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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2008, Volume 48, Number 6, Pages 1102–1110 (Mi zvmmf4582)  
This article is cited in 8 scientific papers (total in 8 papers)

Newton's method as applied to the Riemann problem for media with general equations of state

N. Ya. Moiseev, T. A. Mukhamadieva

All-Russia Research Institute of Technical Physics, Russian Federal Nuclear Center, Box 245, Snezhinsk, 456770, Russia
Full-text PDF (1313 kB) Citations (8)
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Abstract: An approach based on Newton's method is proposed for solving the Riemann problem for media with normal equations of state. The Riemann integrals are evaluated using a cubic approximation of an isentropic curve that is superior to the Simpson method in terms of accuracy, convergence rate, and efficiency. The potentials of the approach are demonstrated by solving problems for media obeying the Mie–Grüneisen equation of state. The algebraic equation of the isentropic curve and some exact solutions for configurations with rarefaction waves are explicitly given.
Key words: gasdynamic equation, Riemann problem, Newton's method, Mie–Grüneisen equation of state.
Received: 19.10.2007
Revised: 12.12.2007
English version:
Computational Mathematics and Mathematical Physics, 2008, Volume 48, Issue 6, Pages 1039–1047
DOI: https://doi.org/10.1134/S0965542508060134
Bibliographic databases:
Document Type: Article
UDC: 519.634
Language: Russian
Citation: N. Ya. Moiseev, T. A. Mukhamadieva, “Newton's method as applied to the Riemann problem for media with general equations of state”, Zh. Vychisl. Mat. Mat. Fiz., 48:6 (2008), 1102–1110; Comput. Math. Math. Phys., 48:6 (2008), 1039–1047
Citation in format AMSBIB
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    • This publication is cited in the following 8 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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