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Zh. Vychisl. Mat. Mat. Fiz., 2008, Volume 48, Number 6, Pages 1102–1110 (Mi zvmmf4582)  

This article is cited in 7 scientific papers (total in 7 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

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.

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English version:
Computational Mathematics and Mathematical Physics, 2008, 48:6, 1039–1047

Bibliographic databases:

UDC: 519.634
Received: 19.10.2007
Revised: 12.12.2007

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
\by N.~Ya.~Moiseev, T.~A.~Mukhamadieva
\paper Newton's method as applied to the Riemann problem for media with general equations of state
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2008
\vol 48
\issue 6
\pages 1102--1110
\jour Comput. Math. Math. Phys.
\yr 2008
\vol 48
\issue 6
\pages 1039--1047

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    This publication is cited in the following articles:
    1. N. Ya. Moiseev, I. Yu. Silant'eva, “High-accuracy difference schemes for solving gasdynamic equations by the Godunov method with antidiffusion”, Comput. Math. Math. Phys., 49:5 (2009), 827–841  mathnet  crossref  zmath  isi  elib
    2. G. P. Prokopov, A. V. Severin, “Ekonomichnaya realizatsiya metoda Godunova”, Preprinty IPM im. M. V. Keldysha, 2009, 029, 24 pp.  mathnet
    3. G. P. Prokopov, “K voprosu o priblizhennykh realizatsiyakh metoda Godunova”, Preprinty IPM im. M. V. Keldysha, 2011, 004, 31 pp.  mathnet
    4. Crochet M.W., Gonthier K.A., “A Riemann Problem Solution Methodology for a Class of Evolutionary Mixture Equations with an Arbitrary Number of Components”, Appl. Numer. Math., 76 (2014), 145–165  crossref  mathscinet  zmath  isi  scopus
    5. N. Ya. Moiseev, E. A. Shestakov, “Solution of the Riemann problem in twoand three-temperature gas dynamics”, Comput. Math. Math. Phys., 55:9 (2015), 1547–1553  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    6. T. Raeder, V. A. Tenenev, M. R. Koroleva, O. V. Mishchenkova, “Nonlinear Processes in Safety Systems for Substances with Parameters Close to a Critical State”, Rus. J. Nonlin. Dyn., 17:1 (2021), 119–138  mathnet  crossref  mathscinet
    7. T. Raeder, V. A. Tenenev, A. A. Chernova, “Incorporation of Fluid Compressibility into the Calculation of the Stationary Mode of Operation of a Hydraulic Device at High Fluid Pressures”, Rus. J. Nonlin. Dyn., 17:2 (2021), 195–209  mathnet  crossref
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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