launder BE, Reece GJ , Rodi W (1975) Progress in the development of a Reynolds-stress turbulence closure. Journal of Fluid Mechanics  68(3), 537–566.
CrossRef |

Lawson DI (1954) Fire and the atomic bomb. Department of Scientific and Industrial Research and Fire Offices’ Committee, Fire Research Bulletin No. 1 (London)

Lee SL (1972) Fire research. Applied Mechanics Reviews  25(3), 503–509.


Linn RR (1997) A transport model for prediction of wildfire behaviour. Los Alamos National Laboratory, Science Report LA-13334-T. (Los Alamos, NM)

Linn RR , Cunningham P (2005) Numerical simulations of grass fires using a coupled atmosphere–fire model: basic fire behavior and dependence on wind speed. Journal of Geophysical Research  110, D13107.
CrossRef |

Linn RR, Harlow FH (1998a) FIRETEC: a transport description of wildfire behaviour. In ‘Second Symposium on Fire and Forest Meteorology’, 11–16 January 1998, Pheonix, AZ, pp. 14–19. (American Meteorological Society: Boston, MA)

Linn RR, Harlow FH (1998b) Use of transport models for wildfire behaviour simulations. In ‘III International Conference on Forest Fire Research, 14th Conference on Fire and Forest Meteorology’, Luso, Portugal, 16–20 November 1998. (Ed. DX Viegas) Vol. 1, pp. 363–372. (Associacao para o Desenvolvimento da Aerodinamica Industrial (ADAI): Portugal)

Linn R, Reisner J, Colman JJ , Winterkamp J (2002a) Studying wildfire behavior using FIRETEC. International Journal of Wildland Fire  11(3–4), 233–246.
CrossRef |

Linn RR, Reisner JM, Winterkamp JL, Edminster C (2002b) Utility of a physics-based wildfire model such as FIRETEC. In ‘Proceedings of the IV International Conference on Forest Fire Research 2002 Wildland Fire Safety Summit’, 18–23 November 2002, Luso, Portugal (Ed. DX Viegas) p. 101. (Millpress Science Publishers: Rotterdam, the Netherlands)

Linn R, Winterkamp J, Colman J, Edminster C , Bailey JD (2005) Modeling interactions between fire and atmosphere in discrete element fuel beds. International Journal of Wildland Fire  14(1), 37–48.
CrossRef |

Lymberopoulos N, Tryfonopoulos T, Lockwood FC (1998) The study of small and meso-scale wind field–forest fire interaction and buoyancy effects using the AIOLOS-F simulator. In ‘III International Conference on Forest Fire Research, 14th Conference on Fire and Forest Meteorology, Vol. 1’, 16–20 November 1998, Luso, Portugal. (Ed. DX Viegas) pp. 405–418. (Associacao para o Desenvolvimento da Aerodinamica Industrial (ADAI): Portugal)

Margerit J , Séro-Guillaume O (2002) Modelling forest fires. Part II: Reduction to two-dimensional models and simulation of propagation. International Journal of Heat and Mass Transfer  45(8), 1723–1737.
CrossRef | CAS |

Mell W, Jenkins MA, Gould J , Cheney P (2007) A physics based approach to modeling grassland fires. International Journal of Wildland Fire  16(1), 1–22.
CrossRef |

Mendes-Lopes JMC, Ventura JMP, Amaral JMP (1998) Rate of spread and flame characteristics in a bed of pine needles. In ‘III International Conference on Forest Fire Research, 14th Conference on Fire and Forest Meteorology, Vol. 1’, 16–20 November 1998, Luso, Portugal. (Ed. DX Viegas) pp. 497–511. (Associacao para o Desenvolvimento da Aerodinamica Industrial (ADAI): Portugal)

Morandini F, Santoni PA , Balbi JH (2000) Validation study of a two-dimensional model of fire spread across a fuel bed. Combustion Science and Technology  157, 141–165.
CrossRef | CAS |

Morandini F, Santoni PA , Balbi JH (2001a) The contribution of radiant heat transfer to laboratory-scale fire spread under the influences of wind and slope. Fire Safety Journal  36(6), 519–543.
CrossRef |

Morandini F, Santoni PA , Balbi JH (2001b) Fire front width effects on fire spread across a laboratory scale sloping fuel bed. Combustion Science and Technology  166, 67–90.
CrossRef | CAS |

Morandini F, Santoni PA, Balbi JH, Ventura JM , Mendes-Lopes JM (2002) A two-dimensional model of fire spread across a fuel bed including wind combined with slope conditions. International Journal of Wildland Fire  11(1), 53–63.
CrossRef |

Morandini F, Simeoni A, Santoni PA , Balbi JH (2005) A model for the spread of fire across a fuel bed incorporating the effects of wind and slope. Combustion Science and Technology  177(7), 1381–1418.
CrossRef | CAS |

Morandini F, Silvani X, Rossi L, Santoni PA, Simeoni A, Balbi JH, Rossi JL , Marcelli T (2006) Fire spread experiment across Mediterranean shrub: influence of wind on flame front properties. Fire Safety Journal  41(3), 229–235.
CrossRef |

Morvan D , Dupuy J (2001) Modeling of fire spread through a forest fuel bed using a multiphase formulation. Combustion and Flame  127(1–2), 1981–1994.
CrossRef | CAS |

Morvan D , Dupuy JL (2004) Modeling the propagation of a wildfire through a Mediterranean shrub using a multiphase formulation. Combustion and Flame  138(3), 199–210.
CrossRef | CAS |

Morvan D , Larini M (2001) Modeling of one-dimensional fire spread in pine needles with opposing air flow. Combustion Science and Technology  164(1), 37–64.
CrossRef | CAS |

Morvan D, Larini M, Dupuy JL, Fernandes P, Miranda AI, Andre J, Séro-Guillaume O, Calogine D, Cuinas P (2004) Behaviour modelling of wildland fires: a state of the art. Deliverable D-03-01, EUFIRELAB. Available at http://eufirelab.org/prive/directory/units_section_3/D-03-01/D-03-01.pdf [Verified 25 May 2009]

Morvan D, Dupuy JL, Rigolot E , Valette JC (2006) FIRESTAR: a physically based model to study wildfire behaviour. Forest Ecology and Management  234, S114.
CrossRef |

Pagni PJ (1975) Flame spread over thin solid fuels. Journal of Heat Transfer  97(1), 153–155.


Pagni PJ, Peterson TG (1973) Flame spread through porous fuels. In ‘Proceedings of the 14th (International Symposium) on Combustion’, Pittsburgh, PA. pp. 1099–1107. (The Combustion Institute: Pittsburgh, PA)

Pastor E, Zarate L, Planas E , Arnaldos J (2003) Mathematical models and calculation systems for the study of wildland fire behaviour. Progress in Energy and Combustion Science  29(2), 139–153.
CrossRef |

Perry GLW (1998) Current approaches to modelling the spread of wildland fire: a review. Progress in Physical Geography  22(2), 222–245.


Pitts WM (1991) Wind effects on fires. Progress in Energy and Combustion Science  17(2), 83–134.
CrossRef |

Porterie B, Morvan D, Larini M , Loraud JC (1998a) Wildfire propagation: a two-dimensional multiphase approach. Combustion Explosion, and Shock Waves  34(2), 139–150.
CrossRef |

Porterie B, Morvan D, Loraud JC, Larini M (1998b) A multiphase model for predicting line fire propagation. In ‘III International Conference on Forest Fire Research, 14th Conference on Fire and Forest Meteorology’, Luso, Portugal, 16–20 November 1998. (Ed. DX Viegas) Vol. 1, pp. 343–360. (Associacao para o Desenvolvimento da Aerodinamica Industrial (ADAI): Portugal)

Porterie B, Morvan D, Loraud JC , Larini M (2000) Fire spread through fuel beds: modeling of wind-aided fires and induced hydrodynamics. Physics of Fluids  12(7), 1762–1782.
CrossRef | CAS |

Porterie B, Consalvi JL, Loraud JC, Giroud F , Picard C (2007) Dynamics of wildland fires and their impact on structures. Combustion and Flame  149(3), 314–328.
CrossRef | CAS |

Pyne SJ, Andrews PL, Laven RD (1996) ‘Introduction to Wildland Fire.’ 2nd edn (Wiley: New York)

Rehm RG , Baum HR (1978) The equations of motion for thermally driven, buoyant flows. Journal of Research of the National Bureau of Standards  83(3), 297–308.


Rehm R, Evans D, Mell W, Hostikka S, McGrattan K, Forney G, Boulding C, Baker E (2003) Neighborhood-scale fire spread. In ‘Fifth Symposium on Fire and Forest Meteorology’, 16–20 November 2003, Orlando, FL. Paper J6E.7. (American Meteorological Society: Boston, MA)

Reisner JM, Bossert JE, Winterkamp JL (1998) Numerical simulations of two wildfire events using a combined modeling system (HIGRAD/BEHAVE). In ‘Second Symposium on Fire and Forest Meteorology’, 11–16 January 1998, Phoenix, AZ, pp. 6–13. (American Meteorological Society: Boston, MA)

Reisner J, Wynne S, Margolin L , Linn R (2000a) Coupled atmospheric–fire modeling employing the method of averages. Monthly Weather Review  128(10), 3683–3691.
CrossRef |

Reisner JM, Knoll DA, Mousseau VA, Linn RR (2000b) New numerical approaches for coupled atmosphere–fire models. In ‘Third Symposium on Fire and Forest Meteorology’, 9–14 January 2000, Long Beach, CA. pp. 11–14. (American Meteorological Society: Boston MA)

Rogers JC, Miller T (1963) Survey of the thermal threat of nuclear weapons. Stanford Research Institute, Technical Report SRI Project No. IMU-4201. Unclassified version, Contract No. OCD-OS-62-135(111). (Menlo Park, CA)

Rothermel RC (1972) A mathematical model for predicting fire spread in wildland fuels. USDA Forest Service, Intermountain Forest and Range Experimental Station, Research Paper INT-115. (Odgen, UT)

Santoni PA (1998) Elaboration of an evolving calculation domain for the resolution of a fire spread model. Numerical Heat Transfer, Part A: Applications  33(3), 279–298.
CrossRef | CAS |

Santoni PA , Balbi JH (1998) Modelling of two-dimensional flame spread across a sloping fuel bed. Fire Safety Journal  31(3), 201–225.
CrossRef | CAS |

Santoni PA, Balbi JH , Dupuy JL (1999) Dynamic modelling of upslope fire growth. International Journal of Wildland Fire  9(4), 285–292.
CrossRef |

Santoni PA, Simeoni A, Rossi JL, Bosseur F, Morandini F, Silvani X, Balbi JH, Cancellieri D , Rossi L (2006) Instrumentation of wildland fire: characterisation of a fire spreading through a Mediterranean shrub. Fire Safety Journal  41(3), 171–184.
CrossRef |

Séro-Guillaume O , Margerit J (2002) Modelling forest fires. Part I: A complete set of equations derived by extended irreversible thermodynamics. International Journal of Heat and Mass Transfer  45(8), 1705–1722.
CrossRef |

Simeoni A, Santoni P, Larini M , Balbi J (2001a) On the wind advection influence on the fire spread across a fuel bed: modelling by a semi-physical approach and testing with experiments. Fire Safety Journal  36(5), 491–513.
CrossRef |

Simeoni A, Santoni PA, Larini M , Balbi JH (2001b) Proposal for theoretical improvement of semi-physical forest fire spread models thanks to a multiphase approach: application to a fire spread model across a fuel bed. Combustion Science and Technology  162(1), 59–83.
CrossRef | CAS |

Simeoni A, Larini M, Santoni PA , Balbi JH (2002) Coupling of a simplified flow with a phenomenological fire spread model. Comptes Rendus. Mécanique  330(11), 783–790.
CrossRef |

Simeoni A, Santoni PA, Larini M , Balbi JH (2003) Reduction of a multiphase formulation to include a simplified flow in a semi-physical model of fire spread across a fuel bed. International Journal of Thermal Sciences  42(1), 95–105.
CrossRef | CAS |

Thomas PH (1967) Some aspects of the growth and spread of fire in the open. Journal of Forestry  40, 139–164.
CrossRef |

Thomas PH (1971) Rates of spread of some wind-driven fires. Journal of Forestry  44, 155–175.
CrossRef |

Van Wagner CE (1967) Calculations on forest fire spread by flame radiation. Canadian Department of Forestry and Rural Development Forestry Branch, Technical Report, Departmental Publication No. 1185. (Ottawa, ON)

Vaz GC, Andre JCS , Viegas DX (2004) Fire spread model for a linear front in a horizontal solid porous fuel bed in still air. Combustion Science and Technology  176(2), 135–182.
CrossRef | CAS |

Weber RO (1991a) Modelling fire spread through fuel beds. Progress in Energy and Combustion Science  17(1), 67–82.
CrossRef |

Weber RO (1991b) Toward a comprehensive wildfire spread model. International Journal of Wildland Fire  1(4), 245–248.
CrossRef |

Williams FA (1982) Urban and wildland fire phenomenology. Progress in Energy and Combustion Science  8, 317–354.
CrossRef | CAS |

Williams FA (1985) ‘Combustion Theory: the Fundamental Theory of Chemically Reacting Flow Systems.’ 2nd edn. (Addison-Wesley Publishing Company: Reading, MA)

Wolff MF, Carrier GF , Fendell FE (1991) Wind-aided firespread across arrays of discrete fuel elements. II. Experiment. Combustion Science and Technology  77, 261–289.
CrossRef |

Yakhot V , Orszag SA (1986) Renormalization group analysis of turbulence. I. Basic theory. Journal of Scientific Computing  1(1), 3–51.
CrossRef |

Zhou X , Mahalingam S (2001) Evaluation of reduced mechanism for modeling combustion of pyrolysis gas in wildland fire. Combustion Science and Technology  171(1), 39–70.
CrossRef | CAS |

Zhou X , Pereira J (2000) A multidimensional model for simulating vegetation fire spread using a porous media submodel. Fire and Materials  24(1), 37–43.
CrossRef | CAS |

Zhou X, Mahalingam S , Weise D (2005a) Modeling of marginal burning state of fire spread in live chaparral shrub fuel bed. Combustion and Flame  143(3), 183–198.
CrossRef | CAS |

Zhou X, Weise D , Mahalingam S (2005b) Experimental measurements and numerical modeling of marginal burning in live chaparral fuel beds. Proceedings of the Combustion Institute  30(2), 2287–2294.
CrossRef |

Zhou X, Mahalingam S , Weise D (2007) Experimental study and large eddy simulation of effect of terrain slope on marginal burning in shrub fuel beds. Proceedings of the Combustion Institute  31(2), 2547–2555.
CrossRef |



Export Citation Cited By (105)