UDC 519.6
The paper developed and verified a mathematical model for the operational forecasting of the dynamics of forest fires, based on a system of partial differential equations. The model includes a non-stationary heat conduction equation, convective heat transfer by air flows, and the combustion kinetics of cellulose materials, taking into account the humidity. The scientific novelty of the work lies in the adaptation of a physically grounded approach of heat engineering to the problems of modeling natural fires, which allowed to take into account the influence of meteorological factors and the properties of combustible materials. A computational algorithm based on an implicit difference scheme and the method of forward sweep is implemented. Quantitative relationships have been established: an increase in wind speed from 1 to 6 m/s leads to a 4.3-fold increase in front speed, while an increase in humidity from 5 % to 30 % reduces it by 1.8 times. Verification based on experimental data showed a discrepancy of no more than 12 %. The practical significance for the Russian Ministry of Emergency Situations is to create a tool for predicting the time it takes for a fire to reach populated areas and optimizing firefighting operations.
forest fires, mathematical modeling, heat transfer equation, diffusion-convection model, wind speed, numerical methods, and spread prediction
1. Ob utverzhdenii Pravil tusheniya lesnyh pozharov: prikaz Ministerstva prirodnyh resursov i ekologii Rossii ot 1 apr. 2022 g. № 244. Dostup iz inf.-pravovogo portala «Garant».
2. Rothermel R.C. A mathematical model for predicting fire spread in wildland fuels. USDA Forest Service Research Paper INT-115, 1972.
3. Grishin A.M. Matematicheskoe modelirovanie lesnyh pozharov i novye sposoby bor'by s nimi. Novosibirsk: Nauka: Sib. otd-nie, 1992. 404 s.
4. Sullivan A.L. Wildland surface fire spread modelling, 1990–2007. International Journal of Wildland Fire. 2009. Vol. 18. № 4. P. 349–368.
5. Samarskij A.A. Teoriya raznostnyh skhem. M.: Nauka, 1989.
6. Anderson H.E. Aids to determining fuel models for estimating fire behavior. USDA Forest Service, 1982.
7. Pyne S.J. Introduction to wildland fire. John Wiley & Sons, 1996.
8. Finney M.A. FARSITE: Fire Area Simulator. USDA Forest Service, 1998.
9. Valendik E.N., Kosov I.V. Vozdejstvie konduktivnogo teplovogo potoka nizovogo pozhara na razvitie podstilochno-gumusovogo // Lesnoe hozyajstvo. 2008. № 5. P. 43–45.
10. Cheney N.P., Gould J.S., Catchpole W.R. The influence of fuel, weather and fire shape variables on fire-spread in grasslands // International Journal of Wildland Fire. 1993. Vol. 3. № 1. P. 31–44.
11. Morvan D., Dupuy J.L. Modeling the propagation of a wildfire through a Mediterranean shrub using a multiphase formulation // Combustion and Flame. 2004. Vol. 138. № 3. P. 199–210.
12. Dimitrakopoulos A.P., Papaioannou K.K. Flammability assessment of Mediterranean forest fuels // Fire Technology. 2001. Vol. 37. № 2. P. 143–152.
13. Wilson R.A. A reexamination of fire spread in free-burning porous fuel beds // USDA Forest Service Research Paper INT-289. 1982.
14. Frankman D., Webb B.W., Butler B.W. Influence of absorption by environmental water vapor on radiation transfer in wildland fires // Combustion Science and Technology. 2008. Vol. 180. № 3. P. 509–518.
15. Cruz M.G., Alexander M.E., Wakimoto R.H. Modeling the likelihood of crown fire occurrence in conifer forest stands // Forest Science. 2004. Vol. 50. № 5. P. 640–658.
16. Andrews P.L. BehavePlus fire modeling system: past, present, and future // Proceedings of the 7th Symposium on Fire and Forest Meteorological Society. 23–25 October 2007. P. 1–13.
17. Metodika prognoza razvitiya lesnyh pozharov na osnove geoinformacionnyh sistem / Pushkin A.A. [i dr.] // Trudy BGTU. Seriya 1: Lesnoe hozyajstvo, prirodopol'zovanie i pererabotka vozobnovlyaemyh resursov. 2025. № 1 (288).
18. GOST R 22.1.09-99. M0onitoring i prognozirovanie lesnyh pozharov. Dostup iz inform.-pravovogo portala «Garant».
19. Byram G.M. Combustion of forest fuels. McGraw-Hill, 1959.
20. Matthews S. A process-based model of fine fuel moisture // International Journal of Wildland Fire. 2006. Vol. 15. № 2. P. 155–168.
