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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2017, Volume 57, Number 2, Pages 316–338
DOI: https://doi.org/10.7868/S0044466917020028 (Mi zvmmf10524) 		 
This article is cited in 31 scientific papers (total in 31 papers)

Simulation of shallow water flows with shoaling areas and bottom discontinuities

A. I. Aleksyukab, V. V. Belikovb

a Faculty of Mechanics and Mathematics, Moscow State University, Moscow, Russia
b Water Problems Institute, Russian Academy of Sciences, Moscow, Russia
Full-text PDF (1848 kB) Citations (31)
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DOI: https://doi.org/10.7868/S0044466917020028
Abstract: A numerical method based on a second-order accurate Godunov-type scheme is described for solving the shallow water equations on unstructured triangular-quadrilateral meshes. The bottom surface is represented by a piecewise linear approximation with discontinuities, and a new approximate Riemann solver is used to treat the bottom jump. Flows with a dry sloping bottom are computed using a simplified method that admits negative depths and preserves the liquid mass and the equilibrium state. The accuracy and performance of the approach proposed for shallow water flow simulation are illustrated by computing one- and two-dimensional problems.
Key words: shallow water equations, finite-volume method, Riemann problem, discontinuous bottom surface, dry-bottom areas.
Received: 28.05.2015
Revised: 23.06.2016
English version:
Computational Mathematics and Mathematical Physics, 2017, Volume 57, Issue 2, Pages 318–339
DOI: https://doi.org/10.1134/S0965542517020026
Bibliographic databases:
Document Type: Article
UDC: 519.634
Language: Russian
Citation: A. I. Aleksyuk, V. V. Belikov, “Simulation of shallow water flows with shoaling areas and bottom discontinuities”, Zh. Vychisl. Mat. Mat. Fiz., 57:2 (2017), 316–338; Comput. Math. Math. Phys., 57:2 (2017), 318–339
Citation in format AMSBIB
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    • This publication is cited in the following 31 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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