Mathematical Models of Inverse Problems for Finding the Main Characteristics of Air Pollution Sources
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Mathematical Models of Inverse Problems for Finding the Main Characteristics of Air Pollution Sources Artur O. Zaporozhets
&
Vladyslav V. Khaidurov
Received: 14 September 2020 / Accepted: 15 November 2020 # Springer Nature Switzerland AG 2020
Abstract The paper describes optimization of mathematical models for determining the main characteristics of the source of environmental pollution. A modification of the classical Newton’s method for finding a numerical solution of the constructed mathematical models for identifying the parameters of an environmental pollutant has been developed. A modification of the classical Newton’s method is obtained, which makes it possible to reduce the total number of calculations in the process of determining the main characteristics of the pollution source. A number of software-implemented computational experiments have been carried out for the model for determining the height of the pipe of the pollution source and the concentration of emissions on it, the model for determining the full location of the pipe of the pollution source and the concentration of emissions from the source. The possibility of complete localization of the pollution source in less than 40 measurement iterations using 1 post of the air pollution monitoring system has been established. The proposed method makes it possible to reduce by 3 times the number of simulation iterations for detecting a source of pollution in comparison with classical methods for solving inverse problems during monitoring of air pollution.
A. O. Zaporozhets (*) : V. V. Khaidurov Institute of Engineering Thermophysics of NAS of Ukraine, Kyiv, Ukraine e-mail: [email protected]
Keywords Turbulent diffusion equations . Atmospheric pollution . Inverse problem . Pollution source . Optimization model . Newton’s method
1 Introduction Environmental problems in the modern world occupy one of the priority places among the scientific community (Oves et al. 2018; Sładkowski 2020; Kapustnyk et al. 2019). This is primarily caused by a rapid increase in the average temperature on the planet (Assad et al. 2019; Lelieveld et al. 2016; Gasparrini et al. 2017; Caloiero 2017) due to an increase in greenhouse gases in the air (Meyer and Newman 2020; Van Vuuren et al. 2017; Zhu-Barker et al. 2017), which in turn is associated with the development of industry (Fraccascia and Giannoccaro 2019; Meng et al. 2017), an increase in the number of automobile (Kumar and Gupta 2016; Shiraki et al. 2020) and aviation (Hudda et al. 2020) transport, and other natural phenomena and anomalies (Herndon 2018). This also results in a general deterioration in the condition of atmospheric air. Several approaches are now being used to reduce the amount of air pollutants: 1. Modernization of existing power equipment to improve its technical and economic characteristics (Zaporozhets 2019; Babak et al. 2020; Zaporozhets 2020; Dzikuć et al. 2020; Li et al. 2019); 2. Using of new types of fuel (biofuels, hydrogen, etc.) (Li et al. 2019; Tang et al. 2019; Devarajan et al.
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