Khrapov S.S., Agafonnikova E.O., Klikunova A.Y., Radchenko V.P., Baskakov E.V., Savin E.S., Makoveev I.S., Khrapov N.S. Numerical modeling of self-consistent dynamics of shallow waters, traction and suspended sediments: I. Influence of commercial sand min

https://doi.org/10.15688/mpcm.jvolsu.2022.3.3

Sergey S. Khrapov
Candidate of Physical and Mathematical Sciences, Associate Professor,
Department of Information Systems and Computing Modeling,
Volgograd State University
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https://orcid.org/0000-0003-2660-2491
Prosp. Universitetsky, 100, 400062 Volgograd, Russian Federation

Ekaterina O. Agafonnikova
Associate Professor, Department of Information Systems and Computing Modeling,
Volgograd State University
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https://orcid.org/0000-0002-2862-4531
Prosp. Universitetsky, 100, 400062 Volgograd, Russian Federation

Anna Y. Klikunova
Senior Lecturer, Department of Information Systems and Computing Modeling,
Volgograd State University
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https://orcid.org/0000-0002-4055-4601
Prosp. Universitetsky, 100, 400062 Volgograd, Russian Federation

Viktor P. Radchenko
Senior Lecturer, Department of Information Systems and Computing Modeling,
Volgograd State University
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https://orcid.org/0000-0002-3786-3884
Prosp. Universitetsky, 100, 400062 Volgograd, Russian Federation

Evgeniy V. Baskakov
Assistant, Department of Information Systems and Computing Modeling,
Volgograd State University
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https://orcid.org/0000-0003-2296-3740
Prosp. Universitetsky, 100, 400062 Volgograd, Russian Federation

Egor S. Savin
Assistant, Department of Information Systems and Computing Modeling,
Volgograd State University
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https://orcid.org/0000-0002-7915-121X
Prosp. Universitetsky, 100, 400062 Volgograd, Russian Federation

Ilya S. Makoveev
Assistant, Department of Information Systems and Computing Modeling,
Volgograd State University
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https://orcid.org/0000-0002-8037-3514
Prosp. Universitetsky, 100, 400062 Volgograd, Russian Federation

Nikita S. Khrapov
Student 11 «A» class,
Municipal educational institution «Lyceum No. 11 of Voroshilovsky district of Volgograd»
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St. Eletskaya, 9 B, 400120 Volgograd, Russian Federation

Abstract. A mathematical model of the joint dynamics of shallow waters, entrained and suspended sediments is constructed, which takes into account nonlinear fluid dynamics and bottom deformations. The dynamics of shallow waters is described by the Saint-Venant equations taking into account the spatially inhomogeneous distribution of the terrain. The transport of entrained sediments is described by the Exner equation generalized to the case of an inhomogeneous distribution of the parameters of the underlying surface. The dynamics of suspended sediments is described by the transport equation, which includes convective transport by water flow and the process of diffusion of the suspension in the liquid layer. For numerical integration of the Saint-Venant, Exner equations and suspended sediment dynamics, a stable and well-tested CSPH-TVD method of the second order of accuracy is used, the parallel CUDA algorithm of which is implemented in the form of a software package «EcoGIS-Simulation» for highperformance computing on supercomputers with graphics coprocessors (GPU). The conditions for the development of a quarry of non-metallic building materials (NSM) located at the mouth of the Partridge Volozhka of the Volga-Akhtuba floodplain on the 2549–2550 km section of the Volga River are considered. To study the safety of navigation from the lower reaches of the Volga hydroelectric dam to the entrance to the VDSK, numerical hydrodynamic modeling of the dynamics of channel processes in this section of the Volga River was carried out. Based on the results of mathematical modeling of the joint dynamics of surface waters, entrained and suspended sediments in the riverbed of the Volga River, it is concluded that the development of the NSM quarry considered in the work does not significantly affect the safety of navigation both along the main ship course «The lower reaches of the Volga hydroelectric dam — VDSK» and on additional — «Volgograd zaton» and «Volozhka Partridge».

Key words: hydrodynamics of surface waters, shallow water model, entrained and suspended sediments, numerical modeling, CSPH-TVD method, parallel computing, CUDA algorithm, supercomputers with GPU.

Creative Commons License
Numerical modeling of self-consistent dynamics of shallow waters, traction and suspended sediments: I. Influence of commercial sand mining on the safety of navigation in the channel of the Volga river by Khrapov S.S., Agafonnikova E.O., Klikunova A.Y., Radchenko V.P., Baskakov E.V., Savin E.S., Makoveev I.S., Khrapov N.S. is licensed under a Creative Commons Attribution 4.0 International License.

Citation in EnglishMathematical Physics and Computer Simulation. Vol. 25 No. 3 2022, pp. 31-57

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