Venherskyi P. Numerical modeling of surface and groundwater flows and their interaction in the catchment area

The work relates to mathematical modeling and numerical study of the problem of interaction in the watershed of surface water and groundwater flow in the hydrodynamic and kinematic approximations. The equation of surface water runoff in the hydrodynamic approximation were derived from the equations of motion Navier-Stokes with averaging flow of depth and considering all the components of the stress tensor and the different factors on the free and bottom surfaces of flow. For surface water flow in the kinematic approximation is constructed and investigated regularized model with the addition of artificial viscosity. To describe the movement of underground water used Busyneska equation and formulated initial boundary and variational formulation of problems in the case of dependence coefficient of filtration of unknown value piezometric pressure. We derive a system of basic equations of groundwater filtration in the hydrodynamic approximation of general laws of conservation of energy, mass. The model of compatible motion of surface and groundwater flow and deduced the condition of their interaction on the watershed. To improve solutions for large values Reynoldca numbers (Re> 100) in surface water runoff problem in the hydrodynamic approximation proposed stabilization scheme FEM. Developed and researched class of interval methods for solving systems of equations with dominant diagonal. A web component that allows you to automatically generate data on river systems are in a selected area. approximation schemes.