Abstract
The conducted researches served as the basis for obtaining difference scheme for numerical realization of the two-dimensional model of mass transfer of a pollutant in the aeration zone of the soil of the agrolandscape with a piecewise smooth surface under the condition of instantaneous deposition of the pollutant onto the surface (as an example, Cs137 was taken as a pollutant on the basis of its passive behavior in the ground and the availability in the considered ground areas of agricultural uses due to the Chernobyl accident). The properties of differential operators of the model and their difference analogues were studied, which allowed to substantiate the cost-effective difference scheme for the numerical solution of the problem of pollutant migration for given agrolandscape. The correctness and efficiency of the constructed two-layer implicit difference scheme is shown. This allowed to switch to the use of a chain of one-dimensional implicit tasks, in which the transition from one layer to another occurs in two steps. Obtained general computing costs allowed to assert that the proposed schemes are cost-effective difference schemes. In turn, the use of an economical difference scheme made it possible to construct a method for the practical determination of the presence of a process of water erosion in the system of hydraulic rampart-terrace.
Highlights
The study of dissemination of anthropogenic pollution in the environment is an important scientific and applied task
The most popular in practical research are those that use as mathematical models of the regression equation and differential equations based on the use of physical laws related to the movement of moisture and heat flows
Among all publications should highlight research in agriculture and ecology, such as in [3,4,5]. Processes considered in these publications mostly are one-dimensional for horizontal or vertical profile and researchers use different methods to solve the problems of mass transfer
Summary
The study of dissemination of anthropogenic pollution in the environment is an important scientific and applied task. Processes considered in these publications mostly are one-dimensional for horizontal or vertical profile and researchers use different methods to solve the problems of mass transfer In these papers, the authors mainly use models derived from regression dependencies and models described by exact solutions of differential equations. The objects of our research are: β the mathematical model of mass transfer in a bounded area with a piecewise-continuous surface, taking into account the nature of contamination and the existence of a unique solution of the corresponding differential problem; β the difference analogue of a differential operator and the construction of a cost-effective difference scheme for the numerical solution of the problem of pollutant migration in the aeration zone of a given agrolandscape.
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