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Sibirskii Zhurnal Vychislitel'noi Matematiki
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Sibirskii Zhurnal Vychislitel'noi Matematiki, 2019, Volume 22, Number 3, Pages 281–299
DOI: https://doi.org/10.15372/SJNM20190303 (Mi sjvm715) 		 
This article is cited in 9 scientific papers (total in 9 papers)

Exact solutions of shallow water equations for the water oscillation problem in a simulated basin and their implementation in verifying numerical algorithms

N. A. Matskevichab, L. B. Chubarovba

a Institute of Computational Technologies, Siberian Branch, Russian Academy of Sciences, pr. Akad. Lavrent’eva 6, Novosibirsk, 630090 Russia
b Novosibirsk State University, ul. Pirogova 2, Novosibirsk, 630090 Russia
Full-text PDF (5900 kB) Citations (9)
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DOI: https://doi.org/10.15372/SJNM20190303
Abstract: We present the approaches to solving a problem of shallow water oscillations in a parabolic basin (including an extra case of a horizontal plane). A series of assumptions about the form of solution and effects of Earth‘s rotation and bottom friction are made. Then the resulting ODE systems are solved. The corresponding free surfaces have first or second order. The conditions of finiteness and localization of a flow are analyzed. The solutions are used in the verification of numerical algorithm of the large particles method, the efficiency of the carried out tests is discussed.
Key words: wave run-up, free surface, Coriolis force, bottom friction, mathematical modeling, shallow water equations, exact solutions, ordinary differential equations, numerical algorithms, large particles method, verification.
Received: 13.08.2018
Revised: 07.11.2018
Accepted: 07.05.2019
English version:
Numerical Analysis and Applications, 2019, Volume 12, Issue 3, Pages 234–250
DOI: https://doi.org/10.1134/S1995423919030030
Bibliographic databases:
Document Type: Article
UDC: 51.72, 532.591
Language: Russian
Citation: N. A. Matskevich, L. B. Chubarov, “Exact solutions of shallow water equations for the water oscillation problem in a simulated basin and their implementation in verifying numerical algorithms”, Sib. Zh. Vychisl. Mat., 22:3 (2019), 281–299; Num. Anal. Appl., 12:3 (2019), 234–250
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  • https://www.mathnet.ru/eng/sjvm/v22/i3/p281
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    2. I. Magdalena, Natanael, “Influences of coriolis force and friction on fluid dynamics in specific paraboloid basins”, Physics of Fluids, 36:4 (2024)  crossref
    3. Chang Liu, Antwan D. Clark, “Semi-analytical solutions of shallow water waves with idealised bottom topographies”, Geophysical & Astrophysical Fluid Dynamics, 117:1 (2023), 35  crossref
    4. Chang Liu, Antwan D. Clark, “Analysing the impact of bottom friction on shallow water waves over idealised bottom topographies”, Geophysical & Astrophysical Fluid Dynamics, 117:2 (2023), 107  crossref
    5. Stelian Ion, Dorin Marinescu, Stefan Gicu Cruceanu, 2023 13th International Symposium on Advanced Topics in Electrical Engineering (ATEE), 2023, 1  crossref
    6. Ion S., Marinescu D., Cruceanu S.-G., “Numerical Scheme For Solving a Porous Saint-Venant Type Model For Water Flow on Vegetated Hillslopes”, Appl. Numer. Math., 172 (2022), 67–98  crossref  mathscinet  isi  scopus
    7. M.-O. Bristeau, B. Di Martino, A. Mangeney, J. Sainte-Marie, F. Souille, “Some analytical solutions for validation of free surface flow computational codes”, J. Fluid Mech., 913 (2021), A17  crossref  mathscinet  isi  scopus
    8. M. Forghani, Y. Qian, J. Lee, M. W. Farthing, T. Hesser, P. K. Kitanidis, E. F. Darve, “Application of deep learning to large scale riverine flow velocity estimation”, Stoch. Environ. Res. Risk Assess., 35:5, SI (2021), 1069–1088  crossref  isi  scopus
    9. A.I. Uvarov, N.A. Parkhomenko, A.S. Garagul, “Mathematical models of water surface for geodetic support of construction in agro-industrial complex”, Zemleustrojstvo, kadastr i monitoring zemel' (Land management, cadastre and land monitoring), 2021, no. 8  crossref
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