ЗАСТОСУВАННЯ СПРЯЖЕНОГО РІВНЯННЯ ДЛЯ РОЗВЯЗКУ ЗАДАЧ У ПРОБЛЕМІ ЗАБРУДНЕННЯ АТМОСФЕРНОГО ПОВІТРЯ

Abstract

The purpose of the work is to develop a numerical model for solving associated problems in the field of atmospheric air pollution during the emission of chemically hazardous substances in the event of accidents or terrorist attacks. The model is oriented to the rapid assessment of possible emission source allocation zones, so that at a given point of "interest" the concentration does not exceed the threshold level. The research method consists in applying the method of numerical integration of the two-dimensional differential equation of mass transfer, which simulates the propagation of a chemically dangerous substance in the atmospheric air. An equation is considered that is conjugate to the mass transfer equation. With the help of this equation, a zone is determined where the location of the emission source can lead to the emergence of dangerous concentrations, for a certain time, at the point of "interest". This information makes it possible to identify subzones where the emission of a dangerous substance, in case of an accident, a terrorist act will lead to undesirable consequences. For the solution of the conjugate problem, the approach proposed by G.I. Marchuk. On the basis of the developed numerical model, it is possible to carry out solutions as a direct problem – the calculation of contamination zones in the atmosphere at a known position of the emission source and the associated problem. The results of a numerical experiment are presented.