Bulletin of TUIT: Management and Communication Technologies


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.

First Page


Last Page



[1] Aloyan A.E. Dynamics and kinetics of gas impurities and aerosols in the atmosphere / Course of lectures. - M.: IWM RAS, 2002. - 201 p., [2] Naats V. I., Naats I. E., Ryskalenko R. A., Yartseva E. P. Mathematical models and computational experiment in the problem of monitoring and forecasting the ecological state of the atmosphere: monograph / Stavropol: SKFU Publishing House, 2016. - 376 s. [3] V. Naats, I. E. Naats. Mathematical models and numerical methods for environmental monitoring of the atmosphere. - M.: FIZMATLIT, 2010. - 328 p. [4] Gendunov B.M., Glazunov G.P. Wind erosion of soil and dust. – - M.: FIZMATLIT, 2007. - 240 p. [5] Mednikov E.P. Turbulent transfer and deposition of aerosols. М.: Science, 1980. – 176 p. [6] S. Anan K.V. Mathematical modelling of air pollution project in thermal energy: dis. ... cand. “Bulletin of TUIT: Management and Communication Technologies” 9 Ravshanov N., Shafiev T.R., Tashtemirova N. 2018, 2 (44) / tech. sciences. Sri Venkateshwara University, Tirupati, 2014. [7] R.I. Larsen. A new mathematical model considering the time and frequency of averaging the concentration of air pollutants // Journal of the Association for the Control of Air Pollution. 2012. №19. Pp. 24-30. [8] Assimakopoulos V. Numerical modelling of dispersion of atmospheric: No. U164940. – London: ProQuest Dissertations Publishing, 2002. – URL: https://search.proquest.com/docview/1785357133 [9] Stepanenko S.N., Voloshin V.G. The Euler K-GDM model for calculating the concentration in the atmospheric air of harmful substances contained in industrial emissions // Ukrainian Hydrometeorological Journal. - 2009. –№5. - p. 5-14. [10] Penenko V.V., Tsvetovoy E.A. Mathematical models for studying the risks of environmental pollution. // applied mechanics and technical physics. 2004. V. 45, №2 P. 136-146 [11] Belyaev N.N. Numerical models for the prediction of air pollution from motor vehicle emissions / N. N. Belyaev, E. S. Slavinskaya, R. V. Kirichenko // Science and transport progress. - 2016. - № 6 (66). - p. 25-32. [12] Mishigova G.V. Modelling the process of air pollution. // Bulletin of the DGTU. 2012. №8 (69). Pp. 12-17. Modelling [13] Kondrakov O.V., Kryuchin O.V., Volosatov M.Yu., Kletrov S.Yu. the spread of pollutants in the atmosphere based on the “torch” model // Tomsk State University Bulletin. 2011. №1. Pp. 196-199 [14] Khashirova T.Yu., Akbasheva G.A., Shakova O.A., Akbasheva E.A. Modelling of air pollution / Journal "Fundamental Research". 2017. №8. Pp. 325-330 [15] Bespalov M.S. Modelling the spread of impurities in the atmosphere as a tool for air protection activities / PEMME, Volume XXVII, № 1, 2016 [16] Mashikhina P. B. Modelling the distribution of impurities in the atmosphere with the regard to the terrain // Bulletin of Dnipropetrovsk National University of Railway Transport named after Academician V. Lazaryan. - 2009. - №27. - p. 138-142. [17] Ravshanov N., Muradov F.A., Nabibulina L.M. Numerical simulation of the process of transfer and diffusion of active aerosol particles in the boundary layer of the atmosphere. Problems of computational mathematics and applied informatics. 2016. №2. P.47-59. [18] Ravshanov, N. Tashtemirova N. Advanced model of transfer process and diffusion of harmful substances in the atmospheric boundary layer // Theoretical & Applied Science. – 2017. – № 2(46). – Pp. 129-138. [19] Sharipov D. A Mathematical Model and Computational Experiment for the Study and Forecast of the Concentration of Harmful Substances in the Atmosphere // American Journal of Computation, Communication and Control. – 2016. – № 2(6). – Pp. 48-54. [20] Sharipov D.K., Muradov F.A., Ravshanov Z.N. Numerical simulation of the process of transfer and diffusion of active aerosol particles in the boundary layer of the atmosphere. Problems of computational mathematics and applied informatics. 2016. №2. P.47-59.



To view the content in your browser, please download Adobe Reader or, alternately,
you may Download the file to your hard drive.

NOTE: The latest versions of Adobe Reader do not support viewing PDF files within Firefox on Mac OS and if you are using a modern (Intel) Mac, there is no official plugin for viewing PDF files within the browser window.