V. V. Sidoryakina, A. I. Sukhinov, “Well-posedness analysis and numerical implementation of a linearized two-dimensional bottom sediment transport problem”, Zh. Vychisl. Mat. Mat. Fiz., 57:6 (2017), 985–1002; Comput. Math. Math. Phys., 57:6 (2017), 978

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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2017, Volume 57, Number 6, Pages 985–1002
DOI: https://doi.org/10.7868/S0044466917060138 (Mi zvmmf10549)

This article is cited in 42 scientific papers (total in 42 papers)

Well-posedness analysis and numerical implementation of a linearized two-dimensional bottom sediment transport problem

V. V. Sidoryakina^a, A. I. Sukhinov^b

^a Chekhov Taganrog Institute, Branch of Rostov State University of Economics, Taganrog, Russia
^b Don State Technical University, Rostov-on-Don, Russia

Full-text PDF (1075 kB) Citations (42)

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DOI: https://doi.org/10.7868/S0044466917060138

Abstract: A two-dimensional linearized model of coastal sediment transport due to the action of waves is studied. Up till now, one-dimensional sediment transport models have been used. The model under study makes allowance for complicated bottom relief, the porosity of the bottom sediment, the size and density of sediment particles, gravity, wave-generated shear stress, and other factors. For the corresponding initial-boundary value problem the uniqueness of a solution is proved, and an a priori estimate for the solution norm is obtained depending on integral estimates of the right-hand side, boundary conditions, and the norm of the initial condition. A conservative difference scheme with weights is constructed that approximates the continuous initial-boundary value problem. Sufficient conditions for the stability of the scheme, which impose constraints on its time step, are given. Numerical experiments for test problems of bottom sediment transport and bottom relief transformation are performed. The numerical results agree with actual physical experiments.

Key words: sediment transport model, coastal zone, bottom surface, solution uniqueness, estimate for the norm of the solution to an initial-boundary value problem.

Funding agency	Grant number
Russian Science Foundation	17-11-01286

Received: 29.03.2016

English version:
Computational Mathematics and Mathematical Physics, 2017, Volume 57, Issue 6, Pages 978–994
DOI: https://doi.org/10.1134/S0965542517060124

Bibliographic databases:

Document Type: Article

UDC: 519.634

Language: Russian

Citation: V. V. Sidoryakina, A. I. Sukhinov, “Well-posedness analysis and numerical implementation of a linearized two-dimensional bottom sediment transport problem”, Zh. Vychisl. Mat. Mat. Fiz., 57:6 (2017), 985–1002; Comput. Math. Math. Phys., 57:6 (2017), 978–994

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This publication is cited in the following 42 articles:

V. V. Sidoryakina, “Sufficient Conditions for the Convergence of Solutions of the Linearized Problem to the Solution of the Original Nonlinear Problem of Multifractional Sediment Transport in Shallow Water”, CMIT, 9:1 (2025), 20
V. V. Sidoryakina, D. A. Solomakha, “Parallel Algorithms for Numerical Solution of Spatially Three-Dimensional Diffusion-Convection Equations in Coastal Systems Based on Splitting Schemes”, CMIT, 8:1 (2024), 29
A. I. Sukhinov, A. E. Chistyakov, V. V. Sidoryakina, I. Yu. Kuznetsova, A. M. Atayan, “Ispolzovanie parallelnykh vychislenii dlya otsenki protsessa perenosa zagryaznyayuschikh veschestv v melkovodnykh vodoemakh”, Izv. Sarat. un-ta. Nov. ser. Ser.: Matematika. Mekhanika. Informatika, 24:2 (2024), 298–315
Alexander Sukhinov, Valentina Sidoryakina, Denis Solomakha, Lecture Notes in Networks and Systems, 1044, Current Problems of Applied Mathematics and Computer Systems, 2024, 11
V. V. Sidoryakina, A. I. Sukhinov, “Construction of solutions and study of their closeness in $L_2$ for two boundary value problems for a model of multicomponent suspension transport in coastal systems”, Comput. Math. Math. Phys., 63:10 (2023), 1918–1928
Valentina V. Sidoryakina, Environmental Science and Engineering, Sustainable Development of Water and Environment, 2023, 317
Alexander Sukhinov, Valentina Sidoryakina, V. Pukhkal, S. Uvarova, “Two-dimensional-one-dimensional splitting scheme for the numerical solution of problems of transport of multicomponent suspensions using θ coordinates”, E3S Web of Conf., 458 (2023), 03019
A. I. Sukhinov, A. E. Chistyakov, V. V. Sidoryakina, I. Yu. Kuznetsova, A. M. Atayan, M. V. Porksheyan, Communications in Computer and Information Science, 1868, Parallel Computational Technologies, 2023, 244
V. V. Sidoryakina, “Existence and Uniqueness of the Initial-Boundary Value Problem Solution of Multicomponent Sediments Transport in Coastal Marine Systems”, CMIT, 7:2 (2023), 73
V. V. Sidoryakina, D. A. Solomakha, “Symmetrized Versions of the Seidel and Successive OverRelaxation Methods for Solving Two-Dimensional Difference Problems of Elliptic Type”, CMIT, 7:3 (2023), 12
A.I. Sukhinov, V.V. Kholodkov, E.A. Protsenko, S.V. Protsenko, I. Tanaino, T. Dzholdosheva, “Dynamically changing bottom relief modeling based on spatially inhomogeneous 3D mathematical model of wave hydrodynamics”, E3S Web of Conf., 402 (2023), 03030
Alexander Sukhinov, Elena Protsenko, Valentina Sidoryakina, Sofya Protsenko, PROCEEDING OF THE 7TH INTERNATIONAL CONFERENCE OF SCIENCE, TECHNOLOGY, AND INTERDISCIPLINARY RESEARCH (IC-STAR 2021), 2601, PROCEEDING OF THE 7TH INTERNATIONAL CONFERENCE OF SCIENCE, TECHNOLOGY, AND INTERDISCIPLINARY RESEARCH (IC-STAR 2021), 2023, 050009
Vladimir Litvinov, Nelli Rudenko, Natalya Gracheva, Alexander Chistyakov, I. Malygina, “A software package for solving grid equations in areas with geometry “stretched” along one of the spatial directions”, E3S Web Conf., 363 (2022), 02021
A. E. Chistyakov, V. V. Sidoryakina, S. V. Protsenko, “Development of algorithms for constructing two-dimensional optimal boundary-adaptive grids and their software implementation”, Vestnik Donskogo gosudarstvennogo tehničeskogo universiteta, 21:3 (2021), 222
A I Sukhinov, E A Protsenko, V V Sidoryakina, S V Protsenko, “Numerical simulation of bottom topography transformation taking into account the coastal shore protection structures”, J. Phys.: Conf. Ser., 1745:1 (2021), 012102
V V Sidoryakina, “3D Cartesian vertically boundary-adaptive grids construction for coastal hydrophysics problems”, IOP Conf. Ser.: Mater. Sci. Eng., 1029 (2021), 012116
A. I. Sukhinov, A. A. Sukhinov, V. V. Sidoryakina, “Uniqueness of solving the problem of transport and sedimentation of multicomponent suspensions in coastal systems”, Applied Mathematics, Computational Science and Mechanics: Current Problems, Journal of Physics Conference Series, 1479, IOP Publishing Ltd, 2020, 012081
Alexander I. Sukhinov, Alexander E. Chistyakov, Elena A. Protsenko, Valentina V. Sidoryakina, Sofya V. Protsenko, Communications in Computer and Information Science, 1263, Parallel Computational Technologies, 2020, 279
A Sukhinov, V Sidoryakina, V. Breskich, A. Zheltenkov, Y. Dreizis, “Additive two-dimensional splitting schemes for solving 3D suspension transport problems on optimal boundary-adaptive grids with uniform spacing's in the vertical direction”, E3S Web Conf., 224 (2020), 02017
“Abstracts of talks given at the 3rd International Conference on Stochastic Methods”, Theory Probab. Appl., 64:1 (2019), 124–169

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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