Mathematical and descrete models in the tasks of emergency pollution of atmospheric air

M. Biliaiev1, I. Kalashnikov2, V. Kozachina1, O. Berlov3

1Dnipro National University of Railway Transport named after Academician V. Lazaryan, Dnipro, Ukraine

2Kharkiv Department of the Branch «Design and Research Institute of Railway Transport» of the joint stock company «Ukrainian Railway», Kharkiv, Ukraine

3Pridneprovsk State Academy of Civil Engineering and Architecture», Dnipro, Ukraine

Coll. res. pap. nat. min. univ. 2019, 57:149-157


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Purpose.The purpose of the work is to develop a mathematical model for assessing the dynamics of air pollution in the case of non-stationary emission of a chemically hazardous substance at an industrial facility.

Methodology.To solve the problem, we used the equation for the velocity potential, on the basis of which the velocity field of the air flow was determined, and the equation of convective-diffusion dispersion of a chemically dangerous agent in atmospheric air. The equation of convective-diffusion scattering of an impurity allows one to take into account the velocity field of the wind flow, atmospheric diffusion, and the intensity of the emission of a chemically dangerous agent. In the numerical integration of the equation for the velocity potential, a locally one-dimensional difference scheme is used. The unknown value for the velocity potential at each step of the splitting is determined by the running account method. For the numerical solution of the equation of convective-diffusion scattering of an impurity, two splitting schemes were used. A feature of the schemes used is the determination of the unknown value of the concentration of a chemically dangerous substance by means of a running account.

The resultsBased on the developed numerical models, a specialized software package has been created. The developed software package was applied to assess the level of air pollution in the event of emission of a chemically hazardous substance at a railway station. The developed numerical models can be implemented on computers of low and medium power, which allows them to be widely used for solving various problems in the field of emergency air pollution.

Scientific novelty.The effective numerical models for calculating the zones of chemical contamination during the emission of hazardous substances into the atmosphere are considered. Models can be used to solve problems when developing an emergency response plan at an industrial facility or transport.

Practical significance.The developed numerical models can be used to assess the risk of toxic damage to people in open areas in case of emergency emission of chemically hazardous substances.

Keywords:chemical pollution of the atmosphere, emergency situations, numerical simulation.


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