Model of distribution of pollutant substances in a multilayered medium with a periodic radiation source

Abstract

Based on the equations of turbulent diffusion for convection-diffusion-decay processes, an algorithm has been developed for calculating the distribution of pollutants in a diffusion medium that are emitted by a time-periodic radiation source. The medium is a multilayer packet of layers with plane-parallel interfaces, the radiation source can be located either at the boundaries of the packet of layers or inside it. The solution is constructed in Fourier images using the symbols of the Green functions of boundary value problems for periodic sources. The inverse two-dimensional Fourier transform is calculated numerically. It is shown in the paper that the boundary value problem for a periodic source can be reduced to solving a slightly modified boundary value problem for stationary equations of turbulent diffusion. Methods for solving a stationary boundary value problem are developed in detail in previous works of the authors. It is noted that for a periodic source, in comparison with a stationary source, the computational volumes grow in proportion to the number of harmonics in the Fourier expansion of the periodic component of the source. An example of a numerical solution of the spatial boundary-value problem for a two-layer packet with an internal periodic radiation source is given. The example takes into account nine members of the Fourier series in the source statement. The developed numerical-analytical model has high accuracy and flexibility and can be used to simulate various periodic diffusion-convection-reaction processes, and to obtain various estimates in the field of ecology and environmental protection. The proposed method is effective for solving boundary value problems for semi-bounded multilayer media for which the traditionally used finite element and finite difference methods are not applicable.