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Matem. Mod., 2016, Volume 28, Number 2, Pages 86–96 (Mi mm3701)  

This article is cited in 3 scientific papers (total in 3 papers)

On justification of the Godunov scheme in multidimensional case

V. F. Tishkin, V. T. Zhukov, E. E. Myshetskaya

Keldysh Institute of Applied Mathematics, Moscow, Russia

Abstract: Classical Godunov scheme for numerical solution of 3D gasdynamics equations is justified for multidimensional case. It is istimated an error introduced by replacing the exact solution of the multidimensional Riemann problem at solving one-dimensional problems with the data on the left and right of the interface of each cell without taking account of complicated flow in the vicinity of the vertices of the cell. It is shown that in the case of plane interfaces the error is the first order with respect to time step and approximate solution converges to solution of semidiscrete equations. The Euler explicit time integration metod for these equations represents the Godunov scheme.

Keywords: computational fluid dynamics, Godunov scheme, multidimensional Riemann solvers.

Funding Agency Grant Number
Russian Foundation for Basic Research 13-01-12079-офи_м
14-01-00145_а


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English version:
Mathematical Models and Computer Simulations, 2016, 8:5, 548–556

Document Type: Article
Received: 29.06.2015

Citation: V. F. Tishkin, V. T. Zhukov, E. E. Myshetskaya, “On justification of the Godunov scheme in multidimensional case”, Matem. Mod., 28:2 (2016), 86–96; Math. Models Comput. Simul., 8:5 (2016), 548–556

Citation in format AMSBIB
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\by V.~F.~Tishkin, V.~T.~Zhukov, E.~E.~Myshetskaya
\paper On justification of the Godunov scheme in multidimensional case
\jour Matem. Mod.
\yr 2016
\vol 28
\issue 2
\pages 86--96
\mathnet{http://mi.mathnet.ru/mm3701}
\elib{http://elibrary.ru/item.asp?id=25707627}
\transl
\jour Math. Models Comput. Simul.
\yr 2016
\vol 8
\issue 5
\pages 548--556
\crossref{https://doi.org/10.1134/S2070048216050124}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84988027104}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. R. V. Zhalnin, E. E. Peskova, O. A. Stadnichenko, V. F. Tishkin, “Modelirovanie techeniya mnogokomponentnogo reagiruyuschego gaza s ispolzovaniem algoritmov vysokogo poryadka tochnosti”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 27:4 (2017), 608–617  mathnet  crossref  elib
    2. Yu. A. Kriksin, V. F. Tishkin, “Entropiinaya regulyarizatsiya razryvnogo metoda Galerkina v odnomernykh zadachakh gazovoi dinamiki”, Preprinty IPM im. M. V. Keldysha, 2018, 100, 22 pp.  mathnet  crossref
    3. Yu. A. Kriksin, V. F. Tishkin, “Gibridnyi podkhod k resheniyu odnomernykh uravnenii gazovoi dinamiki”, Matem. modelirovanie, 30:8 (2018), 17–31  mathnet
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