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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2018, Volume 58, Number 9, Pages 1488–1504
DOI: https://doi.org/10.31857/S004446690002528-1 (Mi zvmmf10784) 		 
This article is cited in 6 scientific papers (total in 6 papers)

Monotonicity of the CABARET scheme approximating a hyperbolic system of conservation laws

O. A. Kovyrkinaa, V. V. Ostapenkoab

a Lavrent’ev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, Russia
b Novosibirsk State University, Novosibirsk, Russia
Citations (6)
References:
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DOI: https://doi.org/10.31857/S004446690002528-1
Abstract: The monotonicity of the CABARET scheme for approximating a quasilinear hyperbolic system of conservation laws is investigated. The conditions are obtained under which this scheme is monotonicity-preserving with respect to the invariants of the linear approximation of the approximated system. The system of shallow water equations is considered as an example. The capabilities of the scheme in the computation of discontinuous solutions with shock waves are illustrated by test calculations of Riemann problems.
Key words: hyperbolic system of conservation laws, monotonicity of CABARET scheme, shallow water theory, discontinuous waves.
Funding agency Grant number
Russian Foundation for Basic Research 16-01-00333_а
Received: 30.08.2017
English version:
Computational Mathematics and Mathematical Physics, 2018, Volume 58, Issue 9, Pages 1435–1450
DOI: https://doi.org/10.1134/S0965542518090129
Bibliographic databases:
Document Type: Article
UDC: 519.63
Language: Russian
Citation: O. A. Kovyrkina, V. V. Ostapenko, “Monotonicity of the CABARET scheme approximating a hyperbolic system of conservation laws”, Zh. Vychisl. Mat. Mat. Fiz., 58:9 (2018), 1488–1504; Comput. Math. Math. Phys., 58:9 (2018), 1435–1450
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/zvmmf10784
  • https://www.mathnet.ru/eng/zvmmf/v58/i9/p1488
    • This publication is cited in the following 6 articles:
    1. Olyana A. Kovyrkina, Vladimir V. Ostapenko, “On the accuracy of shock-capturing schemes when calculating Cauchy problems with periodic discontinuous initial data”, Russian Journal of Numerical Analysis and Mathematical Modelling, 39:2 (2024), 97  crossref
    2. Dmitry V. Kulyamin, Sergey V. Kostrykin, Pavel A. Ostanin, Valentin P. Dymnikov, “Numerical model of Earth ionosphere F region based on three-dimensional transport and ambipolar diffusion equations”, Russian Journal of Numerical Analysis and Mathematical Modelling, 38:6 (2023), 361  crossref
    3. A. A. Kozhemyachenko, A. V. Favorskaya, “Grid convergence analysis of grid-characteristic method on Chimera meshes in ultrasonic nondestructive testing of railroad rail”, Comput. Math. Math. Phys., 63:10 (2023), 1886–1903  mathnet  mathnet  crossref  crossref
    4. M. D. Bragin, O. A. Kovyrkina, M. E. Ladonkina, V. V. Ostapenko, V. F. Tishkin, N. A. Khandeeva, “Combined numerical schemes”, Comput. Math. Math. Phys., 62:11 (2022), 1743–1781  mathnet  mathnet  crossref  crossref
    5. O. A. Kovyrkina, V. V. Ostapenko, “On accuracy of MUSCL type scheme when calculating discontinuous solutions”, Math. Models Comput. Simul., 13:5 (2021), 810–819  mathnet  crossref  crossref
    6. V. V. Ostapenko, V. A. Kolotilov, “Primenenie skhemy CABARET dlya rascheta razryvnykh reshenii giperbolicheskoi sistemy zakonov sokhraneniya”, Dokl. RAN. Matem., inform., prots. upr., 501 (2021), 62–66  mathnet  crossref  zmath  elib
    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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