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.
In the electromagnetic field simulation of modern servo drives, the computation of higher time and space harmonics is essential to predict torque pulsations, radial forces, ripple torques and cogging torque. Field computation by conformal map ping (CM) techniques is a time-effective method to compute the radial and tangential field components. In the standard CM approach, computational results of cogging torque simulations as well as overload operations observe deviations to nonlinear finite element (FE) simulations due to the neglection of slot leakage and saturation effects. This paper presents an extension of the classical CM. Additional CM parameters are computed from single finite element computations so as to consider both effects listed above in the model over a wide operation range of the electrical drive. The proposed approach is applied to a surface permanent magnet synchronous machine (SM-PMSM), and compared to numerical results obtained by finite element analysis (FEA). An accuracy similar to that of FE simulations is obtained with however the low computation time that is characteristic for analytical models.