Mathematical modeling of the pollutants overland flow and transport

Modeling of the natural and technogenic processes in diverse geomorphological environments is one of the basic tools for forecasting and preventing unfavorable development of the urban ecology. One of the causes of its deterioration lies in pollution. The paper considers mathematical modeling of the spread of pollutants transported with water. The complicated process of pollutant spread was modeled as an aggregate of four simpler models such as overland water flow, influent seepage, pollutants transport with surface runoff, and pollutant deposition (accumulation) on the land surface. The model relies on the diffusion equation with supplementary addends in the right-hand side of which one reflects the effect of the terrain relief and the other, which depends on the lithologic structure of the territory, defines the intensity of pollutant uptake rate by the land surface. This equation is satisfied in the two-dimensional domain corresponding physically to an area covered with water. Both the form of the boundary and topology of this area are time-dependent because of appearance of dry “islands” surrounded by water.