NUMERICAL MODELING OF DIFFUSION OF CONTAMINANTS IN RIVERS WITH REGARD OF DIFFUSE TERM

This paper deals with the problems of modeling and forecasting the spread of pollutants in the water flow in the river. The state reports of the Ministry of natural resources and ecology are analyzed, on the basis of which the importance of tracking the discharge of pollutants into the rivers, which are carriers of pollutants from the water flow rate, was shown. Of particular importance is the importance of predicting the spread of the concentration of pollutants in the river bed and the further discharge of water into water bodies. In this article we consider twodimensional modeling of the process of diffusion of pollutants in rivers, taking into account the diffuse factor. The symmetric parabolic equation of the second order was used as the basic one. Numerical modeling of the equations for different flow rates of water in the river and the velocity of the diffusion process was done in Matlab software. Three-dimensional profiles of concentration distribution depending on the river flow rate in the range of 0.1-1 m/s and the pollutant diffusion rate in the range of 0.5-10 m/s are plotted. It is shown that at low diffusion rates the concentration is almost constant, and the high diffusion rate gives a sharp increase in the concentration at the initial time, followed by a smooth decline.

1. State and use of water resources in the Republic of Karachay-Cherkessia. // Materials of the 1st Republican scientific and practical conference on April 28, 2000 "Medical and social problems of iodine deficiency in the biosphere and the human body"// Ministry of health, Ministry of health, Stavropol state medical Academy, Circassian medical College. Cherkessk, 2000. - p. 18-25.

2. Samarskiy, A.A., Numerical methods for solving convection – diffusion [Text] / A.A. Samarskiy, P.N. Vabischevitch – M.: URSS. - 1999. - 248 p.

3. Kurbatov, E.A. MATLAB 7. Tutorial [Text] / E.A. Kurbatova – Williams, 2005. - 256 p.

4. Porshnev, S.V. MATLAB 7. Basics of operation and programming. Textbook. [Text] / S.V. Porshnev. Publishing house Bean. Laboratory of knowledge, - 2006. - 320 p.

5. Vishnevetskiy V.Yu., Starchenko I.B. Numerical modeling of diffusion of contaminants in rivers: one – and two-dimensional problems // Modeling, Optimization and Information Technology. Scientific Journal, 2019. V. 7, № 1. https://moit.vivt.ru/wp-content/uploads/2019/01/Vishnevetskiy Starchenko_1_19_1.pdf. Retrieved: 26.02.2019. doi: 10.26102/2310- 6018/2019.24.1.005