A BRIEF OVERVIEW OF MODERN RESEARCH OF THE PROCESSES DYNAMICS IN UNSTEADY WATER FLOWS USING THE SHALLOW WATER EQUATION

Berdyshev A.S. Abdiramanov Zh.A. Blieva D.N. Akhtaeva N.S.
2021 al-Farabi Kazakh State National University

KazNU Bulletin. Mathematics, Mechanics, Computer Science Series
2021 #112 Issue 4 170 - 180 pp.

In hydrodynamics (hydraulics), there are numerous approaches to solving the problem of water flow dynamics control in river beds and channels, while the results of each methods differ, and estimates of their reliability do not always exist. The shallow water equation (or Saint-Venant’s equations in one-dimensional form) is often used by hydraulic engineers in their practice. Its apparent simplicity and ability to describe well enough the behavior of rivers and flows make it a useful tool for many applications, such as the regulation of navigable rivers and irrigation networks in agriculture. The main direction of research in the field of numeric problems described by Saint-Venant equations is the development of numerical methods of computation implemented on super-powerful computers. Development of numerical models of surface water dynamics in the shallow water approximation is actively advancing during the recent years. The article is devoted to a review of mathematical studies of the dynamics of processes in unsteady water flows using differential equations, as well as an assessment of these approaches from the point of view of the model’s reflection of real processes. The work is aimed at analyzing different approaches to modeling the dynamics of processes in non-stationary water flows. The objectives of the study include the analysis of scientific publications with different approaches to modeling the shallow water equation, taking into account factors, parameters, and modeling methods.

a system of hyperbolic differential equations , dynamics of unsteady river currents , high-performance computing , numerical methods , Saint-Venant equations

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Abay Kazakh National Pedagogical University, Almaty, Kazakhstan
Institute of Information and Computational Technologies, Almaty, Kazakhstan

Abay Kazakh National Pedagogical University
Institute of Information and Computational Technologies

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