Modelling of the Diffusion-Convection Process of a Pollutant with a Periodic Source
The Krasnodar region with its unique natural resources requires a thorough environmental assessment, an adequate evaluation of the harmful effects the technical and economic facilities have on natural processes, as well as means to forecast the consequences of their influence on the region’s ecosystem.The use of various approaches to modeling the process of the pollutant spread allows implementing methods applicable for the assessment of the state of the regional ecological system. The work is devoted to the development of numerical-analytical methods for solving problems of the impurities migration in the atmosphere and the aquatic environment, based on the use of integral transformations and new efficient algorithms for the construction of the Green’s symbols functions for a multilayer medium.The paper considers a periodic convection-diffusion problem that describes the propagation and decay of substances in a multilayer medium. Emission sources are modeled by functions that allow for selection of a periodic function that can be represented as a Fourier series, as a time-dependent multiplier. We present a method for constructing a solution to a boundary value problem, which is based on the construction of an integral representation for the solution in Fourier images. Calculations of the substance concentration function for the problem of convection-diffusion-decay with a periodic localized source, implemented according to the described algorithm, are presented. In the numerical model, the calculation of the Fourier integral is based on the higher-order Gauss-Kronrod formulas.The presented model allows accounting for the daily, weekly and seasonal technological and natural work cycles of polluting enterprises. The results can find practical application in identification of contaminated zones and territories resulting from planned and emergency emissions into the atmosphere or water areas.