NONLINEAR MATHEMATICAL MODEL FOR MONITORING AND FORECASTING THE PROCESS OF DISTRIBUTING AEROSOL PARTICLES IN THE ATMOSPHERE

In this article there was developed a mathematical model for predicting, monitoring and assessing the ecological state of the atmosphere and underlying surface by passive and active impurities, where the varying velocity of particles in the atmosphere are considered. The successful solution of the tasks of monitoring and predicting the level of atmospheric pollution by harmful substances released from production facilities into the environment is based on the use of mathematical models that take into account the physical characteristics of the propagation of impurities, the relationship between the concentrations of impurities and environmental parameters: change in wind speed and direction over time, harmful absorption coefficient substances into the atmosphere, the rate of deposition of fine particles, soil properties, etc. To determine the speed of movement of fine particles in the atmosphere, a system of nonlinear equations has obtained, where the basic physic mechanical properties of the particles and the velocity of the air mass in the atmosphere were considered, which play an important role. A qualitative analysis of the solution has been carried out and a numerical algorithm has been compiled for conducting a computational experiment on a computer. Since the developed nonlinear mathematical model is described by a multidimensional nonlinear partial differential equation with the corresponding initial and boundary conditions, a numerical algorithm using an implicit finite-difference scheme is developed to solve it.