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This paper deals with development of computational schemes to solve of system equations with lagging argument governing the rainwater runoff along the surface catchment and transport of impurity which permeates into the water flow from soil at the certain areas of this surface. This system consists of two types of equations: the first of them describes the changes of water layer thickness over the slope surface given the precipitation and evaporation, and the second one – the mass transfer of impurity coming into the surface water during its filtration in zone of incomplete saturation of soil. Computational scheme to solve the system of nonlinear differential equations are developed with the finite-difference methods using a priori information about the solution behavior. The numerical model is implemented in the software for computer simulation of the processes with simultaneous graphic visualization of the computing results.

Numerical model of rainwater runoff over the catchment surface and transport of contaminant incoming to water stream from soil