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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2018, Volume 58, Number 6, Pages 988–1012
DOI: https://doi.org/10.7868/S004446691806011X (Mi zvmmf10709) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Decay of unstable strong discontinuities in the case of a convex-flux scalar conservation law approximated by the CABARET scheme

N. A. Zyuzinaab, V. V. Ostapenkoab

a Lavrent'ev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, Russia
b Novosibirsk State University, Novosibirsk, Russia
Citations (3)
References:
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DOI: https://doi.org/10.7868/S004446691806011X
Abstract: Monotonicity conditions for the CABARET scheme approximating a quasilinear scalar conservation law with a convex flux are obtained. It is shown that the monotonicity of the CABARET scheme for Courant numbers r∈(0.5,1] does not ensure the complete decay of unstable strong discontinuities. For the CABARET scheme, a difference analogue of an entropy inequality is derived and a method is proposed ensuring the complete decay of unstable strong discontinuities in the difference solution for any Courant number at which the CABARET scheme is stable. Test computations illustrating these properties of the CABARET scheme are presented.
Key words: monotone CABARET scheme, scalar conservation law, strong discontinuity, difference analogue of entropy inequality.
Funding agency Grant number
Russian Foundation for Basic Research 16-01-00333_а
Received: 13.03.2017
English version:
Computational Mathematics and Mathematical Physics, 2018, Volume 58, Issue 6, Pages 950–966
DOI: https://doi.org/10.1134/S0965542518060155
Bibliographic databases:
Document Type: Article
UDC: 519.63
Language: Russian
Citation: N. A. Zyuzina, V. V. Ostapenko, “Decay of unstable strong discontinuities in the case of a convex-flux scalar conservation law approximated by the CABARET scheme”, Zh. Vychisl. Mat. Mat. Fiz., 58:6 (2018), 988–1012; Comput. Math. Math. Phys., 58:6 (2018), 950–966
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    • This publication is cited in the following 3 articles:
    1. Alexander Sukhinov, Alexander Chistyakov, Inna Kuznetsova, Yulia Belova, Elena Rahimbaeva, “Development and Research of a Modified Upwind Leapfrog Scheme for Solving Transport Problems”, Mathematics, 10:19 (2022), 3564  crossref
    2. A. I. Sukhinov, I. Yu. Kuznetsova, A. E. Chistyakov, E. A. Protsenko, Yu. V. Belova, “Studying the Accuracy and Applicability of the Finite Difference Scheme for Solving the Diffusion–Convection Problem at Large Grid Péclet Numbers”, J Appl Mech Tech Phy, 62:7 (2021), 1255  crossref
    3. A.I. Sukhinov, I.Y. Kuznetsova, A.E. Chistyakov, E.A. Protsenko, Y.V. Belova, “Study of the accuracy and applicability of the difference scheme for solving the diffusion-convection problem at large grid Péclet numbers”, Comp. Contin. Mech., 13:4 (2020), 437  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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