<p>An approach to modeling an ideal flow in an aquatic environment bounded by flow lines and equipotential surfaces, in particular in a reservoir with tributaries, is proposed. Analysis of the hydrological regime of a water body indicates a complex interaction between the underground and surface water masses. In this study, the influence of both surface and underground waters that support the baseflow (for example, tributaries to the reservoir) is proposed to be modeled at the initial stage as sections (sources) of transverse disturbances of the base flow. Slow (near-ideal) water flows in such reservoirs are considered, which can be described, as in soils, using an analog of Darcy’s law. Depending on the values of potentials (pressures) on the corresponding equipotential lines, different cases of flow formation in the reservoir (physical area) and, therefore, configurations of the corresponding areas of complex potential, are possible. The methodology for modeling such processes is based on the development and adaptation of numerical methods of complex analysis, which makes it possible to efficiently describe and predict the dynamics of water systems at the global level and make decisions regarding the management of the process under consideration. Approximate solutions to the corresponding, so-called inverse boundary-value problems for conformal mappings (for areas with sections of disturbance of the boundary flow lines) are found using an algorithm based on the sequential parameterization of the values of conformal invariants, boundary and internal nodes of the grid area using the ideas of the block iteration method. Along with calculating the water flow separation curves, the proposed approach makes it possible to simultaneously find the characteristic flow function, complex potential, total discharge, and the values of various overflows, construct a hydrodynamic grid in a given area, calculate the velocity field, and control the process.</p>