NUMERICAL MODELING OF DIFFUSION OF CONTAMINANTS IN RIVERS: ONE – AND TWO-DIMENSIONAL PROBLEMS
V.Y. Vishnevetskiy , I.B. Starchenko
The work is devoted to the actual problem of modeling and thus subsequently predicting the spread of pollution by water flow in rivers. This task is particularly relevant in the aspect of flow accounting in the main channel of river tributaries. The general problems of modeling of ecological systems were considered; the importance of methodological approach was shown. Further, the problem was decomposed into the study of the river bed, as in the rivers there are significant water flow rates and the spread of pollutants can be explosive. This article deals with the diffusion of pollutants in rivers in the framework of one – and two-dimensional problems. The equations of transport of substances along the trajectories for the one – dimensional case and the non-stationary convection-diffusion equation in the divergent form for the two-dimensional case with the corresponding boundary conditions were used as initial ones. The equations were solved numerically using Matlab software. Profiles of distribution of concentrations of pollutants for water flow rates in the river in the range of 1-10 m were plotted. It was shown that for small velocities there is a smooth increase in concentration, then with an increase in the velocity there is a sharp jump with further saturation, and then for large flow velocities there are oscillations associated with relaxation processes.
Keywords: : dispersion, concentration, pollutants, numerical solution of equations, one-and two-dimensional problems.