About a~mode of ground waters at a~seepage under hydraulic engineering structures

E. N. Bereslavskiy ; L. A. Aleksandrova ; E. V. Pesterev

Matematičeskoe modelirovanie, Tome 23 (2011) no. 2, pp. 27-40

Résumé

The present work is direct continuation of paper of authors [1]. In it on the basis of the theory of the flat established seepage of an incompressible liquid under Darcy law in a uniform and isotropic ground the following tasks linked to filtration currents with unknown borders under hydraulic engineering structures are considered. 1. The smooth underground contour of subsurface rectangular locks of a constant velocity of filtration in that case when the water-permeable basis is spread by a water thrust which consists of two curvilinear and one (average) horizontal sites (a characterize constancy of velocity of a flow) is plotted. 2. The fluid current under a rabbet Zhukovsky through irrigated soil a file with the underlaying very nontight water-bearing horizon containing pressure head underground waters is probed; the left semi-infinite part of its roof is modeled by impenetrable initialization. For study of these movements the mixed multiparameter boundary value problems of the theory of analytical functions are formulated. Their decision is realized by means of a semiinverse way of a hodograph of velocity of P. J. Polubarinova-Kochina and I. N. Kochina, P. J. Polubarinova-Kochina (grounded on application of the analytical theory of the linear differential equations of Fuchs class) method, and also the developed ways of conformal mapping of areas of a special kind which are characteristic for tasks of an underground hydromechanics. Results of numerical calculations are cited, and the hydrodynamic analysis of effect of physical parameters of models on a picture of currents is given. The limiting cases of these tasks probed earlier in work [1] are marked.

Détail

Keywords: filtering, groundwater, groove, velocity hodograph, conformal mappings.
Mots-clés : dam