Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia
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Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia, 2020, Volume 492, Pages 31–37
DOI: https://doi.org/10.31857/S2686954320030224 (Mi danma68) 		 
This article is cited in 7 scientific papers (total in 7 papers)

MATHEMATICS

On $L^2$-dissipativity of a linearized explicit finite-difference scheme with quasi-gasdynamic regularization for the barotropic gas dynamics system of equations

A. A. Zlotnikab, T. A. Lomonosova

a National Research University "Higher School of Economics", Moscow, Russian Federation
b Keldysh Institute of Applied Mathematics of Russian Academy of Sciences, Moscow, Russian Federation
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DOI: https://doi.org/10.31857/S2686954320030224
Abstract: We study an explicit two-level symmetric (in space) finite-difference scheme for the multidimensional barotropic gas dynamics system of equations with quasi-gasdynamic regularization linearized at a constant solution (with an arbitrary velocity). A criterion and both necessary and sufficient conditions for the $L^2$-dissipativity of the solutions to the Cauchy problem for the scheme are derived by the spectral method. In them, the Courant number is uniformly bounded with respect to the Mach number.
Keywords: barotropic gas dynamics equations, quasi-gasdynamic system of equations, explicit two-level finite-difference scheme, stability.
Funding agency Grant number
Russian Science Foundation 19–11–00169
This work was supported by the Russian Science Foundation, project no. 19-11-00169.
Presented: B. N. Chetverushkin
Received: 17.08.2019
Revised: 09.04.2020
Accepted: 10.04.2020
English version:
Doklady Mathematics, 2020, Volume 101, Issue 3, Pages 198–204
DOI: https://doi.org/10.1134/S1064562420030229
Bibliographic databases:
Document Type: Article
UDC: 519.634
Language: Russian
Citation: A. A. Zlotnik, T. A. Lomonosov, “On $L^2$-dissipativity of a linearized explicit finite-difference scheme with quasi-gasdynamic regularization for the barotropic gas dynamics system of equations”, Dokl. RAN. Math. Inf. Proc. Upr., 492 (2020), 31–37; Dokl. Math., 101:3 (2020), 198–204
Citation in format AMSBIB
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\paper On $L^2$-dissipativity of a linearized explicit finite-difference scheme with quasi-gasdynamic regularization for the barotropic gas dynamics system of equations
\jour Dokl. RAN. Math. Inf. Proc. Upr.
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\vol 492
\pages 31--37
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\crossref{https://doi.org/10.31857/S2686954320030224}
\zmath{https://zbmath.org/?q=an:7424588}
\elib{https://elibrary.ru/item.asp?id=42929992}
\transl
\jour Dokl. Math.
\yr 2020
\vol 101
\issue 3
\pages 198--204
\crossref{https://doi.org/10.1134/S1064562420030229}
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    • This publication is cited in the following 7 articles:
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