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Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia, 2022, Volume 505, Pages 30–36
DOI: https://doi.org/10.31857/S2686954322040191
(Mi danma273)
 

MATHEMATICS

Conditions for dissipativity of an explicit finite-difference scheme for a linearized multidimensional quasi-gasdynamic system of equations

A. A. Zlotnikab

a National Research University "Higher School of Economics", Moscow, Russia
b Keldysh Institute of Applied Mathematics of Russian Academy of Sciences, Moscow, Russia
References:
Abstract: We study an explicit two-level finite-difference scheme for a linearized multidimensional quasi-gasdynamic system of equations. For an initial-boundary value problem on a nonuniform rectangular mesh, sufficient conditions of Courant-type for $L^2$-dissipativity are derived for the first time by applying the energy method. For the Cauchy problem on a uniform mesh, both necessary and sufficient conditions for $L^2$-dissipativity in the spectral method are improved. A new form of specifying the relaxation parameter is indicated which guarantees that the Courant-type number is uniformly bounded from above and below with respect to both the mesh and the Mach number.
Keywords: gas dynamics equations, quasi-gasdynamic system of equations, linearization, explicit finite-difference scheme, dissipativity.
Funding agency Grant number
Russian Science Foundation 19-11-00169
22-11-00126
This work was supported by the Russian Science Foundation, project nos. 19-11-00169 (Sections 2, 3) and 22-11-00126 (Section 4).
Presented: B. N. Chetverushkin
Received: 16.03.2022
Revised: 23.05.2022
Accepted: 03.06.2022
English version:
Doklady Mathematics, 2022, Volume 106, Issue 1, Pages 236–242
DOI: https://doi.org/10.1134/S1064562422040196
Bibliographic databases:
Document Type: Article
UDC: 519.633.8+517.958:533.7
Language: Russian
Citation: A. A. Zlotnik, “Conditions for dissipativity of an explicit finite-difference scheme for a linearized multidimensional quasi-gasdynamic system of equations”, Dokl. RAN. Math. Inf. Proc. Upr., 505 (2022), 30–36; Dokl. Math., 106:1 (2022), 236–242
Citation in format AMSBIB
\Bibitem{Zlo22}
\by A.~A.~Zlotnik
\paper Conditions for dissipativity of an explicit finite-difference scheme for a linearized multidimensional quasi-gasdynamic system of equations
\jour Dokl. RAN. Math. Inf. Proc. Upr.
\yr 2022
\vol 505
\pages 30--36
\mathnet{http://mi.mathnet.ru/danma273}
\crossref{https://doi.org/10.31857/S2686954322040191}
\elib{https://elibrary.ru/item.asp?id=49344493}
\transl
\jour Dokl. Math.
\yr 2022
\vol 106
\issue 1
\pages 236--242
\crossref{https://doi.org/10.1134/S1064562422040196}
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