Моделювання Локальної Кінематичної Структури Течії При Злитті Річок

Introduction. The aim of this study is to develop a mathematical model of the local kinematic structure of flow at river confluences, design a computational algorithm for its implementation, and investigate the applicability of the proposed approach. Materials and Methods. The mathematical model is based on Darcy's law and the continuity equation. Methods of complex analysis are employed to investigate the flow by reformulating the problem as an inverse boundary value problem. The numerical implementation is carried out using the finite difference method, the Gauss–Seidel method, block iterations, and Hermite interpolation. Results. A mathematical model of the local kinematic structure of flow at river confluences has been developed, along with an algorithm for its numerical implementation. Based on the proposed algorithm, an information and computational system has been developed to determine the main hydrodynamic characteristics, analyze the computed data, and visualize the results in the form of a hydrodynamic flow grid. A numerical experiment has been conducted to investigate a characteristic flow configuration. Conclusions. The proposed approach makes it possible to obtain a baseline approximation of the kinematic flow structure at river confluences without significant computational costs and can serve as a basis for further modeling of water mass movement in branched river systems.