Mathematical Modeling of Pollutant Dispersion in the Air from Industrial Emissions

A boundary problem is formulated to describe the processes of multi-component pollutant transport in the air in the presence of point sources. Using the concept of local potential, a theorem is developed that enables the construction of an algorithm for solving the problem via the finite element method (FEM). The choice of FEM is justified by its key advantages: (1) FEM provides an approximate solution in the form of an analytical expression; (2) it formalizes the procedure for satisfying boundary conditions by selecting a functional where one or both boundary conditions are natural; (3) it allows for constructing an approximation even in cases with discontinuous coefficients or when the non-homogeneous term of the differential operator includes a sum of Dirac delta functions. Furthermore, an algorithm is developed for solving a nonlinear boundary va¬lue problem with variable coefficients, featuring a singularity represented as a sum of unit Dirac delta functions. The mathematical model of pollutant dispersion above a given surface considers the effect of initial dispersion of pol-luted air and is formulated as a two-point boundary value problem for a system of diffe¬rential equations governing the material balance of organic pollutants in the air. The mathematical model formulated in this work describes the process of polluted airflows around an emission source located on a surface, leading to a nonlinear boundary value problem. The solution is obtained using FEM, which enables the construction of variable approximations in the presence of singularities such as Dirac delta functions. The variational formulation of the boundary problem is developed using the Ritz method, incorporating the local potential concept proposed by Glansdorff and Prigogine.