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.
Astashov et al. (2026) studied this question.