Mathematical modeling of flows from canals

Abstract

In the hydrodynamic formulation, two-dimensional steady filtration in homogeneous isotropic ground from canals through a soil layer to the underlying highly permeable pressure water-bearing stratum is considered in the presence of the ground capillarity and evaporation from the free surface. To study filtration, a combined multiparametric boundary-value problem of the theory of analytical functions is formulated, which is solved using the P. Ya. Polubarinova-Kochina method and procedures of conformal mapping of regions of a special kind that are characteristic of the problems of subsurface hydromechanics. On the basis of this model an algorithm of calculating the capillary water spreading and the filtration discharge is developed for the situations where in water filtration from canals provision is made for the ground capillarity, evaporation from the free-surface of groundwater, and the additional pressure from the side of water of the underlying wellpermeable bed. With the aid of the obtained accurate analytical relations and numerical calculations a hydrodynamic analysis is made of the structure and character of specific features of the modeled process as well as of the effect of all physical parameters of the scheme on the filtration characteristics.