Kokovska Y. Computer simulation of the processes of forming the flow of water in the channels with uneven bottom.

The dissertation is devoted to the construction and research of models of channel flow in hydrodynamic and kinematic approximations, as well as the development of numerical schemes for solving the obtained variation problems using the finite element method (FEM). In this paper the initial-boundary problem of the channel flow of fluid in the pseudoprismic channel was build, in which unknown values are cross-sectional area and flow velocity. The variational problem is formulated and the conditions for its correctness are derived. The discretization of spatial variables with the help of FEM for piecewise linear and piecewise-quadratic basis functions was performed. For time discretization, a one-time recurrent scheme was used. Under conditions of equilibrium of the forces of resistance and earthly gravity, the equations of the channel flow acquire the form of a kinematic wave. A comparison of models in hydrodynamic and kinematic approximations on test cases is carried out. The motion of water in the river network of the catchment is investigated, the conditions for connecting flows in the channels are derived, the water mass balance has been verified. The stability of the established channel flow is investigated depending on the main natural phenomena influencing on it. The dependence of the stability criterion on the angle of inclination of the middle bottom line of channel and the average speed correction is shown. The software for implementation the algorithms of numerical scheme has been developed and tested on test examples for different types of channels.