Development of the Turbulent Diffusion Model of Fine Suspended Substances in the Lower Atmosphere Layer

Abstract

A promising direction for solving the problem of air pollution by fine substances is the use of numerical modeling in the development of mathematical models of the transport of pollutants in the atmosphere. An urgent problem in applying mathematical models with numerical algorithms and software is constructing a qualitative model that would meet both the physical parameters and fulfill all the optimal conditions of numerical analysis. The main objective of this study was to develop an algorithm of a mathematical model based on the equation of distribution of impurities in a turbulent medium. That allows considering the simultaneous influence of wind speed, turbulence of atmospheric air, pollution parameters, direction, and wind force on the size of scattering zones. The unique feature of the study is the use of the coordinate splitting equation of impurities distribution in a turbulent environment with subsequent normalization and parameterization of conditions. Finding integrands functions in the calculation algorithm allows obtaining a stable computational algorithm of the proposed propagation model of fine suspended particles. The solution of the function implemented in the Mathcad Prime 7 software. Distributions of concentrations and their levels for various values of turbulence of atmospheric air and dangerous wind speed are received. The most significant number of fine particles is at a distance of up to 4 km from the emission source. Still, there is also the transfer of contaminants at more than 5 km (up to 57 % of the initial emission concentration). The model has convenient software and algorithmic software, the time of calculation of graphic visualizations up to 20 minutes on medium-power computers. The obtained mathematical model can use in systems of forecasting man-caused load on the environment for the prompt solution of environmental problems.