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Bulletin of Abai KazNPU. Series of Physical and mathematical sciences
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Vol. 79 No. 3 (2022)

NUMERICAL SOLUTION OF A MIXED PROBLEM FOR A TWO-DIMENSIONAL SYSTEM OF SAINT-VENANT EQUATIONS

Published September 2022

218

72

A. Berdyshev+−
Abai Kazakh National Pedagogical University, Institute of Information and Computational Technologies, Almaty
https://orcid.org/0000-0002-1228-8246
R. Aloev+−
National University of Uzbekistan named after Mirzo Ulugbek, Tashkent
https://orcid.org/0000-0003-4734-3070
A. Akbarova+−
National University of Uzbekistan named after Mirzo Ulugbek, Tashkent
https://orcid.org/0000-0001-6119-7212
Zh. Abdiramanov+−
Abai Kazakh National Pedagogical University, Institute of Information and Computational Technologies, Almaty
https://orcid.org/0000-0003-3820-7253
Abai Kazakh National Pedagogical University, Institute of Information and Computational Technologies, Almaty
National University of Uzbekistan named after Mirzo Ulugbek, Tashkent
National University of Uzbekistan named after Mirzo Ulugbek, Tashkent
Abai Kazakh National Pedagogical University, Institute of Information and Computational Technologies, Almaty
DOI: 10.51889/3983.2022.30.71.009
Abstract

The work is devoted to the construction and study of a numerical method for solving the Saint-Venant equation. These equations are of great practical importance in modern hydraulic engineering and are suitable for describing natural processes in the atmosphere, rivers, and oceans, as well as for modeling tides. Questions of formulation of mixed problems for the two-dimensional system of Saint-Venant equations, are studied. A new upwind difference scheme of splitting in spatial directions is constructed for solving the mixed problem of the two-dimensional Saint-Venant equation, which describes flows without turbulent diffusion components. The stability of the difference scheme concerning energy norms is established. The results of numerical experiments for model problems are presented, including a numerical simulation of water flow in the Ugam River. The numerical calculation is based on the use of the two-point sweep method.

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Keywords
Two-dimensional system of Saint-Venant equations upwind difference scheme of splitting on directions stability
Language

English

How to Cite

[1]
Berdyshev, A., Aloev, R., Akbarova, A. and Abdiramanov, Z. 2022. NUMERICAL SOLUTION OF A MIXED PROBLEM FOR A TWO-DIMENSIONAL SYSTEM OF SAINT-VENANT EQUATIONS. Bulletin of Abai KazNPU. Series of Physical and mathematical sciences. 79, 3 (Sep. 2022), 73–82. DOI:https://doi.org/10.51889/3983.2022.30.71.009.