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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2020, Volume 60, Number 4, Pages 639–651
DOI: https://doi.org/10.31857/S0044466920040080 (Mi zvmmf11063) 		 
This article is cited in 10 scientific papers (total in 10 papers)

Study of entropy properties of a linearized version of Godunov's method

S. K. Godunova, V. V. Denisenkob, D. V. Klyuchinskiic, S. V. Fortovab, V. V. Shepelevb

a Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090 Russia
b Institute for Computer-Aided Design, Russian Academy of Sciences, Moscow, 123056 Russia
c Novosibirsk State University, Novosibirsk, 630090 Russia
Citations (10)
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DOI: https://doi.org/10.31857/S0044466920040080
Abstract: The ideas of formulating a weak solution for a hyperbolic system of one-dimensional gas dynamics equations are presented. An important aspect is the examination of the scheme for the fulfillment of the nondecreasing entropy law, which must hold for weak solutions and is obligatory from a physics point of view. The concept of a weak solution is defined in a finite-difference formulation with the help of the simplest linearized version of the classical Godunov scheme. It is experimentally shown that this version guarantees an entropy nondecrease. As a result, the growth of entropy on shock waves can be simulated without using any correction terms or additional conditions.
Key words: gas dynamics equations, weak solution, Godunov’s scheme, entropy nondecrease, Riemann problem, shock waves, discontinuous solutions.
Funding agency Grant number
Russian Science Foundation 17-11-01293
This work was supported by the Russian Science Foundation, project no. 17-11-01293.
Received: 14.11.2019
Revised: 14.11.2019
Accepted: 16.12.2019
English version:
Computational Mathematics and Mathematical Physics, 2020, Volume 60, Issue 4, Pages 628–640
DOI: https://doi.org/10.1134/S0965542520040089
Bibliographic databases:
Document Type: Article
UDC: 519.63
Language: Russian
Citation: S. K. Godunov, V. V. Denisenko, D. V. Klyuchinskii, S. V. Fortova, V. V. Shepelev, “Study of entropy properties of a linearized version of Godunov's method”, Zh. Vychisl. Mat. Mat. Fiz., 60:4 (2020), 639–651; Comput. Math. Math. Phys., 60:4 (2020), 628–640
Citation in format AMSBIB
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    • This publication is cited in the following 10 articles:
    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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    References:11
     
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