This paper is devoted to mathematical modeling and computer simulation of diffusion and transport of chemicals in rivers. We present one-, two-, and three-dimensional models in terms of time-dependent convection-diffusion-reaction differential equations, further we give the finite difference approximation and appropriate numerical algorithms for these models, and finally we discuss briefly the computer implementation of this methodology in a user friendly software package. To verify the model and the computer code we have used it to study the diffusion and transport of chemicals, in this case NO 3 and PO 4 , in two rivers in Western Georgia flowing into the Black Sea. Namely, we considered the river Khobistskali subject to pollution sources Ochkhomuri and Chanistskali river Choga polluted with NO 3 .In order to evaluate the quality, the accuracy, and the performance of the methods and the developed software we have applied one-, two-and three-dimensional models to the same case, for which we had data from measurements. By analyzing the difference between the measured and the simulated values of controlled chemicals in the rivers, we have estimated the effect of agricultural activities along the banks of the river (in the interval between two sections) on the pollution degree of the Khobistskali river. In this sense, the example is schematic, since the number, the arrangement, and the capacities of pollution sources of Khobistskali only partially correspond to the real situation. Though, the geometry of the rivers, the arrangement of the control sections, and the concentrations of polluting substances in the rivers matches well the real data.

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