Nonlinear mathematical model and numerical algorithm for monitoring and predicting the concentration of harmful substances in the atmosphere

Abstract

The article developed a nonlinear mathematical model and an effective numerical algorithm for monitoring and forecasting the process of spreading industrial emissions in the atmosphere, taking into account the orography of the area and the speed of movement of fine substances. Multidimensional partial differential equations describe the model with corresponding initial, internal, and boundary conditions of the third kind to consider mass transfer across the interface. In the work, to prove the adequacy of the developed mathematical apparatus, the calculated data are compared with field data taken from a specific object, in which the computational algorithm provides sufficient accuracy of the solution, based on which it can be concluded that the developed mathematical model and the numerical algorithm have a certain advantage over others numerical methods.

Creation of a software tool for monitoring and forecasting the process of transport and diffusion of harmful substances in the atmosphere

“…The mathematical model employed in this research considers the velocities of particles carrying harmful substances in different directions. This approach allows for a more comprehensive understanding of the movement and behavior of pollutants in the atmosphere [6]:…”

“…Due to the complexity of the problem, finding an exact analytical solution is challenging. To address this, the researchers in [7][8][9] have employed an implicit finite-difference scheme in time to approximate the solution.…”

A Combined Approach for Predicting the Distribution of Harmful Substances in the Atmosphere Based on Parameter Estimation and Machine Learning Algorithms

“…Modeling of air pollution based on the solution of partial differential equations is a fairly reliable and well-established approach [2][3][4]. For example, Aydosov [5] developed a mathematical model for dispersion and transport of pollutants from an instantaneous point source in the atmosphere with partial absorption of surface impurities using a transport equation with a source term.…”