Mathematical model and numerical algorithm for studying the process of dispersion of dust and fine aerosols in the atmosphere
DOI:
https://doi.org/10.71310/pcam.1_63.2025.05Keywords:
wind speed and direction, decrease in the concentration of pollutants, deposition velocity, direct method, semi-implicit difference schemeAbstract
Environmental pollution is one of the most critical issues of our time, as it leads to the deterioration of human health, the degradation of flora and fauna, and the suppression of vegetation. To study and predict the process of the spread of harmful substances in the surface layer of the atmosphere, a mathematical model has been developed that takes into account: the decrease in the concentration of pollutants in the atmosphere due to decomposition and photochemical transformation; changes in wind patterns over time and depending on the orography of the area; changes in the diffusion coefficient and the turbulent mixing coefficient vertically under stable and unstable stratification. The model is based on the fundamental laws of fluid mechanics, such as the conservation of mass, momentum, and impulse. Additionally, a calculation methodology is used that considers hydrodynamic factors of weather and climate, such as the capture of aerosol particles by plants, interaction with the ground, changes in wind speed and direction, as well as the turbulence coefficient both vertically and horizontally. To ensure a high order of accuracy and stability of the difference schemes, a semi-implicit finite-difference scheme and the "direct"method are applied to integrate the given problem.
References
Михайлюта C.B., Леженин A.A., Тасейко О.В., Битехтина М.А. Экологическая индустрия: ветровые потоки в городской застройке Красноярска. // Инженерная экология. – 2012. – N3. – С. 26–37.
Локощенко М.А., Еланский Н.Ф., Трифанова А.В. Влияние метеорологических условий на загрязнение воздуха в Москве. // Экология человека Вестник Российской Академии естественных наук – 2014. – №1 – C. 64–67.
Elminir H.K. Dependence of urban air pollutants on meteorology //Science of the total environment. – Т. 350. – №. 1–3. – 2005. – С. 225–237.
Чжоу Ц. и др. Влияние температуры окружающей среды и влажности атмосферы на динамику диффузии утечки фтористого водорода на основе метода вычислительной гидродинамики. // Токсики. – Т. 12. – №. 3. – 2024. – 184. c.
Shuangchen M. et al. Environmental influence and countermeasures for high humidity flue gas discharging from power plants Renewable and Sustainable Energy Reviews. // – 2017. – Т. 73. – С. 225–235.
Zhang J. P. et al. The impact of circulation patterns on regional transport pathways and air quality over Beijing and its surroundings. // Atmospheric Chemistry and Physics. – 2012. – Т. 12. – №. 11. – С. 5031–5053.
Aky¨uz M., ¸Cabuk H. Meteorological variations of PM2. 5/PM10 concentrations and particleassociated polycyclic aromatic hydrocarbons in the atmospheric environment of Zonguldak, Turkey. // Journal of hazardous materials. – 2009. – Т. 170. – №. 1. – С. 13–21.
Said S.A. M. et al. The effect of environmental factors and dust accumulation on photovoltaic modules and dust-accumulation mitigation strategies. // Renewable and Sustainable Energy Re-views. – 2018. – Т. 82. – С. 743-760.
Amamou A., Mahjoub H., Al-Farhany K., Said N.M., Bournot H. Experimental and CFD analyses of pollutant dispersion around an isolated cylindrical building. //Waves in Random and Complex Media, 1–35. https://doi.org/10.1080/17455030.2023.2179861 – 2023.
Noyes P.D. et al. The toxicology of climate change: environmental contaminants in a warming world. // Environment international. – 2009. – Т. 35. – №. 6. – С. 971–986.
Huang X., Wang H., Gao L. 2020. Numerical simulation of airflow and dispersion in 3D street canyons: the effect of atmospheric temperature stratification. // Environmental Technolo-gy, 44(17), – P. 2563–2580. – 2022. https://doi.org/10.1080/09593330.2022.2036247
Coccia M. The effects of atmospheric stability with low wind speed and of air pollution on the accelerated transmission dynamics of COVID-19. // International Journal of Environmental Studies. – 2021. – Т. 78. – №. 1. – С. 1–27.
Popov O. et al. Emergencies at potentially dangerous objects causing atmosphere pollution: peculiarities of chemically hazardous substances migration. // Systems, Decision and Control in Energy I. – Cham : Springer International Publishing, 2020. – С. 151–163.
Zhao L. et al. Influence of atmospheric fine particulate matter (PM2.5) pollution on indoor environment during winter in Beijing. // Building and Environment. – 2015. – Т. 87. – С. 283–291.
Hernandez G. et al. Temperature and humidity effects on particulate matter concentrations in a sub-tropical climate during winter. // International proceedings of chemical, biological and environmental engineering. – 2017. – Т. 102. – №. 8. – С. 41–49.
Грундстрем М. и др. Изменение и ковариация PM10, концентрации частиц, NOx и NO2 в городском воздухе – Связь со скоростью ветра, вертикальным градиентом температуры и типом погоды. // Атмосферная среда. – 2015. – Т. 120. – С. 317–327.
Sharan M., Gopalakrishnan S.G. Mathematical modeling of diffusion and transport of pollutants in the atmospheric boundary layer. // Pure and Applied Geophysics. – 2003. – Т. 160. – С. 357–394.
Ravshanov N., Sharipov D. Advanced mathematical model of transfer and dif-fusion process of harmful substances in the atmospheric boundary layer. // Journal of Advance Research in Com-puter Science Engineering. ISSN. – 2016. – С. 2456–3552.
Мурадов Ф.А., Таштемирова Н.Н., Эшбоева Н.Ф., Гозиев Х.И. Численное моделирование трехмерного поля скорости ветра в атмосфере. // Проблемывычислительной и прикладной математики. – 2024. – No 1(55). – С. 48–56.
Lakehal D. On the modelling of multiphase turbulent flows for environmental and hydrodynamic applications. // International Journal of Multiphase Flow. – 2002. – Т. 28. – №. 5. – С. 823–863.
Temirbekov N. et al. Mathematical and computer modeling of atmospheric air pollutants transformation with input data refinement. // Indonesian Journal of Electrical Engineering and Computer Science. – 2023. – Т. 32. – №. 3. – С. 1405–1416.
Guha A. Transport and deposition of particles in turbulent and laminar flow. // Annu. Rev. Fluid Mech. – 2008. – Т. 40. – №. 1. – С. 311-341.
Giardina M., Buffa P. A new approach for modeling dry deposition velocity of particles. // Atmospheric Environment. – 2018. – Т. 180. – С. 11–22.
Pisso, I., Sollum, E., Grythe, H., Kristiansen, N. I., Cassiani, M., Eckhardt, S., Arnold, D., Morton, D., Thompson, R. L., Groot Zwaaftink, C. D., Evangeliou, N., Sodemann, H., Haimberger, L., Henne, S., Brunner, D., Burkhart, J. F., Fouilloux, A., Brioude, J., Philipp, A., Seibert, P., and Stohl, A. The Lagrangian particle dispersion model FLEXPART version. // Geosci. Model Dev., 12, – P. 4955–4997. https://doi.org/10.5194/gmd-12-4955-2019, – 2019.
Фаддеева В.Н. Метод прямых в применении к некоторым краевым задачам. // Труды Математического института АН СССР им. В.А. Стеклова, т. XXVIII (28), М., – 1949.
Каримбердиева С. Численные решения дифференциально-разностных уравнений в параллелопипиде, шаре и цилиндре. // Т., «Фан», – 1983. – 112 с.
Фаддеев Д.К., Фаддеева В.Н. Вычислительные методы линейной алгебры. // М., – 1960.
