Software realization problems of mathematical models of pollutants transport in rivers

A software package of realization of mathematical models of pollutants transport in rivers is offered. This package is designed as a up-to-date convenient, reliable tool for specialists of various areas of knowledge such as ecology, hydrology, building, agriculture, biology, ichthyology and so on. It allows us to calculate pollutant concentrations at any point of the river depending on the quantity and the conditions of discharging from several pollution sources. One-, two-, and three-dimensional advection–diffusion mathematical models of river water quality formation both under classical and new, original boundary conditions are realized in the package. New finite-difference schemes of calculation have been developed and the known ones have been improved for these mathematical models. At the same time, a number of important problems which provide practical realization, high accuracy and short time of obtaining the solution by computer have been solved. In particular: (a) the analytical description of plane or spatial region for which the diffusion equations and boundary conditions are investigated, i.e. the analytical description of the bank line and the bottom of the river; (b) the analytical description of dependence of coefficients of the equation on the spatial coordinates; (c) the analytical description of dependence of non-homogeneous parts of the diffusion equation (i.e. the capacities of pollution sources) on the spatial coordinates and on the time; (d) the correct choice of ratios between spatial steps of the grid, and also between them and the step of digitations of time in the difference scheme. 2009 Elsevier Ltd. All rights reserved.