Skip to content

Mathematical Software for Decision Support to Optimize the Standards of Pollutants Dumping into Rivers

The increase in harmful dumping of polluted water into open basins from the mines, sediment bowls, etc., in particular into the rivers, deteriorates the quality of surface waters. In turn, it results in excess of permissible concentrations of pollutants in the river on the whole and in places of potable water intake in particular. This situation also arises upon cross-border migration of pollutants, when the dumping of pollutants in one country leads to excess of permissible concentrations in the territory of the other country.


Therefore, it is necessary to establish the dumping standards upon which the concentration of pollutants will not exceed the norms for consumption in the water intake places.

The mathematical modeling and optimal control methods as well as related software can facilitate the decision-making process signi-ficantly.


There were developed the mathematical methods and software package for modeling of the transport of dissolved contaminants in the open river-beds. The mathematical model is based on the complete Saint-Venant’s system of equations and convective diffusion equation for contaminants concentration modeling.

The developed software package allows defining the dumping standards, assigning allowable concentration at the points of observation. Availability of optimization unit distinguishes the developed software system from almost all currently available software tools. Package can be easily adapted to real conditions by setting the river parameters.


Taras Shevchenko National University of Kyiv

Oleg Stelya