The study presents the critical evaluation of existing drainage systems from legal, eco-nomical, environmental and technical viewpoints. Nearly 80% of agricultural land in Lithuania drained by underground drainage systems covers around 3 million hectares. The prevailing large scale drainage systems with a complex of engineering structures such as conducting ditches, drains and collectors, local roads, bridges or farm road-crossings, dikes, dams, water reservoirs, pumping stations for irrigation and for drainage need today an efficient management solution in a new economic situation. The detailed analysis of legal and economic instruments adopted in transferring the management responsibilities of drainage systems to users has been carried out. The study resulted in a number of practical contributions towards the amendments in the Law on Land Reclamation in Lithuania and the establishment of a system of indicators that would allow rationalisation of subsidy allocations for the maintenance and improvement of the drainage systems. These subsidies from the state budget make at the moment the largest share among the investment sources. The financial and in kind contribution of drainage users is permanently increasing as are the allocations of the structural funds for public projects. The EU pre-accession programme SAPARD started in 2000 has supported some investments in rural areas. Unfortunately, it did not support the drainage infrastructure properly. A critical review of previous measures allowed suggesting new actions within the framework of the actual support from EU structural funds.
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.