UkrainianProfessional Education

Abstract

The article considers the problem of modeling unsteady water flow in channel systems based on the numerical solution of Saint-Venant equations, which are fundamental in describing the dynamics of open flows. The aim of the work is to improve the accuracy and computational stability of forecasting hydraulic processes in natural and artificial channels using an improved numerical calculation scheme that combines simplicity of implementation with guaranteed convergence. The study implements the discretization of continuity equations using an explicit difference scheme adapted to variable depth conditions, as well as uneven channels and local drops, which often occur in real hydraulic systems. Particular attention is paid to the stabilization of calculations using Courant conditions and the optimal selection of grid steps. The calculations are presented in the form of a comparison of water level and flow distributions at characteristic moments in time, which made it possible to evaluate the dynamics of the wave front and confirm the adequacy of the mathematical model. The results show that the proposed numerical approach provides sufficient accuracy even in the presence of sharp changes in channel conditions, and the obtained depth and velocity profiles are well consistent with analytical estimates and the physical essence of the process. In addition, the possibility of using the developed methodology for constructing operational engineering forecasts, in particular for assessing breakthrough waves, flood waves, and other non-stationary hydraulic phenomena, is shown. The results of the work can be used for the calculation of hydraulic structures, modeling of flood situations, optimization of water management systems, and in the educational process when teaching disciplines in hydraulics and hydrological modeling. The proposed numerical method is an effective tool for solving a wide range of practical problems related to the analysis of unsteady water flow and can be the basis for further improvement of models, including taking into account turbulence, channel deformations, and multidimensional effects.

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