The situation when groundwater considerably rises above the “normal” level, water intake, lowering of groundwater levels and other relevant practical tasks require the drainage facilities. The most effective techniques of numerical studies of the corresponding boundary problems at present time are methods of dealing with inverse boundary value problems (conformal and quasi-conformal mappings). As basis of this research we used the case of combining the fictitious domain methods with quasi-conformal mappings of the solution of nonlinear boundary value problems for the calculation of filtra-tion regimes in environments with free boundary areas (depression curves) and zones of “mountainous” areas. This paper reviews the stationary issue of flat-vertical stationary non-pressure liquid filtration to horizontal symmetric drainage. In the paper a practical methodology for solving boundary value problems on conformal mappings is suggested for the calculation of the filtration process in the horizontal symmetrical drainage. The idea of block iterative methods was used during the creation of the corresponding algorithm which is based on the alternating “freeze” of the anticipated conformance parameter, the internal and boundary connections of the curvilinear area. The results of the conducted numerical calculations confirmed the effectiveness of the suggested problem formulations and algorithms of their numerical solution and the possibility of their use in the modelling of nonlinear filtration processesoccurring in horizontal drainage systems, as well as in the design of drainage facilities and optimizing other hydrosystems. Therefore these results are of great importance.

The article discusses the option for the application of the methodology for the solution of boundary value problems on the conformal mapping for the calculation of filtration process in the horizontal systematic drainage, provided that the drain is installed at a different depth. In particular, the case of methods combining fictitious areas and quasiconformal mappings for solving nonlinear boundary conditions problems for calculating filtration regimes in soils with free sections of boundaries (depression curves) and intervals of the “drainage” type. As an example, the authors designed a hydrodynamic flow grid, determined the values of the flows to the drain, established a section line and elicited other process characteristics. The algorithm for the numerical solution of model nonlinear boundary conditions problems of quasiconformal reflection in areas bounded by two equipotential lines and two flow lines, when for one of the sections, the boundary is an unknown (free) curve with fixed and free ends. The conducted numerical calculations prove that the problems and algorithms of their numerical solution, with a relatively small iterations number (k = 141) suggested in the paper, can be applied in the simulation of nonlinear filtration processes that arise in horizontal drainage systems. Total filtration flow obtained Q = 0.9 dm3·s–1; flow for drains Q1 = 0.55 dm3·s–1 and Q2 = 0.35 dm3·s–1 are quite consistent with practically determined values.