Purpose. Development of an effective scheme for numerical calculation of the joint solution of the problem of gas dynamics and the chemical kinetics of combustion of a gas-air medium on the basis of the large-particle method. Methodology. Mathematical modeling, numerical experiment, analysis and generalization chemical kinetics of combustion gas environments it is proposed to introduce concentration function into the numerical scheme of the method of large particles, which allows taking into account the multicomponent composition of the gas medium. This function is defined at the stage of formation of the estimated area and it defines the mole fraction of each substance in each cell of the design scheme. The function is involved in the calculation of the mass flows across the boundaries of computational cells, determining the mass flow for each substance. The concentration function allows introducing equation of chemical kinetics into the numerical scheme in the form of the Arrhenius equation and differentiating chemical reaction components and combustion products. In the problem of calculation of detonation explosions there are strong gradients of pressures, which, at the exit of the shock front on the border of the "free exit" generate non-physical fluctuations of the parameter. To exclude their influence on the process analysis of different types of approximation of the parameters in the fictitious layer design scheme is conducted. From the analysis of physical processes effective form of the boundary conditions of "free exit" for the problem of shock wave propagation in the channel is found. Originality. Due to the introduction of a concentration function, modification of the numerical method of large particles allows for the joint solution of problems of gas dynamics and chemical kinetics of combustion of an explosive gas-air environment. For correct operation of the boundary conditions of "free access" in terms of discontinuous currents approximation scheme of the parameter in a dummy layer based on shock adiabats of a specific gas has been developed. Practical value. The conducted modification of the method of large particles allows carrying out numerical experiment on the calculation of safe distances in case of emergency of gas explosions in coal mines as well as determining the dynamic blast load on structures based on the calculation of distribution of air shock wave on the channel.

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